BRS Symmetry, the Quantum Master Equation and the Wilsonian Renormalization Group | Zendy

Yuji Igarashi | Zendy; Katsumi Itoh | Zendy; Hiroto So | Zendy

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BRS Symmetry, the Quantum Master Equation and the Wilsonian Renormalization Group

Author(s) -

Yuji Igarashi,

Katsumi Itoh,

Hiroto So

Publication year - 2001

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.106.149

Subject(s) - physics , mathematical physics , quantum master equation , effective action , legendre transformation , renormalization , renormalization group , invariant (physics) , gauge theory , quantum , master equation , quantum mechanics , classical mechanics , thermodynamics

Recently we made a proposal for realization of an effective BRS symmetryalong the Wilsonian renormalization group flow. In this paper we show that theidea can be naturally extended for the most general gauge theories. Extensiveuse of the antifield formalism is made to reveal some remarkable structure ofthe effective BRS symmetry. The average action defined with a continuum analogof the block spin transformation obeys the quantum master equation (QME),provided that an UV action does so. We show that the RG flow described by theexact flow equations is generated by canonical transformations in thefield-antifield space. Using the relation between the average action and theLegendre effective action, we establish the equivalence between the QME for theaverage action and the modified Ward-Takahashi identity for the Legendreaction. The QME remains intact when the regularization is removed.Comment: 19 page

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