# How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism

@article{Gwilliam2012HowTD, title={How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism}, author={Owen Gwilliam and Theo Johnson-Freyd}, journal={arXiv: Mathematical Physics}, year={2012} }

The Batalin-Vilkovisky formalism in quantum field theory was originally invented to avoid the difficult problem of finding diagrammatic descriptions of oscillating integrals with degenerate critical points. But since then, BV algebras have become interesting objects of study in their own right, and mathematicians sometimes have good understanding of the homological aspects of the story without any access to the diagrammatics. In this note we reverse the usual direction of argument: we begin by…

## 20 Citations

Homological Perturbation Theory for Nonperturbative Integrals

- Mathematics
- 2012

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of…

Homological Quantum Mechanics

- Mathematics, Physics
- 2021

We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy…

Perturbative Quantum Field Theory and Homotopy Algebras

- Mathematics
- 2020

We review the homotopy algebraic perspective on perturbative quantum field theory: classical field theories correspond to homotopy algebras such as $A_\infty$- and $L_\infty$-algebras. Furthermore,…

Large $N$ phenomena and quantization of the Loday-Quillen-Tsygan theorem

- Mathematics
- 2021

We offer a new approach to large N limits using the Batalin-Vilkovisky formalism, both commutative and noncommutative, and we exhibit how the Loday-Quillen-Tsygan Theorem admits BV quantizations in…

The holomorphic bosonic string

- Mathematics
- 2017

We present a holomorphic version of the bosonic string in the formalism of quantum field theory developed by Costello and collaborators. In this paper we focus on the case in which space-time is flat…

Perturbative Methods in Path Integration

- Mathematics
- 2013

Author(s): Johnson-Freyd, Theodore Paul | Advisor(s): Reshetikhin, Nicolai | Abstract: This dissertation addresses a number of related questions concerning perturbative "path" integrals. Perturbative…

Correlation functions of scalar field theories from homotopy algebras

- Mathematics
- 2022

We present expressions for correlation functions of scalar field theories in perturbation theory using quantum A∞ algebras. Our expressions are highly explicit and can be used for theories both in…

Batalin–Vilkovisky quantization of fuzzy field theories

- Computer ScienceLetters in Mathematical Physics
- 2021

The modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam are applied to noncommutative field theories in the finite-dimensional case of fuzzy spaces and a generalization is developed to theories that are equivariant under a triangular Hopf algebra symmetry.

Abelian Duality for Generalized Maxwell Theories

- MathematicsMathematical Physics, Analysis and Geometry
- 2019

We describe a construction of generalized Maxwell theories – higher analogues of abelian gauge theories – in the factorization algebra formalism of Costello and Gwilliam, allowing for analysis of the…

Symmetry factors of Feynman diagrams and the homological perturbation lemma

- Mathematics, Physics
- 2020

We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that…

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