Speaker
Description
We present a worldline representation of the one-loop effective action for a Dirac particle coupled to external scalar, pseudoscalar, vector and axialvector fields, which allows one to treat the real and the imaginary parts of the effective action in a unified manner, at the price of having a non-Hermitian Hamiltonian. Unlike other existing worldline representations, our new worldline action contains terms with an odd number of Grassmann fields, leading to ordering problems that in the worldline formalism are usually encountered only in curved space, and which we treat employing the Time Slicing regularisation of the path integral with its specific “counterterm Lagrangian”, which we calculate non-perturbatively, to provide unambiguous rules to treat products of distributions occurring in some diagrams of the one-dimensional worldline theory. We then employ the usual worldline machinery to lay out the rules for the calculation of the effective action itself as well as the corresponding one-loop amplitudes. We discuss possible applications of our representation in the computation of higher-loop corrections for the Heisenberg-Euler Lagrangians, as well as the calculation of pair-creation rates of various particles, in the presence of strong external fields.
