Spin geometry and grand unification

Cohen, Marcus S.

doi:10.1007/bf03042042

Cited by 4 publications

(44 citation statements)

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“…Our Lagrangian density, Q 4 , of (1) is the invariant measure on the Einstein group (21) Its integral gives the covering number W of the group manifold E over spacetime, M. Local extrema of the action integral (1) over M are achieved [7], [11] when all 4 pairs are PTC symmetric. From (19),…”

Section: Forms That Can Be Invariantly Integrated! This Ismentioning

confidence: 99%

“…We showed [7], [11], that the term in (KL + KR), the PT-symmetric (neutral) part of the net spin curvature, contains the Palantini action for gravitation. It vanishes in the PT antisymmetric (PTA) case.…”

Section: Ss=2j M Trklakr+ Fm Trqla(kl+kr)aor+ Mj (51)mentioning

confidence: 99%

“…The matrix representations q, (x) and q, (x) of the moving tetrads q" (x) and The Dirac equations for a bispinor particle are [7], [3]: in the chiral representation [9].…”

Section: Appendixmentioning

confidence: 99%

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Clifford residues and charge quantization

Cohen

2002

AACA

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We derive the quantization of action, particle number, and electric charge in a Lagrangian spin bundle over M __ M#\ U Di, Penrose's conformal compactification of Minkowsky space, with the world tubes of massive particles removed.Our Lagrangian density, £g , is the spinor factorization of the Maurer-Cartan 4-form 1l; it's action, S9 , measures the covering number of the 4 internal u (1) x su (2) phases over external spacetime M. Under PTC symmetry, C reduces to the second Chern form TrKL A KR for a left ® right chirality spin bundle. We prove a residue theorem for gl (2, C)-valued forms, which says that, when we "sew in" singular loci Di over which the u (1) x su (2) phases of the matter fields have some extra twists compared to the 8 vacuum modes, the additional contributions to the action, electric charge, lepton and baryon numbers are all topologically quantized. Because left and right chirality 2-forms are chiral dual, forms are quantized over their dual cycles. Thus it is the interaction c2 (E), with a globally nontrivial magnetic field, that forces electric fields to be topologically quantized over spatial 2 cycles, fs2 Kor e e A e`* 4irN.

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Section: Forms That Can Be Invariantly Integrated! This Ismentioning

confidence: 99%

Section: Ss=2j M Trklakr+ Fm Trqla(kl+kr)aor+ Mj (51)mentioning

confidence: 99%

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Clifford residues and charge quantization

Cohen

2002

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“…The solution is a fundamental theory from which both QFT and GR derive, in different regimes. We show here how quantum gravity emerges naturally from such a theory: the Nonlinear Multispinor (NM) model [1], [2].…”

Section: Overview: Vacuum Energy and Inertial Massmentioning

confidence: 99%

“…In g.o. solutions, the cospinor turns out to be [2] the P T C-reversed version of the spinor, with the opposite gl (2, C) phase shift.…”

Section: Spinfluid Flow: the Dilation-boost Currentmentioning

confidence: 99%

Clifford tetrads, null zig zags, and quantum gravity

Cohen

2003

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Quantum gravity has been so elusive because we have tried to approach it by two paths which can never meet: standard quantum field theory and general relativity. These contradict each other, not only in superdense regimes, but also in the vacuum, where the divergent zero-point energy would roll up space to a point. The solution is to build in a regular, but topologically nontrivial distribution of vacuum spinor fields right from the start. This opens up a straight road to quantum gravity, which we map out here.The gateway is covariance under the complexified Clifford algebra of our spacetime manifold M, and its spinor representations, which Sachs dubbed the Einstein group, E. The 16 generators of E transformations obey both the Lie algebra of Spin c -4, and the Clifford (SUSY) algebra of M. We derive Einstein's field equations from the simplest E-invariant Lagrangian density, Lg. Lg contains effective electroweak and gravitostrong field actions, as well as Dirac actions for the matter spinors. On microscales the massive Dirac propagator resolves into a sum over null zig-zags. On macroscales, we see the energy-momentum current, * T , and the resulting Einstein curvature, G.For massive particles, * T flows in the "cosmic time" direction-centri-fugally in an expanding universe. Neighboring centrifugal currents of * T present opposite radiotemporal vorticities Gor to the boundaries of each others' worldtubes, so they advect, i.e. attract, as we show here by integrating Lg by parts in the spinfluid regime. * This paper gives the derivations of the results I reported at the PIMS conference entitled "Brane World and Supersymmetry" in July, 2002 at Vancouver, B.C. It also contains new results on spin-gravity coupling, on how a topologically-nontrivial distribution of vacuum spinors removes singularities and divergences, and how the amplitude of the vacuum spinors determines the gravitational constant and the rate of cosmic expansion Advances in Applied Clifford Algebras 13

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Massive Particles from Massless Spinors

Cohen

2008

Preprint

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Spin geometry and grand unification

Cited by 4 publications

References 11 publications

Clifford residues and charge quantization

Clifford residues and charge quantization

Clifford tetrads, null zig zags, and quantum gravity

Massive Particles from Massless Spinors

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