Spacetime geometry from Dirac spinor theory

Abstract

The quintet of Dirac $4\times 4$ matrices suggests that the fundamental dimension of the internal (spin) space is $n=5$, instead of the conventional dimension $n=4$. Then extending the usual $4\times 4$ tetrads (vierbein), gravity is described in terms of the 5-bein (fünfbein or five legs). We discuss the properties of the spacetime geometry induced from this 5-leg Dirac spinor theory, where the spin connection contains $10\times 4=40$ elements instead of 24 elements in the tetrad formulation of the general relativity theory.

arXiv commentRevtex, 6 pages, no figures, minor editing, references added

References in corpus (15)

• Lorentz-Violating Extension of the Standard Model
• CPT Violation and the Standard Model
• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Gravity from Spinors
• Chirality in unified theories of gravity
• Phase transitions in spinor quantum gravity on a lattice
• Extended Einstein-Cartan theory a la Diakonov: the field equations
• Dynamics of test bodies with spin in de Sitter spacetime
• Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions
• Kerr-Schild--Kundt Metrics are Universal
• From elasticity tetrads to rectangular vielbein
• Gravitational waves in metric-affine gravity theory
• Vielbein with mixed dimensions and gravitational global monopole in the planar phase of superfluid ${}^3$He
• Clifford algebra Cl(0,6) approach to beyond the standard model and naturalness problems

Cited by in corpus (5)

• Thermodynamics and decay of de Sitter vacuum
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• $\mathcal{H}$olographic $\mathcal{N}$aturalness and Pre-Geometric Gravity