Path integrals in curved space and the worldline formalism

We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with external gravity in the framework of the worldline formalism. In particular, we review a recent application of this worldline approach and discuss vector and antisymmetric tensor fields coupled to gravity. This requires the construction of a path integral for the N=2 spinning particle, which is used to compute the first three Seeley-DeWitt coefficients for all p-form gauge fields in all dimensions and to derive exact duality relations.Comment: 16 pages, to appear in the proceedings of "Path Integrals 2005: from Quantum Information to Cosmology" (Prague, June 6-10, 2005), references adde

On a New Method for Computing Trace Anomalies

I describe a new method for computing trace anomalies in quantum field theories which makes use of path-integrals for particles moving in curved spaces. After presenting the main ideas of the method, I discuss how it is connected to the first quantized approach of particle theory and to heat kernel techniques. (Talk given at Journees Relativistes '93).Comment: 4 pages, LaTeX, USITP-93-1

A Locally Supersymmetric Action for the Bosonic String

Recently Berkovits and Vafa have shown that the bosonic string can be viewed as the fermionic string propagating in a particular background. Such a background is described by a somewhat unusual $N=1$ superconformal system. By coupling it to $N=1$ supergravity I construct a local supersymmetric action for the bosonic string.Comment: 7 pages, NBI-93-6

One loop photon-graviton mixing in an electromagnetic field: Part 1

Photon-graviton mixing in an electromagnetic field is a process of potential interest for cosmology and astrophysics. At the tree level it has been studied by many authors. We consider the one-loop contribution to this amplitude involving a charged spin 0 or spin 1/2 particle in the loop and an arbitrary constant field. In the first part of this article, the worldline formalism is used to obtain a compact two-parameter integral representation for this amplitude, valid for arbitrary photon energies and background field strengths. The calculation is manifestly covariant througout.Comment: 27 pages, final published version (minor corrections

On the trace anomaly of a Weyl fermion

We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by the choice of a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for presenting such a calculation stems from recent studies that suggest that the trace anomaly of chiral fermions in four dimensions might contain an imaginary part proportional to the Pontryagin density. We find that the trace anomaly of a Weyl fermion is given by half the trace anomaly of a Dirac fermion, so that no imaginary part proportional to the Pontryagin density is seen to arise.Comment: 25 pages, added references and acknowledgment