The Bargmann-Wigner Equations in Spherical Space

TL;DR

This paper extends the Bargmann-Wigner formalism to spherical spaces across multiple dimensions, deriving wave equations for antisymmetric tensor fields, exploring gauge invariance, including non-Abelian cases, and analyzing quantization effects.

Contribution

It adapts the Bargmann-Wigner formalism to spherical geometries in various dimensions, revealing gauge invariance properties and quantization results for tensor field models.

Findings

Derivation of wave equations for antisymmetric tensor fields on spheres

Identification of gauge invariance and non-Abelian generalizations

Quantization of the O(3) model with vanishing two-point function at one loop

Abstract

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of parameters characterizing them. For spheres embedded in three, four and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two point function shown to vanish at one loop order.