C-t E T Representation

Zamolodchikov's c-theorem is reformulated by using the spectral representation for the two-point function of the stress tensor . This approach makes explicit the unitarity constraints on the field theory and implements a nice physical picture of the renormalization group flow . An attempt is made to generalize the theorem above two space-time dimensions . There are two candidate c-functions, the spectral densities for spin-zero and spin-two intermediate states . The latter one is ruled out by means of examples . The spin-zero density can satisfy a generalized c-theorem, if the corresponding "central charge" is well defined at the fixed points . A meaningful charge is obtained by defining the theory on curved hyperbolic space . However, its limit to flat space needs some assumptions which seem to hold for free theories only . As a by-product, the trace anomaly in four dimensions is related to the spectral densities . Received 20 August 1990