格点量子色动力学导论-(影印版)

内容简介

《格点量子色动力学导论(英文影印版)》讲述了格点场论在量子色动力学中的应用。本书先讲述了格点路径积分，之后讲述了纯规范理论的格点化和数值模拟。然后，本书讲述了格点上的费米子、强子谱、手征对称性等内容。对于动力学费米子和重正化群也做了深入的探讨。，本书还讲述了对强子结构和温度、化学势的格点场论处理。本书适合量子场论和粒子物理领域的研究者和研究生阅读。

目录

1 The path integral on the lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Hilbert space and propagation in Euclidean time . . . . . . . . . . . . 2
1.1.1 Hilbert spaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Remarks on Hilbert spaces in particle physics . . . . . . . . . 3
1.1.3 Euclidean correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 The path integral for a quantum mechanical system. . . . . . . . . . 7
1.3 The path integral for a scalar field theory. . . . . . . . . . . . . . . . . . . 10
1.3.1 The Klein-Gordon field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Lattice regularization of the Klein-Gordon Hamiltonian 11
1.3.3 The Euclidean time transporter for the free case. . . . . . . 14
1.3.4 Treating the interaction term with the Trotter formula . 15
1.3.5 Path integral representation for the partition function. . 16
1.3.6 Including operators in the path integral . . . . . . . . . . . . . . 17
1.4 Quantization with the path integral. . . . . . . . . . . . . . . . . . . . . . . . 19
1.4.1 Different discretizations of the Euclidean action . . . . . . . 19
1.4.2 The path integral as a quantization prescription . . . . . . . 20
1.4.3 The relation to statistical mechanics . . . . . . . . . . . . . . . . . 22
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 QCD on the lattice - a first look. . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 The QCD action in the continuum . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.1 Quark and gluon fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.2 The fermionic part of the QCD action . . . . . . . . . . . . . . . 26
2.1.3 Gauge invariance of the fermion action . . . . . . . . . . . . . . . 28
2.1.4 The gluon action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.5 Color components of the gauge field . . . . . . . . . . . . . . . . . 30
2.2 Naive discretization of fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.1 Discretization of free fermions. . . . . . . . . . . . . . . . . . . . . . . 32
2.2.2 Introduction of the gauge fields as link variables . . . . . . . 33
2.2.3 Relating the link variables to the continuum gauge fields 34
2.3 The Wilson gauge action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.1 Gauge-invariant objects built with link variables. . . . . . . 36
2.3.2 The gauge action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4 Formal expression for the QCD lattice path integral . . . . . . . . . 39
2.4.1 The QCD lattice path integral . . . . . . . . . . . . . . . . . . . . . . 39
References . . . . . . . . . . . . . . . . . . . .