Quantum dynamics of spinless particles on a brane coupled to a bulk gauge field

Abstract

We investigate the effective dynamics for spinless charged particles, in the presence of Abelian gauge field, constrained to an m-dimensional curved pseudo-Riemannian submanifold (brane) of an n-dimensional pseudo-Riemannian manifold (bulk). We employ the confining potential approach and a perturbative expansion for the Klein-Gordon and Schrödinger equations is derived. This allows us to obtain the effective Klein-Gordon and Schrödinger equations on a brane, in terms of the extrinsic curvatures, the intrinsic curvature and the extrinsic torsion. We show that the presence of a bulk gauge field induces a Zeeman coupling whenever the codimension is greater than one, even if the brane and the bulk are flat. The effect of a non-minimal coupling with the Ricci scalar curvature of the bulk is also considered. The results presented here can be applied in at least two physical scenarios: brane gravity, when the brane is four-dimensional, and condensed matter, when the bulk is a four-dimensional flat manifold and the brane is three-or two-dimensional.

Gravitation at the Josephson Junction

“…In real microscopic quantum systems, constrained motion is a result of a strong confining force (electrostatic, rigid chemical bonds, etc.). Therefore, confining potential formalism seems a physically more realistic approach to constraints [15][16][17][18][19][20][21][22][23][24][25].…”