A Cohomological Perspective on Algebraic Quantum Field Theory

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JournalCommunications in Mathematical Physics
DateAccepted/In press - 14 Sep 2017
DateE-pub ahead of print - 15 Feb 2018
DatePublished (current) - 1 May 2018
Issue number1
Volume360
Number of pages41
Pages (from-to)439-479
Early online date15/02/18
Original languageEnglish

Abstract

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model. This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited. To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory.

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© The Author(s) 2018.

    Research areas

  • math-ph, math.CT, math.MP, 81T05, 16E40, 46M15, 81T2

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