Dolan, Brian P. (1995) Symplectic geometry and Hamiltonian flow of the renormalisation group equation. Working Paper. arXiv.

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Abstract

It is argued that renormalisation group flow can be interpreted as being a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate \lq\lq momenta", which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum operator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential in the flow equations. The evolution of any quantity , such as N-point Green functions, under renormalisation group flow can be obtained from its Poisson bracket with the Hamiltonian. Ward identities can be represented as constants of the motion which act as symmetry generators on the phase space via the Poisson bracket structure.

Item Type:	Monograph (Working Paper)
Keywords:	Symplectic geometry; Hamiltonian flow; renormalisation group equation;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10506
Identification Number:	https://doi.org/10.1142/S0217751X95001273
Depositing User:	Dr. Brian Dolan
Date Deposited:	19 Feb 2019 15:14
Publisher:	arXiv
URI:	https://arxiv.org
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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