  We present a proof of the irreversibility of renormalization group flows,
i.e. the c-theorem for unitary, renormalizable theories in four (or generally
even) dimensions. Using Ward identities for scale transformations and spectral
representation arguments, we show that the c-function based on the trace of the
energy-momentum tensor (originally suggested by Cardy) decreases monotonically
along renormalization group trajectories. At fixed points this c-function is
stationary and coincides with the coefficient of the Euler density in the trace
anomaly, while away from fixed points its decrease is due to the decoupling of
positive--norm massive modes.
