A Cohomological Perspective on Algebraic Quantum Field Theory

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

In: Communications in Mathematical Physics, Vol. 360, No. 1, 01.05.2018, p. 439-479.

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Harvard

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

APA

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

Vancouver

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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Hawkins, Eli. / A Cohomological Perspective on Algebraic Quantum Field Theory. In: Communications in Mathematical Physics. 2018 ; Vol. 360, No. 1. pp. 439-479.

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@article{432e586e5d3e403eabc2589879134b28,
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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author = "Eli Hawkins",
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doi = "10.1007/s00220-018-3098-8",
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RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - A Cohomological Perspective on Algebraic Quantum Field Theory

AU - Hawkins, Eli

N1 - © The Author(s) 2018.

PY - 2018/5/1

Y1 - 2018/5/1

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.

AB - 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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