TL;DR
This paper analyzes operator determinants on three-dimensional lens spaces, focusing on numerical methods for Laplacians, twisted fields, and applications to thermodynamics, with extensions to higher dimensions and inhomogeneous spaces.
Contribution
It provides detailed numerical analysis of determinants on lens spaces, including twisted fields and applications to thermodynamics, extending previous work to inhomogeneous and higher-dimensional cases.
Findings
Determinants for twisted fields can be computed using cyclic quantities.
Numerical methods enable analysis of Laplacians for massive fields.
Applications to thermodynamics on sphere quotients are demonstrated.
Abstract
More analysis of operator determinants on homogeneous three dimensional lens spaces is presented with the emphasis on numerics so that Laplacians for massive fields can be dealt with. Polyhedral quotients are also briefly considered. Twisted fields, corresponding to flat connections, are looked at and examples of determinants computed. Twisted cyclic quantities are sufficient to determine those for any twisting on any factor. An application to the thermodynamics on sphere quotients is given. Some computations are made for inhomogeneous lens spaces and higher dimensions are commented on. Minimal coupling is also dealt with.
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