General Relativity and Matter

Sachs, Mendel

doi:10.1007/978-94-015-7666-6

Cited by 65 publications

(81 citation statements)

References 9 publications

(16 reference statements)

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“…We can see that the double Weiner process alluded is also connected with such an effect: The negative time derivative, which does not equal the positive time derivative in this case, represents negative energy states. However if we analyse the stochastic Schrodinger equation question further, and generalise the one dimensional case we consider to three dimensions, then as is well known [22], ı → σ, where σ are the Pauli matrices. In other words, we not only cross over to special relativity, but also recover the non commutative geometry (4) or Snyder's relations alluded to, at the Compton scale.…”

Section: Discussionmentioning

confidence: 99%

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Sidharth

2002

Foundations of Physics Letters

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Section: Discussionmentioning

confidence: 99%

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Sidharth

2002

Foundations of Physics Letters

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“…Even-degree (integral-spin) polynomials build geometric fields; e.g. the tetrads, metric, and curvature tensors [1]. Odd-degree (half-integral-spin) polynomials represent the matter fields of Fermions.…”

Section: Introductionmentioning

confidence: 99%

“…Mendel Sachs' [1] dubbed this group of spin isometries the Einstein group, E. Van der Waerden had shown in 1933 [2] how to build all spin-vector.and spin-tensor representations of any isometry group as polynomials in the tensor products of irreducible left (L) chirality, of ( 89 and right (R) chirality, or (0, 89 spinors. Even-degree (integral-spin) polynomials build geometric fields; e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In curved spacetime [1], [5], [14], [2] this covariance is assured simply by using the sume Curtan moving spin frames (g(x), r (x)) that factor the "external" moving tetrads qa (x) ----g (x) | ~ (x) of Clifford algebra frames us "internal" bases for the matter fields! This is implicit in the old "dotted" (right) and "un-dotted" (left) index convention for transforming spin tensors in the chiral representation, which automatically produces [1], [14], [2] the correct E transformations on the tetrads to preserve covariance of the Dirac equations.…”

Section: Introductionmentioning

confidence: 99%

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Spin geometry and grand unification

Cohen

2001

AACA

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Abstract. Gravitation becomes unified with quantum rnechanics when we recognize that the spacetirne tetrads and the rnatter fields of Ferrnions ate the integral and half-integral spin representations of the Einstein group, E, the global extension of the Poincar› group to a curved spacetirne M. There are 8 fundamental spinor representations of the E group, interchanged by P, T, and C: the degree-one maps of spin space over M. Tensor products of 2 spinor fields build Clifford vectors or 1 forrns, e.g. the spacetime tetrads. It takes tensor products of all 8 spinor ¡ to build a natural 4 forrn; in particular, our E-invariant Lagrangian density /~g E A a (M) C | (M). We propose a simple forrn for /~g: the 8-spinor factorization of the Maurer-Cartan 4-forro, F/4. The spin connections ~~ step off the conjoined left and right internal gl (2,C) phase increments over a spaeetime increment ea. Our action Sg measures the covering nurnber of the spinor phases over spacetime M\ U D j; the Dj ate singular domains or caustics, where J = 1, 2, and-3 chiral pairs of spin waves cross.Here, the rnassive Dirac equations emerge to govern the mass scattering that keep the "null zig-zags" of a bispinor particle confined to a timelike worldtube. We identify the coupled envelopes of 1, 2, and 3 chiral bispinor pairs as the leptons, mesons, and hadrons, respectively.These source topologically---nontrivial gl (2, C) phase distributions in the far-field region, which appear as effective rector potentials. Their vorticities ate the spin eurvatures, whose Herrnitian parts--the gravitational curvatures--speeify how our spacetime manifold 1Vi must expand and curve to accornmodate such anholonomic differentials. The anti-Hermitian parts reproduce the standard electroweak and strong ¡ together with their actions. Lg also contains sorne new cross terrns between electroweak potentials and gravitational curvatures. Do these signal a failure of unitication, or predict new phenomena?

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“…25 From the standpoint of general relativity, the excess energy from spacetime is freely allowed, since all EM energy moves in curved spacetime [33,36,37,[41][42][43]45,63] a priori, and simple conservation of EM energy as usually stated in classical equilibrium electrodynamics need not apply in a general relativistic situation [53,54].…”

Section: H Regauging Can Be Negentropic or Entropicmentioning

confidence: 99%

Energy from the Active Vacuum: The Motionless Electromagnetic Generator

Bearden¹

Advances in Chemical Physics

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General Relativity and Matter

Cited by 65 publications

References 9 publications

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Spin geometry and grand unification

Energy from the Active Vacuum: The Motionless Electromagnetic Generator

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