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arXiv · hep-th/0601136

On Quantum Field Theories in Operator and Functional Integral Formalisms

Aba Teleki·Milan Noga
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Abstract

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.

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Aba Teleki, Milan Noga. 2006-01-19. On Quantum Field Theories in Operator and Functional Integral Formalisms. https://arxiv.org/abs/hep-th/0601136

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