TOPOLOGICAL GENERATION OF GAUGE FIELD MASS BY TOROIDAL SPACETIME

When the fluctuations of a quantum field are 'constrained'-either by boundary conditions or by non-trivial spacetime topology-there occur striking changes in other fields coupled to the constrained quantum field. A particular aspect of this phenomenon will be studied in detail here. Namely, the generation of a 'topological mass' for an Abelian gauge field Amu, by coupling Amu to a scalar field phi , with phi constrained by being defined on partially toroidal spacetime T*En. Each toroidal component Aa (a=1, 2, . . ., N) of Amu=(Aa, A) acquires, through its minimal coupling with phi , a quantum mass mT which the author computes to 1-loop for an equilateral torus TN. mT can be real or imaginary, depending on the dimensions N and n into which spacetime is divided (arbitrary N and n are considered). Real mT parallels electric mass generation in finite-temperature gauge field theory. Imaginary mT is a signal that the vacuum Amu=0 is unstable, and Amu will fluctuate about some non-zero value of its toroidal components Aa, breaking local gauge invariance.