The Phases of Quantum Chromodynamics
From Confinement to Extreme Environments
By John B. Kogut
By Mikhail A. Stephanov
Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (No. 21)
Publisher: Cambridge University Press
Print Publication Year: 2003
Online Publication Date:August 2009
Online ISBN:9780511534980
Hardback ISBN:9780521804509
Paperback ISBN:9780521143387
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511534980.006
Subjects: Particle Physics and Nuclear Physics, Theoretical Physics and Mathematical Physics
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Continuous time and discrete space
Another form of lattice-gauge theory that is very intuitively appealing is the theory's Hamiltonian form. In many problems it is very instructive to make energyestimates, look at wavefunctions, and estimate the masses, sizes, and shapes of bound states etc. that a quantum-mechanical formulation with a Hamiltonian gives. Sometimes these simple things are hard to extract from a path-integral formulation. Mechanisms of confinement, flux-tube dynamics, and chiral-symmetry breaking are also amenable to Hamiltonian analysis. Decon-finement at finite T and transitions as functions of chemical potential will also be discussed in this formulation below. Since there is much more pioneering physics to be done in QCD in extreme environments, it is important to have many approaches available.
In the Hamiltonian formulation one uses a spatial lattice and leaves the time variable continuous, as we have illustrated in several 1 + 1 examples above. The Hamiltonian is the generator of time evolution and acts on quantized states. The Hamiltonian could be obtained methodically from the path-integral formulation by calculating the system's transfer matrix and then taking the time continuum limit [9]. It is more instructive, however, to construct the Hamiltonian from scratch. In fact, we can think about just two spatial points, write the Hamiltonian for that system, and then consider a full three-dimensional spatial lattice.
As in the Euclidean formulation, the key to the construction is the requirement that local color-gauge invariance be an exact symmetry for any lattice spacing a. Let there be two sites with the link between them.
pp. i-iv
pp. v-viii
pp. 1-9
2 - Background in spin systems and critical phenomena : Read PDF
pp. 10-52
3 - Gauge fields on a four-dimensional euclidean lattice : Read PDF
pp. 53-73
4 - Fermions and nonperturbative dynamics in QCD : Read PDF
pp. 74-92
5 - Lattice fermions and chiral symmetry : Read PDF
pp. 93-135
6 - The Hamiltonian version of lattice-gauge theory : Read PDF
pp. 136-157
7 - Phase transitions in lattice-gauge theory at high temperatures : Read PDF
pp. 158-181
8 - Physics of QCD at high temperatures and chemical potentials : Read PDF
pp. 182-235
9 - Large chemical potentials and color superconductivity : Read PDF
pp. 236-279
10 - Effective Lagrangians and models of QCD at nonzero chemical potential : Read PDF
pp. 280-323
11 - Lattice-gauge theory at nonzero chemical potential : Read PDF
pp. 324-354
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