《格點量子色動力學導論（英文影印版）》是2014 年10月30日北京大學出版社出版的圖書，作者是(奧)加特林格。
基本介紹
- 中文名：格點量子色動力學導論（英文影印版）
- 作者：(奧)加特林格
- 出版社：北京大學出版社
- 出版時間：2014年10月30日
- 頁數：364 頁
- 定價：62 元
- 開本：大32開
- 裝幀：平
- ISBN：978-7-301-24896-6
內容簡介,目錄,
內容簡介
本書講述了格點場論在量子色動力學中的套用。本書首先講述了格點路徑積分，之後講述了純規範理論的格點化和數值模擬。然後，本書講述了格點上的費米子、強子譜、手征對稱性等內容。對於動力學費米子和重正化群也做了深入的探討。最後，本書還講述了對強子結構和溫度、化學勢的格點場論處理。本書適合量子場論和粒子物理領域的研究者和研究生閱讀。
目錄
1 The path integral on the lattice.
1.1 Hilbert space and propagation in Euclidean time
1.1.1 Hilbert spaces.
1.1.2 Remarks on Hilbert spaces in particle physics
1.1.3 Euclidean correlators
1.2 The path integral for a quantum mechanical system.
1.3 The path integral for a scalar field theory
1.3.1 The Klein-Gordon field
1.3.2 Lattice regularization of the Klein-Gordon Hamiltonian
1.3.3 The Euclidean time transporter for the free case.
1.3.4 Treating the interaction term with the Trotter formula
1.3.5 Path integral representation for the partition function.
1.3.6 Including operators in the path integral
1.4 Quantization with the path integral
1.4.1 Different discretizations of the Euclidean action
1.4.2 The path integral as a quantization prescription
1.4.3 The relation to statistical mechanics
References
2 QCD on the lattice - a first look.
2.1 The QCD action in the continuum
2.1.1 Quark and gluon fields
2.1.2 The fermionic part of the QCD action
2.1.3 Gauge invariance of the fermion action
2.1.4 The gluon action
2.1.5 Color components of the gauge field
2.2 Naive discretization of fermions
2.2.1 Discretization of free fermions.
2.2.2 Introduction of the gauge fields as link variables
2.2.3 Relating the link variables to the continuum gauge fields
2.3 The Wilson gauge action
2.3.1 Gauge-invariant objects built with link variables
2.3.2 The gauge action
2.4 Formal expression for the QCD lattice path integral
2.4.1 The QCD lattice path integral
References
3 Pure gauge theory on the lattice.
3.1Haar measure
3.1.1 Gauge field measure and gauge invariance
3.1.2 Group integration measure
3.1.3 A few integrals for SU(3) .
3.2 Gauge invariance and gauge fixing
3.2.1 Maximal trees
3.2.2 Other gauges
3.2.3 Gauge invariance of observables
3.3 Wilson and Polyakov loops
3.3.1 Definition of the Wilson loop
3.3.2 Temporal gauge .
3.3.3 Physical interpretation of the Wilson loop
3.3.4 Wilson line and the quark-antiquark pair
3.3.5 Polyakov loop
3.4 The static quark potential
3.4.1 Strong coupling expansion of the Wilson loop
3.4.2 The Coulomb part of the static quark potential
3.4.3 Physical implications of the static QCD potential
3.5 Setting the scale with the static potential.
3.5.1 Discussion of numerical data for the static potential
3.5.2 The Sommer parameter and the lattice spacing
3.5.3 Renormalization group and the running coupling
3.5.4 The true continuum limit
3.6 Lattice gauge theory with other gauge groups
References
4 Numerical simulation of pure gauge theory
4.1 The Monte Carlo method.
4.1.1 Simple sampling and importance sampling
4.1.2 Markov chains
4.1.3 Metropolis algorithm - general idea
4.1.4 Metropolis algorithm for Wilson's gauge action
4.2 Implementation of Monte Carlo algorithms for SU(3)
4.2.1 Representation of the link variables
4.2.2 Boundary conditions
4.2.3 Generating a candidate link for the Metropolis update
4.2.4 A few remarks on random numbers
4.3 More Monte Carlo algorithms
4.3.1 The heat bath algorithm
4.3.2 Overrelaxation .
4.4 Running the simulation
4.4.1Initialization
4.4.2 Equilibration updates .
4.4.3 Evaluation of the observables
4.5Analyzing the data
4.5.1 Statistical analysis for uncorrelated data
4.5.2 Autocorrelation
4.5.3 Techniques for smaller data sets
4.5.4 Some numerical exercises
References
5 Fermions on the lattice
5.1 Fermi statistics and Grassmann numbers
5.1.1 Some new notation .
5.1.2 Fermi statistics
5.1.3 Grassmann numbers and derivatives
5.1.4 Integrals over Grassmann numbers
5.1.5 Gaussian integrals with Grassmann numbers
5.1.6 Wick's theorem
5.2 Fermion doubling and Wilson's fermion action
5.2.1 The Dirac operator on the lattice
5.2.2 The doubling problem .
5.2.3 Wilson fermions
5.3 Fermion lines and hopping expansion
5.3.1 Hopping expansion of the quark propagator
5.3.2 Hopping expansion for the fermion determinant
5.4 Discrete symmetries of the Wilson action
5.4.1 Charge conjugation
5.4.2 Parity and Euclidean reflections
5.4.3 γ
References .
6 Hadron spectroscopy
6.1 Hadron interpolators and correlators .
6.1.1 Meson interpolators
6.1.2 Meson correlators
6.1.3 Interpolators and correlators for baryons
6.1.4 Momentum projection
6.1.5 Final formula for hadron correlators
6.1.6 The quenched approximation
6.2 Strategy of the calculation .
6.2.1 The need for quark sources
6.2.2 Point source or extended source?
6.2.3 Extended sources
6.2.4 Calculation of the quark propagator .
6.2.5 Exceptional configurations
6.2.6 Smoothing of gauge configurations
6.3 Extracting hadron masses
6.3.1 Effective mass curves
6.3.2 Fitting the correlators
6.3.3 The calculation of excited states.
6.4 Finalizing the results for the hadron masses
6.4.1 Discussion of some raw data
6.4.2 Setting the scale and the quark mass parameters
6.4.3 Various extrapolations .
6.4.4 Some quenched results
References
7 Chiral symmetry on the lattice
7.1 Chiral symmetry in continuum QCD
7.1.1 Chiral symmetry for a single flavor
7.1.2 Several flavors
7.1.3 Spontaneous breaking of chiral symmetry
7.2 Chiral symmetry and the lattice
7.2.1 Wilson fermions and the Nielsen-Ninomiya theorem
7.2.2 The Ginsparg-Wilson equation
7.2.3 Chiral symmetry on the lattice
7.3 Consequences of the Ginsparg-Wilson equation
7.3.1 Spectrum of the Dirac operator
7.3.2 Index theorem
7.3.3 The axial anomaly
7.3.4 The chiral condensate
7.3.5 The Banks-Casher relation
7.4 The overlap operator.
7.4.1 Definition of the overlap operator
7.4.2 Locality properties of chiral Dirac operators
7.4.3 Numerical evaluation of the overlap operator
References
8 Dynamical fermions
8.1 The many faces of the fermion determinant
8.1.1 The fermion determinant as observable
8.1.2 The fermion determinant as a weight factor
8.1.3 Pseudofermions
8.1.4 Effective fermion action
8.1.5 First steps toward updating with fermions
8.2 Hybrid Monte Carlo .
8.2.1 Molecular dynamics leapfrog evolution
8.2.2 Completing with an accept-reject step
8.2.3 Implementing HMC for gauge fields and fermions
8.3 Other algorithmic ideas
8.3.1 The R-algorithm
8.3.2 Partial updates
8.3.3 Polynomial and rational HMC
8.3.4 Multi-pseudofermions and UV-filtering
8.3.5 Further developments
8.4 Other techniques using pseudofermions
8.5 The coupling-mass phase diagram
8.5.1 Continuum limit and phase transitions
8.5.2 The phase diagram for Wilson fermions
8.5.3 Ginsparg-Wilson fermions
8.6 Full QCD calculations.
References
9 Symanzik improvement and RG actions
9.1 The Symanzik improvement program
9.1.1 A toy example
9.1.2 The framework for improving lattice QCD
9.1.3 Improvement of interpolators
9.1.4 Determination of improvement coefficients
9.2 Lattice actions for free fermions from RG transformations
9.2.1 Integrating out the fields over hypercubes
9.2.2 The blocked lattice Dirac operator.
9.2.3 Properties of the blocked action
9.3 Real space renormalization group for QCD
9.3.1 Blocking full QCD.
9.3.2 The RG flow of the couplings . .
9.3.3 Saddle point analysis of the RG equation
9.3.4 Solving the RG equations
9.4 Mapping continuum symmetries onto the lattice
9.4.1 The generating functional and its symmetries
9.4.2 Identification of the corresponding lattice symmetries
References
10 More about lattice fermions
10.1 Staggered fermions
10.1.1 The staggered transformation
10.1.2 Tastes of staggered fermions
10.1.3 Developments and open questions
10.2 Domain wall fermions .
10.2.1 Formulation of lattice QCD with domain wall fermions . 250
10.2.2 The 5D theory and its equivalence to 4D chiral fermions
10.3 Twisted mass fermions
10.3.1 The basic formulation of twisted mass QCD
10.3.2 The relation between twisted and conventional QCD
10.3.3 O(a) improvement at maximal twist
10.4 Effective theories for heavy quarks
10.4.1 The need for an effective theory
10.4.2 Lattice action for heavy quarks
10.4.3 General framework and expansion coefficients
References
11 Hadron structure
11.1 Low-energy parameters
11.1.1 Operator definitions
11.1.2 Ward identities
11.1.3 Naive currents and conserved currents on the lattice
11.1.4 Low-energy parameters from correlation functions
11.2 Renormalization.
11.2.1 Why do we need renormalization?
11.2.2 Renormalization with the Rome-Southampton method . 281
11.3 Hadronic decays and scattering.
11.3.1 Threshold region
11.3.2 Beyond the threshold region
11.4 Matrix element
11.4.1 Pion form factor
11.4.2 Weak matrix elements
11.4.3 OPE expansion and effective weak Hamiltonian
References
12 Temperature and chemical potential
12.1 Introduction of temperature
12.1.1 Analysis of pure gauge theory
12.1.2 Switching on dynamical fermions
12.1.3 Properties of QCD in the deconfinement phase
12.2 Introduction of the chemical potential
12.2.1 The chemical potential on the lattice
12.2.2 The QCD phase diagram in the (T, μ) space
12.3 Chemical potential: Monte Carlo techniques
12.3.1 Reweighting
12.3.2 Series expansion.
12.3.3 Imaginary μ
12.3.4 Canonical partition functions
References
A Appendix
A.1 The Lie groups SU(N)
A.1.1 Basic properties
A.1.2 Lie algebra
A.1.3 Generators for SU(2) and SU(3)
A.1.4 Derivatives of group elements
A.2 Gamma matrices
A.3 Fourier transformation on the lattice .
A.4 Wilson's formulation of lattice QCD
A.5 A few formulas for matrix algebra .
References
