SYMPLECTIC-GEOMETRY AND HAMILTONIAN FLOW OF THE RENORMALIZATION-GROUPEQUATION

It is argued that renormalization group flow can be interpreted as a H amiltonian vector flow on a phase space which consists of the coupling s of the theory and their conjugate ''momenta,'' which are the vacuum expectation values of the corresponding composite operators. The Hamil tonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum oper ator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential i n the flow equations. The evolution of any quantity, such as N-point G reen functions, under renormalization group Row can be obtained from i ts Poisson bracket with the Hamiltonian. Ward identities can be repres ented as constants of the motion which act as symmetry generators on t he phase space via the Poisson bracket structure.