Cartan gravity, matter fields, and the gauge principle
Gravity is commonly thought of as one of the four force fields in nature. However, in standard formulations its mathematical structure is rather different from the Yang–Mills fields of particle physics that govern the electromagnetic, weak, and strong interactions. This paper explores this dissonance with particular focus on how gravity couples to matter from the perspective of the Cartangeometric formulation of gravity. There the gravitational field is represented by a pair of variables: (1) a ‘contact vector’ V{sup A} which is geometrically visualized as the contact point between the spacetime manifold and a model spacetime being ‘rolled’ on top of it, and (2) a gauge connection A{sub μ}{sup AB}, here taken to be valued in the Lie algebra of SO(2,3) or SO(1,4), which mathematically determines how much the model spacetime is rotated when rolled. By insisting on two principles, the gauge principle and polynomial simplicity, we shall show how one can reformulate matter field actions in a way that is harmonious with Cartan’s geometric construction. This yields a formulation of all matter fields in terms of first order partial differential equations. We show in detail how the standard second order formulation can be recovered. In particular, the Hodge dual, whichmore »
 Authors:

^{[1]};
^{[2]}
 Imperial College Theoretical Physics, Huxley Building, London, SW7 2AZ (United Kingdom)
 Instituto de Física Fundamental, CSIC, Serrano 113B, 28006 Madrid (Spain)
 Publication Date:
 OSTI Identifier:
 22220749
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Annals of Physics (New York); Journal Volume: 334; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FIELD EQUATIONS; GEOMETRY; GRAVITATIONAL FIELDS; LIE GROUPS; MATTER; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; SPACETIME; SPIN; STRONG INTERACTIONS