Eur. Phys. J. C (2009) 61: 495-518
https://doi.org/10.1140/epjc/s10052-009-0998-y

Regular Article - Theoretical Physics

Path integrals in polar field variables in QFT

¹ Institute of Nuclear Physics, NCSR Demokritos, Athens, Greece
² IMAPP, FNWI, Radboud Universiteit Nijmegen, Nijmegen, The Netherlands

^* e-mail: m.vankessel@science.ru.nl

Received: 8 January 2009
Published online: 8 April 2009

Abstract

We show how to transform a d-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done. Then we show that this conjecture is correct in the case of two toy models. Finally the conjecture will be proven for a general QFT model with two fields.