2006/01/19 by Aba Teleki, Teleki, Aba, Milan Noga +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0601136
9 pages
arxiv created 2006/01/19 · arxiv updated 2009/12/01
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional integral in quantum field theory cannot be regarded as a Newton-Lebesgue integral but rather as a formal object to which one associates distinct numerical values for different processes of its integration. By choosing an appropriate method for the integration of a given functional integral, one can select a single representation out of infinitely many inequivalent representations for an operator whose trace is expressed by the corresponding functional integral. These properties are demonstrated with two exactly solvable examples.