A worldline path integral for a massive charged spin-1 particle reproduces the known one-loop Euler-Heisenberg-type Lagrangian and Schwinger pair production rate for vector bosons.
Functional determinants for general Sturm-Liouville problems
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abstract
Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the Sturm-Liouville type with arbitrary linear boundary conditions. The results hold whether or not the operators have negative eigenvalues. The physically important case of functional determinants of operators with a zero mode, but where that mode has been extracted, is studied in detail for the same range of situations as when no zero mode exists. The method of proof uses the properties of generalised zeta-functions. The general form of the final results are the same for the entire range of problems considered.
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Pair production of massive charged vector bosons from the worldline
A worldline path integral for a massive charged spin-1 particle reproduces the known one-loop Euler-Heisenberg-type Lagrangian and Schwinger pair production rate for vector bosons.