1995/09/05 by Hidenori Sonoda, Sonoda, Hidenori
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Relativity and Gravitational Theory #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9509018
plain TeX with harvmac, 3 PS figures, 21 pages
arxiv created 1995/09/05 · openalex publication_date 1995/09/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper, field theory in curved space was considered, and a formula that expresses the first order variation of correlation functions with respect to the external metric was postulated. The formula is given as an integral of the energy-momentum tensor over space, where the short distance singularities of the product of the energy-momentum tensor and an arbitrary composite field must be subtracted, and finite counterterms must be added. These finite counterterms have been interpreted geometrically as a connection for the linear space of composite fields over theory space. In this paper we will study a second order consistency condition for the variational formula and determine the torsion of the connection. A non-vanishing torsion results from the integrability of the variational formula, and it is related to the Bose symmetry of the product of two energy-momentum tensors. The massive Ising model on a curved two-dimensional surface is discussed as an example, and the short-distance singularities of the product of two energy-momentum tensors are calculated explicitly.