场演算:没有费曼图的量子和统计场理论

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-03-17 DOI:10.3842/SIGMA.2022.044

J. Gough

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引用次数: 0

摘要

对于给定的基空间$M$(时空)，我们考虑$M$上的Guichardet空间上的Guichardet空间。在这里，我们基于Guichardet积分开发了一个“场演算”。这是描述玻色子系统格林函数关系的自然环境。在这里，我们可以遵循Schwinger的建议，发展一种微分(局部场)方法，而不是费曼开创的积分方法。这得益于DEFG (Dyson-Einstein-Feynman-Guichardet)速记法，它极大地简化了表达式。这为Schwinger和Tomonaga的形式化方法提供了一个方便的框架，而不是费曼图。在玻色子创造/湮灭算子的帮助下，我们用这种语言重新定义了戴森-施温格。我们还给出了树展开的组合方法。

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Field Calculus: Quantum and Statistical Field Theory without the Feynman Diagrams

For a given base space $M$ (spacetime), we consider the Guichardet space over the Guichardet space over $M$. Here we develop a ''field calculus'' based on the Guichardet integral. This is the natural setting in which to describe Green function relations for Boson systems. Here we can follow the suggestion of Schwinger and develop a differential (local field) approach rather than the integral one pioneered by Feynman. This is helped by a DEFG (Dyson-Einstein-Feynman-Guichardet) shorthand which greatly simplifies expressions. This gives a convenient framework for the formal approach of Schwinger and Tomonaga as opposed to Feynman diagrams. The Dyson-Schwinger is recast in this language with the help of bosonic creation/annihilation operators. We also give the combinatorial approach to tree-expansions.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.