A unified view of curvature and torsion in metric-affine gauge theory of gravity through affine-vector bundles

After a cursory introduction of the basic ideas behind Born’s Reciprocal Relativity theory, the geometry of the cotangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain nonholonomic modifications of Riemann–Cartan gravity within the context of Finsler geometry. A novel gauge theory of gravity in the [Formula: see text] cotangent bundle [Formula: see text] of spacetime is explicitly constructed and based on the gauge group [Formula: see text] which acts on the tangent space to the cotangent bundle [Formula: see text] at each point [Formula: see text]. Several gravitational actions involving curvature and torsion tensors and associated with the geometry of curved phase-spaces are presented. We conclude with a brief discussion of the field equations, the geometrization of matter, quantum field theory (QFT) in accelerated frames, T-duality, double field theory, and generalized geometry.

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POINCARÉ GAUGE GRAVITY: SELECTED TOPICS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988780600103x ◽

2006 ◽

Vol 03 (01) ◽

pp. 95-137 ◽

Cited By ~ 95

Author(s):

YURI N. OBUKHOV

Keyword(s):

Gauge Theory ◽

Field Equations ◽

Full Generality ◽

Duality Method ◽

Spacetime Manifold ◽

The Family ◽

Theory Of Gravity ◽

Curvature And Torsion ◽

Gauge Gravity ◽

Gauge Theory Of Gravity

In the gauge theory of gravity based on the Poincaré group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy–momentum) and the spin are treated on an equal footing as the sources of the gravitational field. The corresponding spacetime manifold carries the Riemann–Cartan geometric structure with the nontrivial curvature and torsion. We describe some aspects of the classical Poincaré gauge theory of gravity. Namely, the Lagrange–Noether formalism is presented in full generality, and the family of quadratic (in the curvature and the torsion) models is analyzed in detail. We discuss the special case of the spinless matter and demonstrate that Einstein's theory arises as a degenerate model in the class of the quadratic Poincaré theories. Another central point is the overview of the so-called double duality method for constructing of the exact solutions of the classical field equations.

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Integrable dissipative structures in the gauge theory of gravity

Classical and Quantum Gravity ◽

10.1088/0264-9381/14/12/005 ◽

1997 ◽

Vol 14 (12) ◽

pp. 3179-3186 ◽

Cited By ~ 29

Author(s):

L Martina ◽

O K Pashaev ◽

G Soliani

Keyword(s):

Gauge Theory ◽

Dissipative Structures ◽

Theory Of Gravity ◽

Gauge Theory Of Gravity

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The Classical Space-Time from The Chern Simons Gauge Theory of Gravity

Unified Symmetry ◽

10.1007/978-1-4615-1923-2_22 ◽

1995 ◽

pp. 229-239

Author(s):

Freydoon Mansouri

Keyword(s):

Gauge Theory ◽

Space Time ◽

Classical Space ◽

Theory Of Gravity ◽

Chern Simons ◽

Gauge Theory Of Gravity

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A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887807002545 ◽

2007 ◽

Vol 04 (08) ◽

pp. 1239-1257 ◽

Cited By ~ 13

Author(s):

CARLOS CASTRO

Keyword(s):

Gauge Theory ◽

Grand Unification ◽

De Sitter ◽

Sitter Group ◽

Yang Mills ◽

Theory Of Gravity ◽

M Theory ◽

Chern Simons ◽

Topological Part ◽

Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

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CAN TORSION BE TREATED AS JUST ANOTHER TENSOR FIELD?

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512004229 ◽

2012 ◽

Vol 07 ◽

pp. 158-164 ◽

Cited By ~ 3

Author(s):

JAMES M. NESTER ◽

CHIH-HUNG WANG

Keyword(s):

Gauge Theory ◽

Tensor Field ◽

Affine Connection ◽

Cartan Geometry ◽

Civita Connection ◽

Levi Civita Connection ◽

Alternative Gravity Theories ◽

Theory Of Gravity ◽

Gauge Theory Of Gravity ◽

Alternative Gravity

Many alternative gravity theories use an independent connection which leads to torsion in addition to curvature. Some have argued that there is no physical need to use such connections, that one can always use the Levi-Civita connection and just treat torsion as another tensor field. We explore this issue here in the context of the Poincaré Gauge theory of gravity, which is usually formulated in terms of an affine connection for a Riemann-Cartan geometry (torsion and curvature). We compare the equations obtained by taking as the independent dynamical variables: (i) the orthonormal coframe and the connection and (ii) the orthonormal coframe and the torsion (contortion), and we also consider the coupling to a source. From this analysis we conclude that, at least for this class of theories, torsion should not be considered as just another tensor field.

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