Quantum geometry of dirac fermions

Journal Article · Mon Jan 20 04:00:00 EST 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X9200020X· OSTI ID:5298133

Korchemsky, G P ^[1]

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1. Lab. of Theoretical Physics, JINR, Dubna, P.O. Box 79, 101000 Moscow (SU)

This paper reports on a bosonic path integral formalism which is developed for Dirac fermions interacting with a non-Abelian gauge field in D-dimensional Euclidean space-time. The representation for the effective action and correlation functions of interacting fermions as sums over all bosonic paths on the complex projective space CP{sup 2d{minus}1} (2d = 2{sup 1D/21}) is derived where the whole of the spinor structure is absorbed by the one-dimensional Wess-Zumino term. It is the Wess-Zumino term that ensures all necessary properties of Dirac fermions under quantization, i.e. quantized values of the spin, Dirac equation, and Fermi statistics.

• OSTI ID: 5298133
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:2; ISSN IMPAE; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
CORRELATION FUNCTIONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
EUCLIDEAN SPACE
FERMIONS
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
INTEGRALS
INTERACTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
MATHEMATICS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTIZATION
RIEMANN SPACE
SPACE
SPACE-TIME
SPINORS
STATISTICS
WAVE EQUATIONS