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This thesis focuses on an unresolved problem in particle and
nuclear physics: the relation between two important
non-perturbative phenomena in quantum chromodynamics (QCD) - quark
confinement and chiral symmetry breaking. The author develops a new
analysis method in the lattice QCD, and derives a number of
analytical formulae to express the order parameters for quark
confinement, such as the Polyakov loop, its fluctuations, and the
Wilson loop in terms of the Dirac eigenmodes closely related to
chiral symmetry breaking. Based on the analytical formulae, the
author analytically as well as numerically shows that at finite
temperatures there is no direct one-to-one correspondence between
them. The thesis describes this extraordinary achievement using the
first-principle analysis, and proposes a possible new phase in
which quarks are confined and chiral symmetry is restored.
This thesis focuses on an unresolved problem in particle and
nuclear physics: the relation between two important
non-perturbative phenomena in quantum chromodynamics (QCD) - quark
confinement and chiral symmetry breaking. The author develops a new
analysis method in the lattice QCD, and derives a number of
analytical formulae to express the order parameters for quark
confinement, such as the Polyakov loop, its fluctuations, and the
Wilson loop in terms of the Dirac eigenmodes closely related to
chiral symmetry breaking. Based on the analytical formulae, the
author analytically as well as numerically shows that at finite
temperatures there is no direct one-to-one correspondence between
them. The thesis describes this extraordinary achievement using the
first-principle analysis, and proposes a possible new phase in
which quarks are confined and chiral symmetry is restored.
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