Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory
Batalin-Vilkovisky Formalism in Perturbative Algebraic Quantum Field Theory
复制标题
微扰代数量子场论中的 Batalin-Vilkovisky 形式主义
DOI：
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发表时间：
2011
影响因子：
2.4
通讯作者：
K. Rejzner
中科院分区：
文献类型：
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作者：
K. Fredenhagen;K. Rejzner
在对经典场论的Batalin-Vilkovisky形式进行深入讨论的基础上，本文构造了摄动重整化量子场论中的Batalin-Vilkovisky复形。关键的技术成分是将重归一化时序积作为二元积的扩展概念等同于经典场论的点积。最初，在因果摄动理论中，时间顺序积仅仅被理解为局部泛函空间上的多线性映射序列。我们对重整时间顺序积的扩展概念（表示为documentclass[12pt]{minimal} uspackageamsmath{ uspackagewasysym} uspackageamsfonts {uspackpackageamssymb} uspackageamssyb{ uspackageamssfs} uspackagagemathrsfs {uspackageupgreek} setlengthoddsidemargin{-69pt} {egindocument}{}{}{}{}$${cdot_{{}^{mathcal{T}_{
m r}}}}$$ enddocument{）与旧的概念一致}，并且我们发现了一个量子代数的子空间，该子空间相对于documentclass[12pt]minimal {uspackageamsmath} uspackagewasysym{ uspackageamsfonts}是闭的{userpackageamssymb} userpackageamssy{ userpackagemathrsfs} userpackageupgreek {setlengththoddsidemargin} -69pt{ egindocument }{}{}{}{}{}$${cdot_{{}^{mathcal{T}_{
m r}}}}$$ enddocument{。在这个空间上}，重整化的Batalin-Vilkovisky代数是经典代数，但是用时间顺序积的形式写出来，同时用一个算子代替了未重整化理论中定义不清的梯度拉普拉斯算子。我们将其与Brennecke和d<s:1> tsch的异常主区恒等式的异常项进行了识别。与其他方法相反，我们不涉及路径积分形式，也不需要在中间步骤中使用正则化。
On the basis of a thorough discussion of the Batalin-Vilkovisky formalism for classical field theory presented in our previous publication, we construct in this paper the Batalin-Vilkovisky complex in perturbatively renormalized quantum field theory. The crucial technical ingredient is an extended notion of the renormalized time-ordered product as a binary product equivalent to the pointwise product of classical field theory. Originally, in causal perturbation theory, the time-ordered product is understood merely as a sequence of multilinear maps on the space of local functionals. Our extended notion of the renormalized time-ordered product (denoted by documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${cdot_{{}^{mathcal{T}_{
m r}}}}$$end{document}) is consistent with the old one and we found a subspace of the quantum algebra which is closed with respect to documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${cdot_{{}^{mathcal{T}_{
m r}}}}$$end{document} . On this space the renormalized Batalin-Vilkovisky algebra is then the classical algebra but written in terms of the time-ordered product, together with an operator which replaces the ill defined graded Laplacian of the unrenormalized theory. We identify it with the anomaly term of the anomalous Master Ward Identity of Brennecke and Dütsch. Contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps.