Integrability conditions for potential flow of the renormalisation group

The renormalisaton group (RG) flow for a quantum field theory in flat D-dimensional space is considered. Some conditions on the trace of the stress operator are derived which ensure that the RG flow is derivable from a potential on the space of couplings. This requires introducing a metric on the space of interactions and two possibilities are considered. Assuming positive definiteness of the metric the potential provides a function on the space of couplings which is non-increasing along the RG trajectories. Thus any theory which satisfies the integrability conditions also satisfies a c-theorem in D-dimensions. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(93-040) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman