Research output: Contribution to journal › Article

**A Cohomological Perspective on Algebraic Quantum Field Theory.** / Hawkins, Eli.

Research output: Contribution to journal › Article

Hawkins, E 2018, 'A Cohomological Perspective on Algebraic Quantum Field Theory', *Communications in Mathematical Physics*, vol. 360, no. 1, pp. 439-479. https://doi.org/10.1007/s00220-018-3098-8

Hawkins, E. (2018). A Cohomological Perspective on Algebraic Quantum Field Theory. *Communications in Mathematical Physics*, *360*(1), 439-479. https://doi.org/10.1007/s00220-018-3098-8

Hawkins E. A Cohomological Perspective on Algebraic Quantum Field Theory. Communications in Mathematical Physics. 2018 May 1;360(1):439-479. https://doi.org/10.1007/s00220-018-3098-8

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title = "A Cohomological Perspective on Algebraic Quantum Field Theory",

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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N2 - 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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