CanSU 2 gauge theory be constructed with field equations that are not Yang-Mills equations?

1979 ◽  
Vol 26 (2) ◽  
pp. 41-44
Author(s):  
M. Caemeli
Keyword(s):  
Gauge Theory ◽  
Field Equations ◽  
Yang Mills

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 A gauge-theoretic approach to gravity

2012 ◽  
Vol 468 (2144) ◽  
pp. 2129-2173 ◽  
Author(s):  
Kirill Krasnov
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Dynamical Theory ◽  
Uniqueness Theorems ◽  
Theoretic Approach ◽  
Field Equations ◽  
Yang Mills ◽  
Massless Spin ◽  
Invariant Gauge ◽  
Einstein’S General Relativity

Einstein's general relativity (GR) is a dynamical theory of the space–time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang–Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.

scholarly journals SECOND ORDER FORMALISM IN POINCARÉ GAUGE THEORY

2007 ◽  
Vol 16 (04) ◽  
pp. 655-679 ◽  
Author(s):  
M. LECLERC
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Type Equation ◽  
Approximate Solutions ◽  
Higher Order ◽  
Second Order ◽  
Field Equations ◽  
Tetrad Field ◽  
Yang Mills ◽  
Source Current

Changing the set of independent variables of Poincaré gauge theory and considering, in a manner similar to the second-order formalism of general relativity, the Riemannian part of the Lorentz connection as a function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case, the spin density playing the role of the source current in a Yang–Mills type equation for the torsion. The equivalence of the second-order and conventional first-order formalism is established and the corresponding Noether identities are discussed. Finally, a concrete Lagrangian is constructed and by means of a Yasskin-type ansatz, the field equations are reduced to a conventional Einstein–Proca system. Neglecting higher order terms in the spin-tensor, approximate solutions describing the exterior of a spin-polarized neutron star are presented and the possibility of the experimental detection of the torsion fields is briefly discussed.

REFORMULATION OF EINSTEIN GRAVITY AS A FLAT SPACE GAUGE THEORY

1988 ◽  
Vol 03 (05) ◽  
pp. 497-509 ◽  
Author(s):  
K. BABU JOSEPH ◽  
M. SABIR
Keyword(s):  
Gauge Theory ◽  
Flat Space ◽  
Gravitational Theory ◽  
Einstein Gravity ◽  
Gauge Fields ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Linearized Equations ◽  
Yang Mills ◽  
Rank Tensor

Based on an algebraic decomposition of a fourth rank tensor in terms of second rank tensors we suggest a reformulation of Einstein’s gravitational theory as a flat space gauge theory. This has been done by associating a curved manifold with a flat space U(2)×U(2) gauge theory. It is shown that while, in order to reproduce Einstein field equations one has to use a non-Yang-Mills action, the linearized equations follow from a Yang-Mills action. A relation between the metric and gauge fields is obtained. The consistency of the postulates is also verified.

SELF-DUAL POINCARÉ GAUGE THEORY OF GRAVITATION

2002 ◽  
Vol 13 (04) ◽  
pp. 509-516 ◽  
Author(s):  
G. ZET ◽  
V. MANTA
Keyword(s):  
Gauge Theory ◽  
Torsion Tensor ◽  
The Self ◽  
Gauge Fields ◽  
Field Equations ◽  
Yang Mills ◽  
Self Duality ◽  
Minkowski Space Time ◽  
Theory Of Gravitation ◽  
Generally True

A model of Poincaré gauge self-dual theory over the Minkowski space–time, endowed with spherical symmetry, is considered. The self-duality (S-D) conditions are imposed and two sets of the self-duality equations for the gauge fields are obtained: one for the torsion tensor and another for the curvature tensor. An analytical solution of the gauge field equations is also obtained. The Yang–Mills (Y–M) equations of the gauge fields are also derived. It is shown that these Y–M equations can be obtained from the S-D equations, a result which is generally true for any S-D gauge theory. Most of all calculations are performed using the GRTensorII package, running on the MapleV platform.

Self-dual propagating wave solutions in Yang-Mills gauge theory

1979 ◽  
Vol 19 (12) ◽  
pp. 3649-3652 ◽  
Author(s):  
Eve Kovacs ◽  
Shui-Yin Lo
Keyword(s):  
Gauge Theory ◽  
Yang Mills ◽  
Wave Solutions

scholarly journals Non-Abelian variation on the Savvidy vacuum of the Yang-Mills gauge theory

1994 ◽  
Vol 49 (12) ◽  
pp. 6849-6856 ◽  
Author(s):  
Suzhou Huang ◽  
A. R. Levi
Keyword(s):  
Gauge Theory ◽  
Yang Mills

DESITTER GAUGE THEORY OF GRAVITATION

2003 ◽  
Vol 14 (01) ◽  
pp. 41-48 ◽  
Author(s):  
G. ZET ◽  
V. MANTA ◽  
S. BABETI
Keyword(s):  
Gauge Theory ◽  
Riemann Tensor ◽  
Space Time ◽  
Point Of View ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Strength Tensor ◽  
Group A ◽  
Theory Of Gravitation ◽  
Tensor Formula

A deSitter gauge theory of gravitation over a spherical symmetric Minkowski space–time is developed. The "passive" point of view is adapted, i.e., the space–time coordinates are not affected by group transformations; only the fields change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed. An analytical solution of Schwarzschild–deSitter type is obtained in the case of null torsion. It is concluded that the deSitter group can be considered as a "passive" gauge symmetry for gravitation. Because of their complexity, all the calculations, inclusive of the integration of the field equations, are performed using an analytical program conceived in GRTensorII for MapleV. The program allows one to compute (without using a metric) the strength tensor [Formula: see text], Riemann tensor [Formula: see text], Ricci tensor [Formula: see text], curvature scalar [Formula: see text], field equations, and the integration of these equations.

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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

2007 ◽  
Vol 04 (08) ◽  
pp. 1239-1257 ◽  
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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