Poincaré Gauge Theory and Galilean Covariance

Abstract

We analyse the Poincare gauge structure proposed by D. Cangemi and R. Jackiw (CJ) (Ann. Phys. (N.Y.) 225, 229), in association with general Lie algebras and, in particular, with Galilean symmetries. In this context, the CJ method is formulated as an embedding scheme of metric spaces, and aspects of Galilean covariance are then used to analyse: (i) the nonrelativistic limits of the electromagnetic field; (ii) a Galilean counterpart of the CJ theory; (iii) geometrical common structures of Lorentzian and Galilean physics; and (iv) a covariant formalism for classical mechanics. Academic Press

Gauge symmetry in Fokker–Planck dynamics

“…[5,6]). Let G be a five dimensional metric space, with an arbitrary vector denoted by x = (x 1 , x 2 , x 3 , x 4 , x 5 ) = (x, x 4 , x 5 ).…”

“…The basic ingredient in the derivation is Galilean covariance, which has been recently developed in different perspectives, providing a metric, and thus a tensor, structure for non relativistic theory based in a 4+1 Minkowski space [1,2,3,4,5,6,7,8]. As a consequence, a geometric unification of the non relativistic and relativistic physics is accomplished [4,6]. One interesting result is that the possibility to use ideas and concepts of particles physics in transport theory, such as topological terms, symmetry breaking, gauge symmetries, and so on [1,2,9], can be investigated in a systematic and covariant way paralleling the relativistic physics [4,10].…”

The Cangemi–Jackiw Manifold in High Dimensions and Symplectic Structure

“…Let us define a 2N-dimensional phase space as a manifold Γ defined via the following symplectic 2-form w [10], w = dq µ ∧ dp µ ; µ = 1, 2, ..N,…”

Galilean Covariance and the Gravitational Field

“…In terms of space canoni-cal coordinates, one has three components for the space coordinates; one coordinate for time and the fifth component is associated to velocity. The consequence has been several developments for the non-relativistic classical and quantum field theory [13,14,15,16,17,18,19,20,21].…”