A quantum mechanical gauge model and a possible dynamical solution of the strong {ital CP} Problem

Journal Article · Sun Sep 01 04:00:00 EDT 1996 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1996.0097· OSTI ID:389227

Loeffelholz, J ^[1]; Morchio, G ^[2]; Strocchi, F ^[3]

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1. Mathematisches Institut, Universitaet Leipzig, Leipzig (Germany)
2. Dipartimento di Fisica dell`Universita and INFN, Pisa (Italy)
3. Scuola Normale Superiore and INFN, Pisa (Italy)

A model describing a quantum mechanical particle on a circle with minimal electromagnetic interaction with a space independent vector potential, and with a potential {minus}{ital M}cos({var_phi}{minus}{theta}{sub {ital M}}) so that it mimics the massive Schwinger model, is discussed as a prototype of mechanisms and infrared structures which characterize gauge quantum field theories in positive gauges and QCD in particular. The functional integral representation in terms of the field variables which enter in the Lagrangean displays non-standard features, like a complex functional measure (failure of Nelson positivity), a crucial r{cflx o}le of the boundary conditions, and the decomposition into {theta} sectors already in finite volume. In the infinite volume limit, one essentially recovers the standard picture when {ital M}=0 ({open_quote}{open_quote}massless fermions{close_quote}{close_quote}), but one meets substantial differences for {ital M}{ne}0: for generic boundary conditions, independently of the Lagrangean angle of the topological term, the infinite volume limit selects the sector with {theta}={theta}{sub {ital M}} and provides a natural {open_quote}{open_quote}dynamical{close_quote}{close_quote} solution of the strong CP problem. In comparison with previous approaches, the strategy discussed here allows us to exploit the consequences of the {theta} dependence of the free energy density, with a unique minimum at {theta}={theta}{sub {ital M}}. {copyright} 1996 Academic Press, Inc.

• OSTI ID: 389227
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 250; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHIRAL SYMMETRY
CIRCULAR CONFIGURATION
CP INVARIANCE
FEYNMAN PATH INTEGRAL
FREE ENERGY
GAUGE INVARIANCE
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SYMMETRY BREAKING
VACUUM STATES