Renormalization group and scale transformations for renormalized field operators

Journal Article · Wed Dec 15 00:00:00 EST 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.3412· OSTI ID:7134729

Lukierski, J

First we show that the renormalized regularized Lagrangian density satisfies the constraint equation which can be interpreted as the divergence equation for the local normalization current. The normalization current which we introduce in this paper generates a constant multiplication factor in front of the field operator and leads to the appearance of renormalization-group transformations. Using a nonlocal action principle we introduce the charge operator which can be identified with the quantum generator of renormalization-group transformations. Further, we consider the divergence of the canonical dilatation current, and we show how to define the renormalized dilatation charge operator which generates Callan-Symanzik corrections to canonical scaling. We obtain the result that both generators for the renormalization group and renormalized scale transformations exist in a cutoff-free limit in the sense of derivation and both are time-independent, i.e., they implement the symmetries of renormalized theory. Finally, we investigate in our operator framework the breaking of renormalized scale invariance owing to the presence of mass terms. Both off-shell (Gell-Mann--Low) and on-shell (conventional) renormalization schemes are discussed. The dependence of the renormalized scale transformations on a physical mass in different renormalization schemes is exhibited. (AIP)

• Research Organization: ZiF, Universitaet Bielefeld, Bielefeld, West Germany
• OSTI ID: 7134729
• Journal Information: Phys. Rev., D; (United States), Vol. 14:12
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD OPERATORS
RENORMALIZATION
SCALE INVARIANCE
SYMMETRY BREAKING
COUPLING CONSTANTS
GAUGE INVARIANCE
GREEN FUNCTION
LAGRANGIAN FUNCTION
WARD IDENTITY
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
645400* - High Energy Physics- Field Theory