Research output: Contribution to journal › Article

Journal | Communications in Mathematical Physics |
---|---|

Date | Accepted/In press - 14 Sep 2017 |

Date | E-pub ahead of print - 15 Feb 2018 |

Date | Published (current) - 1 May 2018 |

Issue number | 1 |

Volume | 360 |

Number of pages | 41 |

Pages (from-to) | 439-479 |

Early online date | 15/02/18 |

Original language | English |

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.

© The Author(s) 2018.

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

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