0 D ec 1 99 8 Domain walls and torsion potentials

A Lagrangian for flat domain walls in spaces with Cartan torsion and electromagnetic fields is proposed.The Lagrangian is very similar to a recently proposed Lagrangian for domain walls in a Chern-Simons electrodynamics in 2+1 dimensions.We show that in the first approximation of the torsion scalar potential the field equations are reduced to a Klein-Gordon type field equation for the torsion potential and the electromagnetic wave equation.A planar symmetric solution representing a parallel plates electric capacitor interacting with the electric field is given.The photon mass is proportional to the torsion potential and in the time dependent case the angular momentum is computed and is shown to be connected with torsion in analogy with the spin-torsion relation which appears in Einstein-Cartan gravity.When the curvature Ricci scalar is introduced we are able to show that the torsion potential can be associated with Higgs massive vectorial bosons. Departamento de F́ısica Teorica UERJ. Rua São Fco. Xavier 524, Rio de Janeiro, RJ Maracanã, CEP:20550-003 , Brasil. E-Mail.: [email protected] Recently vortices and domain walls in a Chern-Simons (CS) theory with magnetic moment interactions were investigated by Antillon, Escalona and Torres [1].In their paper they work in 2+1 dimensional spacetime.Here following recently investigation on non-Riemannian domain walls in space-times with torsion [2, 3, 4] we worked out avery similar Lagrangian like the one of reference one with the exception that dual field in the (CS) Lagrangian is replaced by torsion and we work in the full four-dimensional spacetime.The equations obtained for the torsion potential and the electromagnetic field are reduced to non-linear Klein-Gordon field equation and to the Proca field equation in the case of the electromagnetic vector potetencial.The controversy concerning the interaction of the electromagnetic fields and torsion [5, 6, 7] here reachs a slightly different approach since the interaction between photons and torsion appears intermediated by a spin-0 massive boson given by the torsion potential ,besides in the first approximation of the torsion potential the Proca equation is reduced to the Maxwell equation and the photon is massless and the theory is gauge invariant in first approximation.As an application we solve the field equations in the first order in the torsion potential for the case of the parallel plates Capacitor.This simple example is analogous to the case of the Casimir effect [8] with torsion to be investigated in a future research.Of course throughout the paper the metric is considered to be flat.Let us assume that our Lagrangian is given by L = − 1 4 F 2 + 1 2 |Dμφ| 2 − V (φ) (1) where the bars denotes the modulus since we considering that the torsion potential φ is real but the covariant derivative defined by Dμ = ∂μ − ifAμ − igSμ (2) is complex.Here F 2 = FμνF μν is the electromagnetic invariant and Fμν = ∂μAν − ∂νAμ is the electromagnetic field tensor.The torsion potential generates the torsion vector through the relation Sμ = ∂μφ.Substitution of the definition (2) into the Lagrangian (1) reduces the previous Lagrangian to L = 1 2 (∂μφ) 2 − 1 4 F 2 − 1 2 (f A + gS)φ − V (φ) (3) or L = 1 2 (1 + f )(∂φ) + 1 2 gAφ − 1 4 F 2 − V (φ) (4)