2014/03/19 by Kazuya Yonekura, Yonekura, Kazuya · 2 citations
Computer Science · Physics and Astronomy · #Advanced Statistical Modeling Techniques #Computational Drug Discovery Methods #hep-ph #hep-th
paper · pdf · doi:10.48550/arxiv.1403.4939
5 pages, 1 figure
arxiv created 2014/03/19 · arxiv updated 2014/03/21
In four dimensional unitary scale invariant theories, arguments based on the proof of the a-theorem suggest that the trace of the energy-momentum tensor T vanishes when the momentum is light-like, p2=0. We show that there exists a local operator O such that the trace is given as T=∂2 O, which establishes the equivalence of scale and conformal invariance. We define the operator as O=∂-2 T, and explain why this is a well-defined local operator. Our argument is based on the assumptions that: (1) A kind of crossing symmetry for vanishing matrix elements holds regardless of the existence of the S-matrix. (2) Correlation functions in momentum space are analytic functions other than singularities and branch cuts coming from on-shell processes. (3) The Wightman axioms are sufficient criteria of the locality of an operator.