General Relativity as a (constrained) Yang-Mills's Theory and a Novel Gravity with Torsion (original) (raw)
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General Relativity as a (Constrained) Yang-Mills Theory and a Novel Gravity with Torsion
General Relativity and Gravitation, 2002
We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D − 1, 2) (or SO(D, 1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR appear as solutions of a genuine SO(D−1, 1)-YM. We also present a theory of gravity with torsion as the most natural extension of this result. The theory comes out to be strictly an YM-theory upon relaxation of a suitable constraint. This work sets out to enforce the close connection between YM theories and GR by means of a new construction.
Algebraic structure of gravity with torsion
Classical and Quantum Gravity, 1994
The BRS transformations for gravity with torsion are discussed by using the Maurer-Cartan horizontality conditions. With the help of an operator δ which allows to decompose the exterior space-time derivative as a BRS commutator we solve the Wess-Zumino consistency condition corresponding to invariant Lagrangians and anomalies.
Torsion formulation of gravity
Classical and Quantum Gravity, 2010
We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.
A Modified Theory of Gravity with Torsion and Its Applications to Cosmology and Particle Physics
International Journal of Theoretical Physics, 2012
In the present paper we consider a theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant; applying this theory to the Dirac field we see that because torsion has coupling that is still undetermined, the Dirac equation is endowed with self-interactions whose coupling constant is yet to be determined: we have discussed different applications according to the value of the constant we have assigned. We discuss how in our approach, the Dirac self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.
A Minimal Model of Lorentz Gauge Gravity with Dynamical Torsion
International Journal of Modern Physics A, 2010
A new Lorentz gauge gravity model with R2-type Lagrangian is proposed. In the absence of classical torsion, the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space–time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin-2 mode of torsion becomes dynamical essentially due to the nonlinear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space–time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced...
A square-torsion modification of Einstein-Cartan theory
Annalen der Physik, 2012
In the present paper we consider a theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant. In particular, we discuss the couplings to Dirac fields and spin fluids: in the case of Dirac fields, we discuss how in our approach, the Dirac self-interactions depend on the coupling constant as a parameter that may even make these nonlinearities manifest at subatomic scales, showing different applications according to the value of the parameter we have assigned; in the case of spin fluids, we discuss FLRW cosmological models arising from the proposed theory.
Effects of spin-torsion in gauge theory gravity
Journal of Mathematical Physics, 1998
The spin-torsion sector of a new gauge-theoretic formulation of gravity is analysed and the relationship to the Einstein-Cartan-Kibble-Sciama theory of gravity is discussed. The symmetries of the Riemann tensor and the conservation laws of the theory are derived. This formalism is applied to the problem of a Dirac field coupled self-consistently to gravity. The equations derived from a minimally-coupled gauge-invariant Lagrangian naturally give the gauge-theoretic analogues of the Einstein-Cartan-Dirac equations. Finally, a semi-classical model for a spinning point-particle moving in a gravitational background with torsion is considered.
Generalized Yang-Mills theory and gravity
Physical Review D, 2016
We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories in general include a graviton, a dilaton and a rank-2 antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via BCJ duality can be made more manifest in this formulation.
Torsion Wave Solutions in Yang-Mielke Theory of Gravity
The approach of metric-affine gravity initially distinguishes it from Einstein’s general relativity. Using an independent affine connection produces a theory with 10 + 64 unknowns. We write down the Yang-Mills action for the affine connection and produce the Yang-Mills equation and the so-called complementary Yang-Mills equation by independently varying with respect to the connection and the metric, respectively. We call this theory the Yang-Mielke theory of gravity. We construct explicit spacetimes with pp-metric and purely axial torsion and show that they represent a solution of Yang-Mills theory. Finally we compare these spacetimes to existing solutions of metric-affine gravity and present future research possibilities.
arXiv (Cornell University), 2017
The generic form of spacetime dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the Principle of General Relativity. It was thus shown that Einstein's General Relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the "free" (uncoupled) gravitational field, and (ii) the energy-momentum tensor is that of scalar fields representing real or complex structureless (spin-0) particles. It followed that all other source fields-such as vector fields representing massive and nonmassive spin-1 particles-need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and non-massive vector fields. The massive vector field has the canonical energy-momentum tensor as the appropriate source term-which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of spacetime. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy-momentum tensor due to its additional U(1) symmetry. Moreover, such vector fields do not generate a torsion of spacetime. The respective sources of gravitation apply for all models of the dynamics of the "free" (uncoupled) gravitational field-which do not follow from the gauge formalism but must be specified based on separate physical reasoning.