Quantum Chromodynamics on the Lattice: An Introductory Presentation (Google eBook)
Springer Science & Business Media, Oct 16, 2009 - Science - 343 pages
Quantum chromodynamics (QCD) is the fundamental quantum ?eld theory of quarks and gluons. In order to discuss it in a mathematically well-de?ned way, the theory has to be regularized. Replacing space–time by a Euclidean lattice has proven to be an e?cient approach which allows for both theor- ical understanding and computational analysis. Lattice QCD has become a standard tool in elementary particle physics. Asthetitlealreadysays:thisbookisintroductory!Thetextisintendedfor newcomerstothe?eld,servingasastartingpoint.Wesimplywantedtohavea bookwhichwecanputintothehandsofanadvancedstudentfora?rstreading on lattice QCD. This imaginary student brings as a prerequisite knowledge of higher quantum mechanics, some continuum quantum ?eld theory, and basic facts of elementary particle physics phenomenology. In view of the wealth of applications in current research the topics p- sented here are limited and we had to make some painful choices. We discuss QCD but omit most other lattice ?eld theory applications like scalar th- ries, gauge–Higgs models, or electroweak theory. Although we try to lead the reader up to present day understanding, we cannot possibly address all on- ing activities, in particular concerning the role of QCD in electroweak theory. Subjects like glueballs, topological excitations, and approaches like chiral p- turbation theory are mentioned only brie?y. This allows us to cover the other topics quite explicitly, including detailed derivations of key equations. The ?eld is rapidly developing. The proceedings of the annual lattice conferences provide information on newer directions and up-to-date results.
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QCD on the lattice a first look
Pure gauge theory on the lattice
Numerical simulation of pure gauge theory
Fermions on the lattice
Chiral symmetry on the lattice
ˆμ algorithm blocking calculation chemical potential chiral condensate chiral symmetry coefficients compute conjugate construction continuum limit correlation functions corresponding defined denotes density derivative det[D Dirac operator discretization eigenvalues Euclidean correlators evaluated expansion expectation value exponential factor fermion action fermion determinant ﬁeld ﬁnd finite flavor formulation Gattringer gauge action gauge configurations gauge coupling gauge field gauge group Ginsparg–Wilson equation gluon Grassmann hadron Hasenfratz interpolators introduced invariant lattice action lattice Dirac operator lattice QCD lattice spacing Lett link variables mass term massless matrix elements meson method momentum Monte Carlo nonvanishing Nucl observables obtain parameter partition function path integral phase Phys physical pion plaquette Polyakov loop properties pseudofermion quantum field theory quark mass quark propagator quenched relation renormalization right-hand side simulation so-called space–time spatial statistical step SU(N updating vacuum expectation value vanishes vector Wilson loop zero γμ