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Worldline approach to vector and antisymmetric tensor fields II
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We extend the worldline description of vector and antisymmetric tensor fields coupled to gravity to the massive case. In particular, we derive a worldline path integral representation for the one-loop effective action of a massive antisymmetric tensor field of rank p (a massive p-form) whose dynamics is dictated by a standard Proca-like lagrangian coupled to a background metric. This effective action can be computed in a proper time expansion to obtain the corresponding Seeley-DeWitt coefficients a0, a1, a2. The worldline approach immediately shows that these coefficients are derived from the massless ones by the simple shift D -> D+1, where D is the spacetime dimension. Also, the worldline representation makes it simple to derive exact duality relations. Finally, we use such a representation to calculate the one-loop contribution to the graviton self-energy due to both massless and massive antisymmetric tensor fields of arbitrary rank, generalizing results already known for the massless spin 1 field (the photon).
Forward citations
Cited by 4 Pith papers
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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.
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