A gauge theory of gravity in curved phase-spaces

2016 ◽  
Vol 13 (07) ◽  
pp. 1650097
Author(s):  
Carlos Castro
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Cotangent Bundle ◽  
Finsler Geometry ◽  
Relativity Theory ◽  
Field Equations ◽  
Double Field Theory ◽  
Theory Of Gravity ◽  
Curvature And Torsion ◽  
Gauge Theory Of Gravity

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.

scholarly journals POINCARÉ GAUGE GRAVITY: SELECTED TOPICS

2006 ◽  
Vol 03 (01) ◽  
pp. 95-137 ◽  
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.

scholarly journals GAUGE THEORY OF GRAVITY REQUIRES MASSIVE TORSION FIELD

1999 ◽  
Vol 14 (16) ◽  
pp. 2531-2535
Author(s):  
RAINER W. KÜHNE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Theory ◽  
Gauge Boson ◽  
Rest Mass ◽  
Quantum Field ◽  
Spin Field ◽  
Torsion Field ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

One of the greatest unsolved issues of the physics of this century is to find a quantum field theory of gravity. According to a vast amount of literature, unification of quantum field theory and gravitation requires a gauge theory of gravity which includes torsion and an associated spin field. Various models including either massive or massless torsion fields have been suggested. We present arguments for a massive torsion field, where the probable rest mass of the corresponding spin three gauge boson is the Planck mass.

scholarly journals Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance

1995 ◽  
Vol 258 (1-2) ◽  
pp. 1-171 ◽  
Author(s):  
Friedrich W. Hehl ◽  
J.Dermott McCrea ◽  
Eckehard W. Mielke ◽  
Yuval Ne'eman
Keyword(s):  
Gauge Theory ◽  
Gravity Field ◽  
Field Equations ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

scholarly journals Metric-Affine Gauge Theory of Gravity: I. Fundamental Structure and Field Equations

1997 ◽  
Vol 06 (03) ◽  
pp. 263-303 ◽  
Author(s):  
Frank Gronwald
Keyword(s):  
Gauge Theory ◽  
Reference Frames ◽  
Classical Field Theory ◽  
Classical Field ◽  
Affine Group ◽  
Field Equations ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity ◽  
Affine Gravity

We give a self-contained introduction into the metric–affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang–Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric–affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of tranlations is explained in detail.

scholarly journals Gauge Theory of Gravity Requires Massive Torsion Field

2019 ◽  
Author(s):  
Rainer Kühne
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Theory ◽  
Gauge Boson ◽  
Rest Mass ◽  
Quantum Field ◽  
Spin Field ◽  
Torsion Field ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

One of the greatest unsolved issues of the physics of this century is to find a quantum field theory of gravity. According to a vast amount of literature unification of quantum field theory and gravitation requires a gauge theory of gravity which includes torsion and an associated spin field. Various models including either massive or massless torsion fields have been suggested. We present arguments for a massive torsion field, where the probable rest mass of the corresponding spin three gauge boson is the Planck mass.

ON TIME DISLOCATION SOLUTION OF EINSTEIN FIELD EQUATIONS

1999 ◽  
Vol 14 (02) ◽  
pp. 93-97 ◽  
Author(s):  
L. C. GARCIA DE ANDRADE
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
External Solution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Birkhoff Theorem ◽  
The Core ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

The theory considered here is not Einstein general relativity, but is a Poincaré type gauge theory of gravity, therefore the Birkhoff theorem is not applied and the external solution is not vacuum spherically symmetric and tachyons may exist outside the core defect.

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