Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology

TL;DR

This paper investigates boundary conditions for various spin fields in quantum cosmology, deriving conditions under which spin-raising operators preserve these boundaries on a 3-sphere, with implications for flat Euclidean backgrounds.

Contribution

It derives conditions for boundary preservation by spin-raising operators across multiple spins and applies spinor analysis to spin-3/2 potentials in quantum cosmology.

Findings

Boundary conditions are preservable only in flat Euclidean backgrounds.

Spin-raising operators maintain boundary conditions for spins 0 to 2.

Spinor analysis clarifies gauge freedom in spin-3/2 potentials.

Abstract

Local boundary conditions involving field strengths and the normal to the boundary, originally studied in anti-de Sitter space-time, have been recently considered in one-loop quantum cosmology. This paper derives the conditions under which spin-raising operators preserve these local boundary conditions on a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component spinor analysis of the four potentials of the totally symmetric and independent field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It is shown that such boundary conditions can only be imposed in a flat Euclidean background, for which the gauge freedom in the choice of the potentials remains.