Scalar formalism for non-Abelian gauge theory

Journal Article · Mon Sep 01 00:00:00 EDT 1986 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526981· OSTI ID:5496129

Hostler, L C

The gauge field theory of an N-italic-dimensional multiplet of spin- 1/2 particles is investigated using the Klein--Gordon-type wave equation )Pi x (1+i-italicsigma) x Pi+m-italic/sup 2/)Phi = 0, Pi/sub ..mu../equivalentpartial/partiali-italicx-italic/sub ..mu../-e-italicA-italic/sub ..mu../, investigated before by a number of authors, to describe the fermions. Here Phi is a 2 x 1 Pauli spinor, and sigma repesents a Lorentz spin tensor whose components sigma/sub ..mu..//sub ..nu../ are ordinary 2 x 2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. The equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum tau-functions, tau(2,1, xxx 3 xxx)equivalent<0-chemically bondT-italic(Psi/sub in/(2) Psi-bar/sub in/(1) xxx A-italic/sub ..mu../(3)/sub in/ xxx S-italic)chemically bond0->, where Psi/sub in/ is a Heisenberg operator belonging to a 4N-italic x 1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics.

• Research Organization: Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853-5001
• OSTI ID: 5496129
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 27:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

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645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
ANGULAR MOMENTUM OPERATORS
BOSON EXPANSION
DIAGRAMS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DYSON REPRESENTATION
ELECTRODYNAMICS
EQUATIONS
FERMIONS
FEYNMAN DIAGRAM
FEYNMAN METHOD
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONALS
FUNCTIONS
GAUGE INVARIANCE
INTEGRALS
INTERACTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
PARTICLE PROPERTIES
PAULI SPIN OPERATORS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK-GLUON INTERACTIONS
SPIN
TRANSFORMATIONS
WAVE EQUATIONS