Kottler, Cartan, and van Dantzig independently uncovered a key property of the Maxwell equations, which, in retrospect, is instrumental for treating noninertial situations. The essence of this KCD procedure is outlined. Present traditions incompatible with the KCD procedure are identified. KCD predicts a rotation-induced magnetoelectric effect in vacuum, as verified by the experiments of Kennard and Pegram. The description of nonvacuum situations still has some unresolved differences awaiting further experimental delineation. Explicit calculations and technical specifications of experiments receive references (...) to the literature. The emphasis of presentation stresses the conceptual reorganization necessary for lifting the Kennard-Pegram experiments out of their present state of obscurity. The question of whether or not KCD is a physically viable counterpart of the Lagrange-Hamilton-Jacobi procedure in mechanics is contingent on the outcome of more detailed experimentation of the Kennard-Pegram type. (shrink)

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the (...) Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons.The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his (...) calculus by developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent.A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms. (shrink)

Nous analysons le développement mathématique et la signification épistémologique du mouvement de géométrisation de la physique théorique, à partir des travaux fondamentaux d’E. Cartan et de H. Weyl jusqu’aux théories de jauge non-abéliennes récentes. Le principal propos de cet article est d'étudier ces développements qui ont été inspirés par les tentatives de résoudre l'un des problèmes centraux de la physique théorique au siècle dernier, c’est-à-dire comment arriver à concilier la relativité générale et la théorie quantique des champs dans un (...) cadre théorique unitaire du monde physique. Ces développements ont produit un changement conceptuel profond concernant tout particulièrement la façon de concevoir les rapports entre structures mathématiques et phénomènes physiques. Nous mettons l’accent sur les points suivants : plutôt que de simplement s’appliquer aux phénomènes, les mathématiques sont impliquées dans leur constitution, autrement dit, les phénomènes sont autant d’effets qui émergent de la structure géométrique de l’espace-temps ; la structure géométrique et topologique de l’espace-temps est à l’origine de la dynamique de ce dernier; les symétries « internes » dictent les différentes interactions entre forces et entre particules ; l’invariance de jauge est un principe « universel » régissant les forces fondamentales et les interactions entre les champs de matière. (shrink)

Compactified Minkowski spacetime is suggested by conformal covariance of Maxwell equations, while E. Cartan's definition of simple spinors leads to the idea of compactified momentum space. Assuming both diffeomorphic to (S 3 × S 1 )/Z 2 , one may obtain in the conformally flat stereographic projection field theories both infrared and ultraviolet regularized. On the compact manifold themselves instead, Fourier integrals of wave-field oscillations would have to be replaced by Fourier series summed over indices of spherical eigenfunctions: n, (...) l, m, m′. Tentatively identifying those wave structures with spacetime itself (in the frame of Big-Bang) and/or with matter and radiation distribution, some large-scale (hydrogenic) and small-scale (lattice) space structures are conjectured. (shrink)

The boundary of a boundary principle in field theories is described. The difference in treatment of the principle in electrodynamics and general relativity is pointed out and reformulated in terms of underlying mathematical structure of the theories. The problem of unifying the treatment is formulated and solved. The role of E. Cartan's concept of the moment of rotation associated with the curvature of a Levi-Civita connection on a frame bundle is shown to be crucial for the unification. The analysis (...) of the boundary of a boundary principle in Kaluza-Klein theory is performed and the recipe for a unified treatment of the principle in electrodynamics and general relativity is shown to follow from the analysis. It is pointed out that the unification cand be extended to Yang-Mills fields easily. (shrink)

A fiber bundle constructed over spacetime is used as the basic underlying framework for a differential geometric description of extended hadrons. The bundle has a Cartan connection and possesses the de Sitter groupSO(4, 1) as structural group, operating as a group of motion in a locally defined space of constant curvature (the fiber) characterized by a radius of curvatureR≈10−13 cm related to the strong interactions. A hadronic matter field ω(x, ζ) is defined on the bundle space, withx the spacetime (...) coordinate and ζ varying in the local fiber. The components of a generalized tensor current ℑ μab (M) (x) are introduced, involving a bilinear expression in the fields ω(x, ζ) and ωΔ(x, ζ) integrated over the local fiber at the pointx. This hadronic matter current is considered as a source current for the underlying fiber geometry by coupling it in a gauge-invariant manner to the curvature expressions derived from the bundle connection coefficients, which are associated here with strong interaction effects, i.e., play the role of meson fields induced in the geometry. Studying discrete symmetry transformations between the 16 differently soldered Cartan bundles, a generalized matter-antimatter conjugation Ĉ is established which leaves the basic current-curvature equations Ĉ-invariant. The discrete symmetry transformation Ĉ turns out to be the direct product of an ordinary charge conjugation for the Dirac point-spinor part of ω(x, ζ) and an internal $\hat P\hat T$ transformation applied globally on the bundle to the fiber (i.e., de Sitter) part of ω(x, ζ). (shrink)

Alexandre Grothendieck foi um dos maiores matemáticos do século 20 e um dos mais atípicos. Nascido na Alemanha a um pai anarquista de origem russa, sua infância foi marcada pela militância política dos seus pais, assim passando por revoluções, guerras e sobrevivência. Descoberto por sua precocidade matemática por Henri Cartan, Grothendieck fez seu doutorado sob orientação de Laurent Schwartz e Jean Dieudonné. As principais contribuições dele são na área da topologia e na geometria algébrica, assim como na teoria das (...) categorias. No final dos anos de 1960, ele se dedicou à militância política e ecológica, organizando a revista Survivre durante três anos. Em 1986, publicou um manuscrito autobiográfico de 1000 páginas, Récoltes et semailles, em que ele descreve sua experiência e sua prática da matemática, assim suas contribuições à comunidade matemática francesa. Pouco comentado na filosofia, as implicações dos seus descobrimentos fora mais recentemente discutidas por Alain Badiou na sua "fenômeno-lógica", em Logiques des mondes e Arkady Plonitsky, Mathgematics, Science and postclassical Theory, pesquisa trata da semelhança entre os aspectos formais da filosofia de Gilles Deleuze e da topologia de Grothendieck. (shrink)

To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R0 appear as islands D(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the (...) domains D(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields ( $(\tilde \xi ^a (x),R(x)) \in {G \mathord{\left/ {\vphantom {G H}} \right. \kern-0em} H}x R^ +$ , given as a section on an associated bundle $\tilde E(B,{G \mathord{\left/ {\vphantom {G H}} \right. \kern-0em} H}x R^ + ,\tilde G)$ over space-time B with structural group $\tilde G$ = G ⊗ D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields $\tilde \xi ^a (x)$ are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the $\tilde G$ -gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the $\tilde G$ -symmetry for regions outside the domains D(i). (shrink)

The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging to (...) the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψ x ρ (ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψ x ρ (ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical. (shrink)

Studies examining the ways in which the training of engineers and scientists shapes their research strategies and scientific identities.

Each month brings new scientific findings that demonstrate the ways in which human activities, from resource extraction to carbon emissions, are doing unprecedented, perhaps irreparable damage to our world. As we hear these climate change reports and their predictions for the future of Earth, many of us feel a sickening sense of _déjà vu_, as though we have already seen the sad outcome to this story. Drawing from recent scholarship that analyzes climate change as a form of “slow violence” that (...) humans are inflicting on the environment, _Climate Trauma_ theorizes that such violence is accompanied by its own psychological condition, what its author terms “Pretraumatic Stress Disorder.” Examining a variety of films that imagine a dystopian future, renowned media scholar E. Ann Kaplan considers how the increasing ubiquity of these works has exacerbated our sense of impending dread. But she also explores ways these films might help us productively engage with our anxieties, giving us a seemingly prophetic glimpse of the terrifying future selves we might still work to avoid becoming. Examining dystopian classics like _Soylent Green _alongside more recent examples like _The Book of Eli_, _Climate Trauma_ also stretches the limits of the genre to include features such as _Blindness_, _The Happening_, _Take Shelter_, and a number of documentaries on climate change. These eclectic texts allow Kaplan to outline the typical blind-spots of the genre, which rarely depicts climate catastrophe from the vantage point of women or minorities. Lucidly synthesizing cutting-edge research in media studies, psychoanalytic theory, and environmental science, _Climate Trauma _provides us with the tools we need to extract something useful from our nightmares of a catastrophic future. (shrink)

RESUMO Neste trabalho, proponho uma leitura de aspectos discursivos do curta-metragem de ficção Recife frio, de Kleber Mendonça Filho, com o objetivo de refletir sobre como a hibridização de gêneros na obra, decorrente da presença de gêneros intercalados no filme, cria sentidos e provoca determinada postura na interlocução com os espectadores. Para tanto, discuto alguns conceitos-chave da teoria bakhtiniana, descrevo momentos específicos do curta-metragem e proponho análises pontuais de determinadas cenas ou sequências. A forma de diálogo com o corpus segue (...) os pressupostos da poética sociológica que perpassa as discussões empreendidas por Bakhtin e pelos demais pesquisadores do Círculo. As reflexões apresentadas apontam para um jogo de cena entre ficção e realidade, que, no curta, são acionados pela presença de elementos que podem ser associados ao gênero documentário. ABSTRACT This paper proposes a reading of discursive aspects in Recife Frio, a short film by Kleber Mendonça Filho. It aims at reflecting on how genre hybridization, which results from the presence of incorporated genres, creates meanings and provokes certain attitudes in the interaction between film and spectators. To do so, I discuss some key concepts of Bakhtinian theory, describe specific moments of the short film, and finally conduct a pointed analysis of specific scenes or sequences. This form of dialogue with the corpus follows the assumptions of the sociological poetics that traverse the discussions done by Bakhtin and the other researchers of the Circle. These reflections point to a play between fiction and reality, which in the film is triggered by the presence of elements that may be associated to the documentary genre. (shrink)

A szabadság dilemmái -- A megrendült öntudat mítoszai -- Irás az éthoszról.

Throughout the long history of Classic Maya hieroglyphs, a logosyllabic writing system used from the late first millennium BCE through the mid-second millennium CE in southern Mesoamerica, the most commonly recorded phonetic value was the syllable u (/ʔu/). With over a dozen different u hieroglyphs, Classic Maya scribes had more options for recording /ʔu/ than any other syllable or logograph. Cognitive approaches to writing systems typically attribute graphemic variation (i.e., alternation between signs with equivalent linguistic value) to semantic differences like (...) animacy or to non-linguistic factors like identity. Distribution of Classic Maya u hieroglyphs, however, suggests that morphosyntactic context influenced which grapheme scribes wrote and when. This case suggests that scribal knowledge of Classic Maya hieroglyphs included ideas about writing's relationship to language. It also highlights the cognitive relevance of morphosyntax for a writing system's users as they differentiate among graphic signs with identical linguistic denotation. (shrink)

Professor Gombrich's last book and first narrative work in over 20 years.

In the Monumentum Ancyranum Augustus makes some interesting and, if we can unravel them, undoubtedly important statements, from which certain deductions seem possible as to the number of his legionary soldiers, the rate of mortality among them, their length of service and the provisions made for them after their dicharge. Quite early in the Monument we get the following general assertion: ‘About five hundred thousand Roman citizens were bound to me by the military oath. Of these, after the due expiry (...) of their service, I settled in colonies or sent back to their own municipia somewhat more than three hundred thousand. And to all of them I gave land purchased by myself, or in lieu of land sums of money out of my own resources.’ From the place of this statement in that part of the record relating to his earlier career we might be tempted to infer that the five hundred thousand legionaries were those who formed his armies at the time of Antony's collapse, and that the discharge of three hundred thousand of them, whether planted in colonies or sent back to their domiciles, took place at one and the same time. With regard to the second point, we shall see presently that the vague and indiscriminate statement made here is cleared up by a later passage , from which it appears that the assignation of land belongs to two distinct schemes of colonizations, separated by sixteen years, and that the restoration of discharged soldiers to their municipalities, to whom alone the words ‘pecuniam pro agris dedi’ are applicable, belongs to a still later date. (shrink)

In this study, originally presented as the Matchette Lectures at Tulane University in 1975, Harris builds his case for theism, which he understands as the conception of and the belief in an infinite and transcendent God, supernatural only in that he transcends the natural world.