dedication 
preface 
preface to the third edition 
preface to the second edition 
preface to the first edition 
1.introduction 
2.the path integral approach to quantization 
2.1the path integral method in quantum mechanics 
2.2 path integral representation of bosonic green functionsinfieldtheory 
2.3the transfer matrix 
2.4 path integral r��epresentation of fermionicgreen functions 
2.5discretizing space��time.the lattice as a regulator ofaquantum field theory 
3.the free scalar field on the lattice 
4.fermions on the lattice 
4.1the doubling problem 
4.2a closer look at fermion doubling 
4.3wilson fermions 
4.4staggered fermions 
4.5 technical details of the staggered fermion formulation 
4.6 staggered fermions in momentum space 
4.7ginsparg��wilson fermions.the overlap operator 
5.abelian gauge fields on the latticeand compact qed 
5.1 preliminaries 
5.2 lattice formulation of qed 
6.non abelian gauge fields on the latticecompact qcd 
7.the wilson loop and the staticquark��antiquark potential 
7.1a look at non��relativistic quantum mechanics 
7.2 the wilson loop and the static qq=potentialin qed 
7.3 the wilson loop in qcd 
8.the qq��potential in some simple models 
8.1the potentialin quenched qed 
8.2the potential in quenched compact qed2 
9.the continuum limit of lattice qcd 
9.1 critical behaviour of lattice qcd and the continuumlimit 
9.2 dependence of the coupling constant on the lattice spacingand the renormalization group �¡�function 
10.lattice sum rules 
10.1 energy sum rule for the harmonic oscillator 
10.2 the su��n�� gauge action on an anisotropic lattice 
10.3 sum rules for the static qq��potential 
10.4determination of the electric�� magnetic and anomalous contribution to the qq potential 
10.5 sum rules for the glueball mass 
11.the strong coupling expansion 
11.1the qq��potential to leading order in strong coupling 
11.2 beyond the leading approximation 
11.3the lattice hamiltonian in the strong coupling limitand the string picture of confinement 
12.the hopping parameter expansion 
12.1path integral r��epresentation of correlation functionsin terms of bosonic variables 
12.2hopping parameter expansion of the fermion propagatorin an externalfield 
12.3hopping parameter expansion of the effective action 
12.4 the hpe and the pauli exclusion principle 
13.weak coupling expansion ������.the ��3��theory 
13.1introduction 
13.2 weak coupling expansion of correlation functions in the ��3��theory 
13.3 the power counting theorem of reisz 
14.weak coupling expansion ������.lattice qed 
14.1 the gauge fixed lattice action 
14.2 lattice feynman rules 
14.3renormalization of the axial vector current in one��looporder 
14.4the abj anomaly 
15.weak coupling expansion ������.lattice qcd 
15.1the link integration measure 
15.2 gauge fixing and the faddeev��popov determinant 
15.3 the gauge field action 
15.4 propagators and vertices 
15.5 relation between al and the a��parameter of continuum qcd 
15.6universality of the axial anomaly in lattice qcd 
16.monte carlo methods 
16.1introduction 
16.2 construction principles for algorithms.markov chains 
16.3 the metropolis method 
16.4 the langevin algorithm 
16.5 the molecular dynamics method 
16.6 the hybrid algorithm 
16.7 the hybrid monte carlo algorithm 
16.8 the pseudofermion method 
16.9application of the hybrid monte carlo algorithmto systems with fermions 
17.some results of monte carlo calculations 
17.1 the string tension and the qq potentialin the su��3�� gaugetheory 
17.2 the qq��potentialin full qcd 
17.3 chiral symmetry breaking 
17.4glueballs 
17.5 hadron mass spectrum 
17.6instantons 
17.7 flux tubes in qq and qqq��systems 
17.8the dual superconductor picture of confinement 
17.9 center vortices and confinement 
17.10 calorons 
18.path��integral representation of the thermodynamical partition functionfor some solvable bosonic and fermionicsystems 
18.1introduction 
18.2path��integral r��epresentation of the partition function in quantum mechanics 
18.3 sum rule for the mean energy 
18.4 test of the energy sum rule.the harmonic oscillator 
18.5the free relativistic boson gas in the path integral approach 
18.6the photon gas in the path integral approach 
18.7 functional methods for fermions.basics 
18.8path integral r��epresentation of the partition functionfor a fermionic system valid for arbitrary time��step 
18.9 a modified fermion action leading to fermion doubling 
18.10the free dirac gas.continuum approach 
18.11 dirac gas of wilson fermions on the lattice 
���� 
19.fimte temperature perturbation theory ofand on the lattice 
20.non��perturbative qcd at finite temperature 
appendix a 
appendix b 
appendix c 
appendix d 
appendix e 
appendix f 
appendix g 
references 
index