Spectrum of Dirac operator and role of winding number in QCD

Journal Article · Tue Dec 15 00:00:00 EST 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.46.5607· OSTI ID:6892726

Leutwyler, H; Smilga, A ^[1]

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1. Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

We show that very general considerations based on the properties of the partition function of QCD allow one to extract information about the eigenvalues of the Dirac operator in vacuum gauge fields. In particular, we demonstrate that the familiar suppression of field configurations with a nontrivial topology occurring for small quark masses is a finite size effect which disappears if the four-dimensional volume [ital V] is large enough. The formation of a quark condensate is connected with the occurrence of small eigenvalues of order [lambda][sub [ital n]][proportional to]1/[ital V].

• OSTI ID: 6892726
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 46:12; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIRAC OPERATORS
EIGENVALUES
QUANTUM CHROMODYNAMICS
PARTITION FUNCTIONS
QUARK CONDENSATION
CHIRAL SYMMETRY
EIGENFUNCTIONS
ENERGY DENSITY
FERMIONS
GAUGE INVARIANCE
MASS
SUM RULES
ULTRAVIOLET DIVERGENCES
VACUUM STATES
EQUATIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SYMMETRY
662120* - General Theory of Particles & Fields- Symmetry
Conservation Laws
Currents & Their Properties- (1992-)
662230 - Quantum Chromodynamics- (1992-)