The Rise of Gauge Theory of Gravity Up to 1961: From Special to General Relativity Theory Analyzing General Relativity Theory A Fresh Start by Yang - Mills and Utiyama Poincare Gauge Theory: Einstein - Cartan( - Sciama - Kibble) Theory as a Viable Gravitational Theory General Structure of Poincare Gauge Theory (Including Quadratic Lagrangians) Translational Gauge Theory Fallacies About Torsion Extending the Gauge Group of Gravity: Poincare Group Plus Scale Transformations: Weyl - Cartan Gauge Theory of Gravity From the Poincare to the Affine Group: Metric-Affine Gravity Conformal Gauge Theory of Gravity (Anti-)de Sitter Gauge Theory of Gravity From the Square Root of Translations to the Super-Poincare Group Specific Subjects of Metric-Affine Gravity and Poincare Gauge Theory: Hamiltonian Structure Equations of Motion for Matter Cosmological Models Exact Solutions Poincare Gauge Theory in Three Dimensions Dislocations and Torsion The Yang Episode: A Historical Case Study.

Gauge Theories Of Gravitation: A Reader With Commentaries

During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills type. The present text offers commentaries on the articles from the most prominent proponents of the theory. In the early 1960s, the gauge idea was successfully applied to the Poincar\'e group of spacetime symmetries and to the related conserved energy-momentum and angular momentum currents. The resulting theory, the Poincar\'e gauge theory, encompasses Einstein's general relativity as well as the teleparallel theory of gravity as subcases. The spacetime structure is enriched by Cartan's torsion, and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions \`a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\'e gauge theory and its generalizations are explored and special topics, such as its Hamiltonian formulation and exact solutions, are studied. This guide to the literature on classical gauge theories of gravity is intended to be a stimulating introduction to the subject.

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Gauge Theories of Gravitation

Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincare gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.

Bianchi identities and the automatic conservation of energy-momentum and angular momentum in general-relativistic field theories

Bianchi Identities and the Automatic Conservation of Energy-Momentum and Angular Momentum in General-Relativistic Field Theories

The spin-torsion sector of a new gauge-theoretic formulation of gravity is analyzed 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 analogs of the Einstein–Cartan–Dirac equations. Finally, a semiclassical model for a spinning point-particle moving in a gravitational background with torsion is considered.

Effects of spin-torsion in gauge theory gravity

Considers the relation between the general theory of relativity and the Einstein-Cartan theory in the case that matter is described by a Dirac field. Thereby the author finds the condition that an (arbitrary) solution of general relativity with a Dirac field is also a solution of the Einstein-Cartan-Dirac theory and vice versa. Exploiting this result the author generates new non-ghost solutions of the Einstein-Cartan-Dirac theory from ghost solutions of general relativity.

M Seitz

Papers

On solutions of the Einstein-Cartan-Dirac theory