The article addresses the theme of spectrality, the givenness of the other who remains here after departure as a ghost. It explores how this spectrality functions in Plato’s funeral oratory in the Menexenus dialogue. In the first part, the article discusses J. Patočka’s account of the specific givenness of the departed, which is experienced as a privation of a former intersubjectively intertwined life. The deceased other causes a twofold crisis. On the one hand, with the death of the (...) other also comes the withering of part of myself, for I am unable to realise possibilities dependent on his or her presence. On the other hand, the meaning of the other’s project, which becomes institutionalised through participation in the events and re-formation of the world, is endangered if no one is willing to take on and realise this meaning as one’s own. The second part of the article discusses how Socrates’ oratory addresses this crisis through specific temporality of the speech, one in which the past provides the present with a paradigm for appropriate civic action which is to be imitated in the future. In this context, he creatively uses the concept of shame to induce an attitude of responsibility for the polis, whose greatness is grounded in the virtuous deeds of spectrally present ancestry. (shrink)

In October 2008, one of the largest bank crashes in history struck Iceland, a country of three hundred and thirty five thousand inhab-itants. The aim of the article is to examine two cultural responses to the crash and the crisis that followed. More precisely, the aim is to analyse how the creation of the haunted house in I Remember You, a crash-horror story by crime writer Yrsa Sigurðardóttir, as well as the spectral half-built houses portrayed by visual artist Guðjón Ketilsson (...) refer quite directly, yet spectrally, to the period. The spec-tral themes of the two works give the opportunity to discuss the moment following the crash as a moment of haunting—but who is haunted and by whom? (shrink)

Yablo has argued (1995) the received view in philosophy, that spectral surface reflectances (SSRs) are the causes of color-experience, is mistaken. SSRs, he says, are not commensurate with our experiences and so are not their causes. This motivated Yablo to posit sui generis, “unscientific” color properties to fill the resultant causal lacunae (cf. Watkins in Australasian Journal of Philosophy 83:33–52, 2005;Watkins in Philosophical Studies 150:123–137, 2010; Gert, in: Brown & Macpherson (eds) Routledge Handbook of Philosophy of Colour, Routledge, 2021). This (...) move, I argue, only works if no physical posits commensurate with our experiences exist to fill the same lacunae. And there are, today, familiar such posits: dispositions to reflect long-, medium-, and short-wavelength light (Bradley & Tye in Journal of Philosophy 98:469, 2001; cf. Koenderink in Color for the Sciences, MIT Press, 2010). Moreover, these dispositions are commensurate with our cone and opponent-neural states too, those states, more than our color-experiences, demanding paradigmatically physical causes. The above, conjoined with the platitude that colors are the causes of color-experience, motivates reducing colors to the noted (physical) dispositions. (shrink)

New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point correlation function. Their behavior results from two different contributions. One corresponds to (universal) random matrix eigenvalue fluctuations, the other to diffusive or chaotic characteristics of the corresponding classical motion. A closed formula expressing spacing autocovariances in terms of classical dynamical zeta functions, including the Perron–Frobenius operator, is derived. (...) It leads to a simple interpretation in terms of classical resonances. The theory is applied to zeros of the Riemann zeta function. A striking correspondence between the associated classical dynamical zeta functions and the Riemann zeta itself is found. This induces a resurgence phenomenon where the lowest Riemann zeros appear replicated an infinite number of times as resonances and sub-resonances in the spacing autocovariances. The theoretical results are confirmed by existing “data.” The present work further extends the already well known semiclassical interpretation of properties of Riemann zeros. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Spectral Productances and Color PrimitivismCallie McGrathViews about the metaphysics of color can be divided broadly into realist and antirealist positions. In the realist camp are views that regard colors as instantiated; the pretheoretic appearance of the world as really being colored is correct. In the antirealist camp are views that regard this appearance as illusory.Realist views can be divided into reductionism and primitivism. The former has it that for (...) each color there is a reductive analysis: a true biconditional of the form "There is an F such that for all x, x is red (or blue, yellow) just in case x is F," where F is some predicate that explains what it is for x without making reference to color.1 To put the matter another way, suppose that one were to describe the world as accurately and exhaustively as possible, except that no explicit reference is ever made to color. According to reductionism, somewhere in such a description colors have nevertheless been attributed, only not using the usual color terms.There are two common varieties of reductionism, which we can call "subjective" and "objective reductionism." According to subjective reductionism, the right-hand side of each biconditional of the above sort makes reference to some effect x has on a perceiving subject.2 For instance, Peacocke gives the following analysis of red: "x is red just in case x is disposed to produce a red* sensation in normal perceivers under standard viewing conditions," where "red*" is a term referring to [End Page 509] a sensation in one's visual field.3 Other such color reductionists attempt to provide an analysis of sensations, such as a particular state of one's brain.Objective reductionism attempts to analyze colors without making reference to a perceiving subject. Some varieties of objective reductionism regard colors as microphysical properties of objects.4 Others propose that colors are reflectance properties of surfaces or, more generally, spectral productance properties of visibilia.5Primitivism is the rejection of reductionism; it is the view that no color is a property that can be described or understood purely in nonchromatic terms. Any biconditional of the sort mentioned above must make mention of color. Or, alternatively, the best one can hope to do to explain what any color is as such is to point to one of its bearers: "redness is that [demonstrating a fire truck, or a ripe beefsteak tomato, and so on]."6 Thus, if the world is described without explicitly using color terminology, something has been left out; there are further facts that must be included to give a complete description of the world.In what follows I outline some views that have been previously advanced to elaborate upon color primitivism. I show how one research program in perceptual psychology entails certain constraints on what colors must be like, and how they motivate one form of objective reductionism, which identifies colors as spectral productance profiles.7 However, productance physicalism is seemingly undermined by the fact that there is a pervasive many–one relationship between spectral productance and each color. I defend a variety of realist primitivism that regards colors as properties constitutively related to spectral productance. This view incorporates the advantages of the productance [End Page 510] view, while providing straightforward answers to the problems primitivism is alleged to face.IWhile primitivists agree about what colors are not, they do not agree about what colors are. Gert rejects the possibility of any metaphysical analysis of colors that goes much beyond ordinary, nonphilosophical discourse about color.8 Most primitivists do not go so far as this quietist sort of primitivism. One can reject reductive analysis of colors without altogether rejecting metaphysical theorizing about color.Most primitivists regard colors as categorical properties.9 This is to say that they reject the idea that colors are any sort of disposition. Benbaji is an exception, arguing that, for instance, red is a disposition to appear red to normal perceivers in standard conditions.10 Since, unlike subjective reductionists, Benjabi does not regard the phrase "appears red" and its cognates as amenable to reductive analysis, his position is a form of primitivism. Broackes suggests that surface colors are certain... (shrink)

We investigated spectral resting-state EEG in persons with chronic stroke-induced aphasia to determine its reliability, sensitivity, and relationship to functional behaviors. Resting-state EEG has not yet been characterized in this population and was selected given the demonstrated potential of resting-state investigations using other neuroimaging techniques to guide clinical decision-making. Controls and persons with chronic stroke-induced aphasia completed two EEG recording sessions, separated by approximately 1 month, as well as behavioral assessments of language, sensorimotor, and cognitive domains. Power in the classic (...) frequency bands was examined via spectral analysis of resting-state EEG data. Results suggest that power in the theta, alpha, and beta bands is reliable for use as a repeated measure. Significantly greater theta and lower beta power was observed in persons with aphasia than controls. Finally, in PWAs theta power negatively correlated with performance on a discourse informativeness measure, while alpha and beta power positively correlated with performance on the same measure. This indicates that spectral rsEEG slowing observed in PWAs in the chronic stage is pathological and suggests a possible avenue for directly altering brain activation to improve behavioral function. Taken together, these results suggest that spectral resting-state EEG holds promise for sensitive measurement of functioning and change in persons with chronic aphasia. Future studies investigating the utility of these measures as biomarkers of frank or latent aphasic deficits and treatment response in chronic stroke-induced aphasia are warranted. (shrink)

Dichotic spectral integration range, or DSIR, was measured for consonant recognition with normal-hearing listeners. DSIR is defined as a frequency range needed from 0 to 8,000 Hz band in one ear for consonant recognition when low-frequency information of the same consonant was presented to the opposite ear. DSIR was measured under the three signal processing conditions: unprocessed, target: intensified target spectro-temporal regions by 6 dB responsible for consonant recognition, and target minus conflicting: intensified target regions minus spectro-temporal regions that increase (...) confusion. Each consonant was low-pass filtered with a cutoff frequency of 250, 500, 750, and 1,000 Hz, and then was presented in the left ear or low-frequency ear. To create dichotic listening, the same consonant was simultaneously presented to the right ear or high-frequency ear. This was high-pass filtered with an initial cutoff frequency of 7,000 Hz, which was adjusted using an adaptive procedure to find the maximum high-pass cutoff for 99.99% correct consonant recognition. Mean DSIRs spanned from 3,198–8,000 Hz to 4,668–8,000 Hz, depending on low-frequency information in the LF ear. DSIRs narrowed with increasing low-frequency information in the LF ear. However, the mean DSIRs were not significantly affected by the signal processing except at the low-pass cutoff frequency of 250 Hz. The individual consonant analyses revealed that /ta/, /da/, /sa/, and /za/ required the smallest DSIR, while /ka/, /ga/, /fa/, and /va/ required the largest DSIRs. DSIRs also narrowed with increasing low-frequency information for the two signal processing conditions except for 250 vs. 1,000 Hz under the target-conflicting condition. The results suggest that consonant recognition is possible with large amounts of spectral information missing if complementary spectral information is integrated across ears. DSIR is consonant-specific and relatively consistent, regardless of signal processing. The results will help determine the minimum spectral range needed in one ear for consonant recognition if limited low spectral information is available in the opposite ear. (shrink)

This article calls for an examination of the spectral operations of the perceptual architecture of colonization in conjunction with the enactment of a decolonial feminism as proposed by María Lugones. The first section discusses both the notion of ghostly subjectivity from Lugones's early work as well as the echoes of this notion in her recent work on the coloniality of gender that emphasizes the gender/race/sex nexus. Subsequently, through a photographic example, the article presents an analysis of the perceptual operations of (...) specter‐making in practices of colonization in light of Lugones's understanding of the “light” and “dark” sides of the coloniality of gender. This analysis highlights not only the intricate nexus between racialization and gender and sex norms both in the past and in the present context, but it also points to the necessity for of a decolonial feminism attuned to perceptual practices or a decolonial aesthesis. (shrink)

Asim Barut once,en passant, asked the question “For what transitions of the hydrogen atom do the spectral lines coincide”? It is a pleasure for us to give the answer in this paper.

The Temporal-Order Judgment (TOJ) paradigm has been widely investigated in previous studies as an accurate measure of temporal resolution and sequencing abilities in the millisecond time range. Two auditory TOJ tasks are often used: (1) a spatial TOJ task, in which two identical stimuli are presented in rapid succession monaurally and the task is to indicate which ear received the first stimulus and which ear received the second one ( left-right or right-left ), and (2) a spectral TOJ task, in (...) which two tones of different frequencies are presented asynchronously to both ears binaurally and the task is to report the sequence of these tones ( low-high or high-low ). The previous literature studies conducted on young volunteers indicated that the measured temporal acuity on these two tasks depended on the procedure used. As considerable data are now available about age-related decline in temporal resolution ability, the aim of the present study was to compare in elderly subjects the pattern of performance on these two tasks. A total of 40 normal healthy volunteers aged from 62 to 78 years performed two TOJ tasks. The measurement was repeated in two consecutive sessions. Temporal resolution was indexed by the Auditory Temporal-Order Threshold (ATOT), i.e., the minimum time gap between successive stimuli necessary for a participant to report a before-after relation with 75% correctness. The main finding of the present study was the indication of differences in the elderly in performance on two tasks. In the spatial task, the distribution of obtained ATOT values did not deviate from the Gaussian distribution. In contrast, the distribution of data in the spectral task deviated significantly from the Gaussian and was spread more to the right. Although lower ATOT values were usually observed in Session 2 than in Session 1, such difference was significant only in the spectral task. We conclude that although temporal acuity and sequencing abilities in the millisecond time range are probably based in neuronal oscillatory activity, the measured ATOTs in the elderly seem to be stimulus-dependent, procedure-related, and influenced by the perceptual strategies used by participants. (shrink)

The notion of the Anthropocene is founded on the premise that traces of human activity on the earth will remain legible in the geological strata for millions of years to come, showing evidence of an anthropogenic 'signature' inscribed in the rock by the human species. Spectrality and Survivance shows how embedded in this understanding of the Anthropocene is a speculative and specular gesture that transforms the notion of the future into an anthropocentric reflection of the present, prohibiting any true (...) engagement with the possibility of a non-anthropocentric and post-anthropocenic world. In this volume, Marija Grech develops an alternative conceptual paradigm from which to think the Anthropocene beyond any limited notion of human language, human thought, human systems of meaning, or even a human world. Grech considers how the geological trace of the Anthropocene might be said to 'survive' outside of the possibility of any human readership, and how the very survival of the human in and beyond the Anthropocene might necessitate such thought. (shrink)

The spectral mapping theorem in a unital Banach algebra is examined for its constructive content.

An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebra with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there corresponds a spectral measure.

In what follows I would like to uncover part of this history [of the phantasmagoria], not just as an exercise in romantic etymology but as a way of approaching a larger topic, namely, the history of the imagination. For since its invention, the term phantasmagoria, like one of Freud’s ambiguous primary words, has shifted meaning in an interesting way. From an initial connection with something external and public , the word has now come to refer to something wholly internal or (...) subjective: the phantasmic imagery of the mind. This metaphoric shift bespeaks, I think, a very significant transformation in human consciousness over the past two centuries—what I shall call here the spectralization or “ghostifying” of mental space. By spectralization I mean simply the absorption of ghosts into the world of thought. Even as we have come to discount the spirit-world of our ancestors and to equate seeing ghosts and apparitions with having “too much” imagination, we have also come increasingly to believe, as if through a kind of epistemological recoil, in the spectral nature of our own thoughts—to figure imaginative activity itself, paradoxically, as a kind of ghost-seeing. Thus in everyday conversation we affirm that our brains are filled with ghostly shapes and images, that we “see” figures and scenes in our minds, that we are “haunted” by our thoughts, that our thoughts can, as it were, materialize before us, like phantoms, in moments of hallucinations, waking dream, or reverie. Terry Castle, associate professor of English at Stanford University, is the author of two books: Clarissa’s Ciphers: Meaning and Disruption in Richardson’s “Clarissa” and Masquerade and Civilization: The Carnivalesque in 18th-Century English Culture and Fiction . She is currently working on a study of the literature and psychology of apparitions in the eighteenth and nineteenth centuries entitled “Spectropia: Ghost-Seeing and the Modern Imagination.”. (shrink)

In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can (...) be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes’ property. We show that an MV-algebra admits a state with the Bayes’ property if and only if it is bipartite. (shrink)

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, (...) and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future. (shrink)

A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)

This far-ranging and ambitious attempt to rethink postcolonial theory's discussion of the nation and nationalism brings the problems of the postcolonial condition to bear on the philosophy of freedom. Closely identified with totalitarianism and fundamentalism, the nation-state has a tainted history of coercion, ethnic violence, and even, as in ultranationalist Nazi Germany, genocide. Most contemporary theorists are therefore skeptical, if not altogether dismissive, of the idea of the nation and the related metaphor of the political body as an organism. Going (...) against orthodoxy, Pheng Cheah retraces the universal-rationalist foundations and progressive origins of political organicism in the work of Kant and its development in philosophers in the German tradition such as Fichte, Hegel, and Marx. Cheah argues that the widespread association of freedom with the self-generating dynamism of life and culture's power of transcendence is the most important legacy of this tradition. Addressing this legacy's manifestations in Fanon and Cabral's theories of anticolonial struggle and contemporary anticolonial literature, including the Buru Quartet by Indonesian writer Pramoedya Ananta Toer, and the Kenyan writer Ngugi Wa Thiong'o's nationalist novels, Cheah suggests that the profound difficulties of achieving freedom in the postcolonial world indicate the need to reconceptualize freedom in terms of the figure of the specter rather than the living organism. (shrink)

This article charts Derrida’s performances in front of the camera and argues that several different film retellings of his 1982 imprisonment in Prague articulate the connections between spectrality and Law. If spectrality disrupts the binary of presence and absence, then we must not only show how there is a ghostly presence within the context of film viewing, but also how being photographed is a matter of embracing blindness and a postal logic. The Prague imprisonment was an intriguing event (...) in Derrida’s life because it seemed to go hand-in-hand with revoking his self-imposed ban on his public image, beginning with his first television interview on Antenne 2. Why does Derrida replay this scene, re-enact it, indefinitely? How does the recurring trope of blindness in his writings relate to both the imprisonment and the experience of being photographed? The television and film retellings in Ghost Dance (McMullen, 1983), D’ailleurs, Derrida (Fathy, 1999), and, finally, Derrida (Dick and Ziering Kofman, 2002) could be a way of changing the ghosts that haunt that scene: from fear and anguish in the first television version to openness towards the other in D’ailleurs, Derrida, where the place and time of the event are not named. (shrink)

The results of Cubitt et al. on the spectral gap problem add a new chapter to the issue of undecidability in physics, as they show that it is impossible to decide whether the Hamiltonian of a quantum many-body system is gapped or gapless. This implies, amongst other things, that a reductionist viewpoint would be untenable. In this paper, we examine their proof and a few philosophical implications, in particular ones regarding models and limitative results. In more detail, we examine the (...) way these theorems model many-body quantum systems, and we question what, if anything, is the physical counterpart of the models used by Cubitt et al. We argue that these models are non-representational and that, even if they are so artificial that it is hard to imagine a physical system arising from them, they nonetheless offer an opportunity to learn about the world and the relation between mathematics and reality. On this basis, we draw the conclusion that their results do not undermine the reductionist viewpoint in a strong sense but leave the question open in a weak sense. (shrink)

Is it possible to construct an alternative framework for the description of physical reality that is not based on space and time? According to Kant, because of the incorrigibility of the spatiotemporal scheme, the contents of any such alternative will be beyond our cognitive grasp. Nonetheless, the possibility of constructing such a descriptive scheme poses itself as an intriguing challenge. In this paper, we attempt to answer this challenge by exploiting an analytical tool extensively used by physicists and engineers: the (...) utilisation of multiple representations of the same data using integral transforms – for example, the Fourier transform. According to the spectral picture we propose, frequencies and wavelengths, related to time and space by the Fourier transform, form an adequate alternative basis for describing physical systems, and one that is of equal richness to the spatiotemporal picture. Furthermore, the routine use of Fourier analysis applied to familiar physical systems suggests ways in which sense organs might be constructed such that they naturally give rise to a spectral representation of the world. Although we might never be able to imagine perceiving the world in this way, we can nonetheless describe the contents of such a mode of perception and relate them precisely to our own world-view. Hence, we suggest in a Kantian spirit, that the spatiotemporal description of the world is not unique. (shrink)

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found (...) to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed. (shrink)

Volume 500, 2009 On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field Laurent Amour, ...

Spectrum inversion is a thought experiment, and I would wager that there is no better diagnostic test to the disciplinary affiliation of a randomly selected member of the audience than your reaction to a thought experiment. It is a litmus test. If you find that you are paying close attention, subvocalizing objections, and that your heart-rate and metabolism go up, you have turned pink: you are a philosopher. If on the other hand the thought experiment leaves you cold, and you (...) wonder why otherwise sensible people would worry about such things, you have turned blue and you are a psychologist. (shrink)

El artículo intenta establecer las configuraciones que asume el humanismo crítico en la escritura de Aimé Césaire en la encrucijada de la diferencia colonial, entendida desde una perspectiva decolonial, y a partir de una noción de espectralidad que deriva y se diferencia de las perspectivas derrideanas. Así entonces, se destaca el hecho de que la escritura de Césaire produce una fuerte impugnación de los procesos de la representación colonial y abre el campo de la experiencia política y cultural signada por (...) la heterogeneidad. The article tries to establish the settings that the critical humanism assumes in Aimé Césaire´s writing at the crossroads of the colonial difference, which is understood from a decolonial perspective, and from a notion of spectrality which derives and differs from the Derridean perspective. So then, the article remarks the fact that Césaire´s writing produces a strong challenge to the processes of colonial representation and it opens the field of political and cultural experience marked by heterogeneity. (shrink)

In Ref. 1 we have considered the finite-dimensional quantum mechanics. There the quantum mechanical space of states wasV=C r. It is known that the second quantization of this space is the space of square-summable functions of finite number of variables(L 2(Rr,dx)) (Segal isomorphism). Creation and annihilation operators were introduced in Ref. 1, and the former coincided with the usual position and momentum operators in the conventional quantum mechanics. In this paper we shall investigate the spectral properties of field operators. We (...) shall show that the isomorphism between the exponential ofV andL 2(Rr,dx) can be understood as the decomposition by generalized eigenvectors of field operators (“Fourier transform”). (shrink)