Instantons in the presence of a fixed density of massless fermions in two dimensions

Journal Article · Fri Feb 15 04:00:00 EST 1980 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.21.1100· OSTI ID:5534786

Aragao de Carvalho, C

We investigate the effects of a fixed finite density of massless fermions on the instantons of the Abelian Higgs model in two Euclidean dimensions. By using an appropriate path-integral formalism, we calculate the generating functional and analyze it by means of a graphical expansion, in which instantons appear as interaction vertices. We find that the fixed-fermion-density constraint introduces a chemical potential ..mu.. as a Lagrange multiplier and that this changes the fermion propagators in the expansion, so as to account for the chemical potential in the usual manner of many-body theory. That, in turn, leads to a ..mu.. dependence for the dynamically generated mass in the case of two flavors and, thus, changes the picture of chiral-symmetry breaking. We also find that the existence of the chemical potential imposes a cutoff on the instanton density, thereby providing a mechanism for instanton suppression, in the same way as the static electric color field used by Callan, Dashen, and Gross to derive a bag picture of hadrons from quantum chromodynamics.

• Research Organization: Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540
• OSTI ID: 5534786
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 21:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BAG MODEL
CHIRAL SYMMETRY
COLOR MODEL
COMPOSITE MODELS
ELEMENTARY PARTICLES
EUCLIDEAN SPACE
EXTENDED PARTICLE MODEL
FERMIONS
FIELD THEORIES
HAMILTONIANS
HIGGS MODEL
INSTANTONS
MANY-BODY PROBLEM
MASSLESS PARTICLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRIX ELEMENTS
MINKOWSKI SPACE
PARTICLE MODELS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
QUASI PARTICLES
RIEMANN SPACE
SPACE
SPACE-TIME
SYMMETRY
SYMMETRY BREAKING
VACUUM STATES