From General Relativity and Relativistic Cosmology to Gauge Theories

1983 ◽  
pp. 166-211
Author(s):  
Benjamin Gal-Or
Keyword(s):  
General Relativity ◽  
Gauge Theories ◽  
Relativistic Cosmology

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

scholarly journals GENERAL RELATIVITY AS A CONSTRAINED GAUGE THEORY

2006 ◽  
Vol 03 (08) ◽  
pp. 1493-1500 ◽  
Author(s):  
STEFANO VIGNOLO ◽  
ROBERTO CIANCI ◽  
DANILO BRUNO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Hamiltonian Formulation

The formulation of General Relativity presented in [1] and the Hamiltonian formulation of Gauge theories described in [2] are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory.

scholarly journals THE EXISTENCE OF TIME

2011 ◽  
Vol 08 (02) ◽  
pp. 273-301 ◽  
Author(s):  
JOSEPH A. SPENCER ◽  
JAMES T. WHEELER
Keyword(s):  
General Relativity ◽  
Euclidean Space ◽  
Configuration Space ◽  
Symplectic Form ◽  
Gauge Theories ◽  
Conformal Group ◽  
Metric Structures ◽  
Theories Of Gravity

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures — the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.

scholarly journals Geometry of mass

2015 ◽  
Vol 373 (2047) ◽  
pp. 20140242 ◽  
Author(s):  
D. D. Dietrich
Keyword(s):  
General Relativity ◽  
Gauge Field ◽  
Gauge Theories ◽  
Teleparallel Gravity ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Pure Torsion ◽  
Massless Theory

We study the effect of mass on geometric descriptions of gauge field theories. In an approach in which the massless theory resembles general relativity, the introduction of the mass entails non-zero torsion and the generalization to Einstein–Cartan–Sciama–Kibble theories. The relationships to pure torsion formulations (teleparallel gravity) and to higher gauge theories are also discussed.

scholarly journals GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY

2013 ◽  
Vol 15 (01) ◽  
pp. 1250061 ◽  
Author(s):  
CHRISTIAN BLOHMANN ◽  
MARCO CEZAR BARBOSA FERNANDES ◽  
ALAN WEINSTEIN
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Cotangent Bundle ◽  
Evolution Equations ◽  
Gauge Theories ◽  
Riemannian Metrics ◽  
Einstein Equations ◽  
Cauchy Hypersurface ◽  
Lagrangian Field Theory ◽  
Hamiltonian Evolution

When the vacuum Einstein equations are cast in the form of Hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold [Formula: see text] of Riemannian metrics on a Cauchy hypersurface Σ. As in every Lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any Hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection. In an appendix, we develop some aspects of diffeology, the basic framework for our treatment of function spaces.

GEOMETRIC STRUCTURES IN PHYSICS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260026 ◽  
Author(s):  
L. J. BOYA
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Quantum Mechanics ◽  
Path Integral ◽  
Riemannian Manifolds ◽  
Symplectic Geometry ◽  
Gauge Theories ◽  
Classical Mechanics ◽  
The Past ◽  
Modern Physics

Geometry and Physics developed independently, until the past twentieth century, where physicists realized geometry is rather flexible and can adapt itself to the needs and characteristics of modern physics. Besides the use of Riemannian manifolds to describe General Relativity, classical mechanics encounters symplectic geometry, not to speak of the bundle connection ingredient of modern gauge theories; even Quantum Mechanics, after the initial Hilbert space period, is seeking nowadays to adapt itself better to a geometrical interpretation, by imperatives of the path integral description and also to incorporate more clearly the symplectic aspects of its classical antecedent.

General Relativity and Deformed Gauge Theories

1999 ◽  
Vol 47 (1-3) ◽  
pp. 225-230
Author(s):  
G. Bimonte ◽  
R. Musto ◽  
A. Stern ◽  
P. Vitale
Keyword(s):  
General Relativity ◽  
Gauge Theories

General relativity and gauge theories

1974 ◽  
Vol 5 (3) ◽  
pp. 287-330 ◽  
Author(s):  
M. Carmeli
Keyword(s):  
General Relativity ◽  
Gauge Theories
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