Alberto S. Cattaneo, Nima Moshayedi
These notes give an introduction to the mathematical framework of the Batalin-Vilkovisky and Batalin-Fradkin-Vilkovisky formalisms. Some of the presented content was given as a mini course by the first author at the 2018 QSPACE conference in Benasque.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Hořava type generating functions
本文提出利用BFV形式主义量子化爱因斯坦方程的非对角解，并通过霍尔瓦类型生成函数编码各向异性缩放和有效宇宙学常数。
We report a rigorous quantization of topological quantum mechanics on $\mathbb{R}_{\geqslant 0}$ and $\mathbf{I}= [0, 1]$ in perturbative BV-BFV formalism. Costello's homotopic renormalization is extended, and incorporated in our construction. Moreover, BV quantization of the same model studied in our previous work is derived from the BV-BFV quantization, leading to a comparison between different interpretations of ''state'' in these two frameworks.
A note on gluing via fiber products in the (classical) BV-BFV formalism
本文研究经典场论中时空流形沿边界粘合的数学表述，并在BV-BFV形式体系下通过若干例子显式构造场空间纤维积的同伦。
We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover, we consider mixed boundary conditions and show that they lead to quantum anomalies, i.e. to a failure of the (modified differential) Quantum Master Equation. We show that it can be restored by adding boundary terms to the action, at the price of introducing corner terms in the boundary operator. We also show that the quantum GBFV operator on the total space …
We describe a globalization construction for the Rozansky-Witten model in the BV-BFV formalism for a source manifold with and without boundary in the classical and quantum case. After having introduced the necessary background, we define an AKSZ sigma model, which, upon globalization through notions of formal geometry extended appropriately to our case, is shown to reduce to the Rozansky-Witten model. The relations with other relevant constructions in the literature are discussed. Moreover, we split the model as a $BF$-like theory and we construct a perturbative quantization of the model in th…
We show how to derive asymptotic charges for field theories on manifolds with "asymptotic" boundary, using the BV-BFV formalism. We also prove that the conservation of said charges follows naturally from the vanishing of the BFV boundary action, and show how this construction generalises Noether's procedure. Using the BV-BFV viewpoint, we resolve the controversy present in the literature, regarding the status of large gauge transformation as symmetries of the asymptotic structure. We show that even though the symplectic structure at the asymptotic boundary is not preserved under these transfor…
We consider the Chern-Simons theory with Wilson lines in 3D and in 1D in the BV-BFV formalism of Cattaneo-Mnev-Reshetikhin. In particular, we allow for Wilson lines to end on the boundary of the space-time manifold. In the toy model of 1D Chern-Simons theory, the quantized BFV boundary action coincides with the Kostant cubic Dirac operator which plays an important role in representation theory. In the case of 3D Chern-Simons theory, the boundary action turns out to be the odd (degree 1) version of the BF model with source terms for the B field at the points where the Wilson lines meet the boun…
The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to perform perturbative quantisation of Lagrangian field theories on manifolds with boundary, and present a special case of Chern-Simons theory as a new example.
The Reduced Phase Space of $N=1, D=4$ Supergravity in the BV-BFV formalism
本文在BV-BFV形式主义中研究了$N=1$，$D=4$超引力的简化相空间，通过KT构造描述边界约束，并探讨了BFV与BV描述的关系。
Equivariant BV-BFV Formalism
本文将等变 BV 形式扩展至带边流形情形，并以 AKSZ 理论作为实际示例。
The goal of this paper is to investigate the Theta invariant --- an invariant of framed 3-manifolds associated with the lowest order contribution to the Chern-Simons partition function --- in the context of the quantum BV-BFV formalism. Namely, we compute the state on the solid torus to low degree in $\hbar$, and apply the gluing procedure to compute the Theta invariant of lens spaces. We use a distributional propagator which does not extend to a compactified configuration space, so to compute loop diagrams we have to define a regularization of the product of the distributional propagators, wh…
As a detailed application of the BV-BFV formalism for the quantization of field theories on manifolds with boundary, this note describes a quantization of the relational symplectic groupoid for a constant Poisson structure. The presence of mixed boundary conditions and the globalization of results is also addressed. In particular, the paper includes an extension to space-times with boundary of some formal geometry considerations in the BV-BFV formalism, and specifically introduces into the BV-BFV framework a "differential" version of the classical and quantum master equations. The quantization…
4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism
本文在BV-BFV形式体系中重构带边4流形的Donaldson-Witten理论，证明其满足修正量子主方程，并联系Nekrasov配分函数、高阶规范理论与枚举几何。
We show how the BV-BFV formalism provides natural solutions to descent equations, and discuss how it relates to the emergence of holographic counterparts of given gauge theories. Furthermore, by means of an AKSZ-type construction we reproduce the Chern-Simons to Wess-Zumino-Witten correspondence from infinitesimal local data, and show an analogous correspondence for BF theory. We discuss how holographic correspondences relate to choices of polarisation relevant for quantisation, proposing a semi-classical interpretation of the quantum holographic principle.
Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism
该研究利用BFV形式体系，得到共架形式下四维引力角隅的局域泊松结构，发现其含耦合内部对称性与微分同胚的Atiyah李代数胚，并阐明了与BF理论的关系。
Classical and quantum Lagrangian field theories with boundary
本文介绍带边界的拉格朗日场论，回顾BV和BFV上同调形式以解决体相和边界理论中的奇点，并探讨如何将两者一致结合以用于微扰量子化。
In this paper we recover the non-perturbative partition function of 2D~Yang-Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D~Yang-Mills theory on surfaces with boundaries and corners in the Batalin-Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting -- the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces -- building blocks -- and choosing a convenient gauge-fixing on the pieces, and assembli…
BV Pushforward of Palatini-Cartan gravity
本文证明 Palatini-Cartan 引力中标准 BV 表述经 BV 前推等价于与边界 BFV 数据相容的 AKSZ 类版本。
The Moyal cohomology of the N=1 spinning particle
针对 N=1 自旋粒子中 BFV 形式的上同调在负度非平凡的问题，通过将 Poisson 括号替换为 Moyal 括号来消除这些上同调类。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。