Chiral invariant gross-Neveu model: Classical versus quantum

Journal Article · Sat Oct 01 04:00:00 EDT 1983 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(83)90003-9· OSTI ID:5375423

Garbaczewski, P

We present a unification of different and independently investigated aspects of the chiral invariant Gross-Neveu model. Special emphasis is placed on the relevane of classical (c-number, non Grassmann) spinor solutions of the G-N field equations for the construction, and thus understanding of the respective quantized Fermi model. To get an insight into the ''quantum meaning of classical field theory'' if specialized to the G-N case, we perform the path integral quantiztion procedure which first leads to the Fermi oscillator problem, and then, after appropriate generalizations, to the quantum Fermi G-N model. Path integrals are carried out with respect to c-number spinor paths only, and in fact no reference is necessary to the Grassmann algebra methods, which are conventionally used to integrate out fermions.

• Research Organization: School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin 4, Ireland
• OSTI ID: 5375423
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 150:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
EIGENVALUES
EQUATIONS
FERMIONS
FEYNMAN PATH INTEGRAL
FIELD EQUATIONS
FIELD THEORIES
HAMILTONIANS
INTEGRALS
LAGRANGIAN FIELD THEORY
LATTICE FIELD THEORY
MATHEMATICAL OPERATORS
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPINORS
SYMMETRY