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… 
Homological Perturbation Theory for Nonperturbative Integrals
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
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
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
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
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
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
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
TLDR
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
  • C. Elliott
  • Mathematics
    Mathematical 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
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
...
...

References

SHOWING 1-10 OF 20 REFERENCES
Homological Perturbation Theory for Nonperturbative Integrals
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
FEYNMAN DIAGRAMS FOR PEDESTRIANS AND MATHEMATICIANS
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I
Batalin–Vilkovisky integrals in finite dimensions
The Batalin–Vilkovisky (BV) method is the most powerful method to analyze functional integrals with (infinite-dimensional) gauge symmetries presently known. It has been invented to fix gauges
The (Secret?) homological algebra of the Batalin-Vilkovisky approach
This is a survey of `Cohomological Physics', a phrase that first appeared in the context of anomalies in gauge theory. Differential forms were implicit in physics at least as far back as Gauss (1833)
The Radiation Theories of Tomonaga, Schwinger, and Feynman
A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a
A Note on the Antibracket Formalism
Certain aspects of the antifield-antibracket formalism for quantization of gauge theories are clarified. In particular, we discuss the geometrical meaning of the antifields, the geometric meaning of
The Radiation Theories of Tomonaga , Schwinger , and Feynman
A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a
Existence theorem for gauge algebra
A general gauge action is defined by postulating a minimum of its properties necessary for the existence of loop expansion in the quantum theory. The structure of the general gauge algebra is derived
Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
The validity of the rules given in previous papers for the solution of problems in quantum electrodynamics is established. Starting with Fermi's formulation of the field as a set of harmonic
...
...