Conformal invariance in gauge theories. II. Yang-Mills theory

Journal Article · Wed Oct 01 04:00:00 EDT 1986 · Theor. Math. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01028890· OSTI ID:6639964

Zaikov, R P

The results of Part 1 are generalized to the non-Abelian case. By analogy with conformal QED, in which interaction with a matter field is realized by means of a four-vector potential that transforms in accordance with a direct sum of two nonprincipal representations, the first step in the present paper is the construction of a new formulation of quantum electrodynamics, in which the four-vector potential is regarded as an independent variable. Although the potential as a whole transforms in accordance with a principal representation, the corresponding conformally invariant two-point functions have a nonzero transverse part, and the Lagrangian is nondegenerate. In the non-Abelian case, one manifestly conformally invariant gauge condition is found, and the corresponding functional determinant is calculated. It is shown that in the gauge-invariant sector this theory is equivalent to the ordinary theory with conformally noninvariant gauge condition. A local effective Lagrangian is constructed, the Faddeev-Popov ''ghost'' fields having in this case scale dimension zero. It is shown that this effective Lagrangian has a residual global supersymmetry of Becchi-Rouet-Stora type.

• Research Organization: Joint Inst. for Nuclear Research, Dubna
• OSTI ID: 6639964
• Journal Information: Theor. Math. Phys.; (United States), Journal Name: Theor. Math. Phys.; (United States) Vol. 67:1; ISSN TMPHA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONFORMAL INVARIANCE
ELECTRODYNAMICS
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
LAGRANGIAN FIELD THEORY
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SCALAR FIELDS
SUPERSYMMETRY
SYMMETRY
VECTOR FIELDS
YANG-MILLS THEORY