The Operator Algebra at the Gaussian Fixed-Point

Abstract

We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in $D=4$ dimensions. This amounts to perturbative construction of the ${\varphi }^4$ theory where the parameters of the theory are momentum dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.

arXiv comment38 pages, Sec II improved with more review, improved notation in Sec IV and Appendix D, Appendix C added, footnotes added

References in corpus (7)

• Fundamentals of the Exact Renormalization Group
• Realization of symmetry in the ERG approach to quantum field theory
• The local Callan-Symanzik equation: structure and applications
• Products of composite operators in the exact renormalization group formalism
• Equivalence of Wilson Actions
• Operator product expansion coefficients in the exact renormalization group formalism
• On the geometry of the theory space in the ERG formalism