Factorization theorems in perturbative quantum field theory
This dissertation deals with factorization properties of Green functions and cross-sections in perturbation theory. It consists of two parts. Part I deals with the factorization theorem for the Drell-Yan cross-section. The new approach developed for this purpose is based upon a renormalization group equation with a generalized anomalous dimension. Using an alternate form of factorization for the Drell-Yan cross-section, derived in perturbation theory, a corresponding generalized anomalous dimension is defined, and explicit Feynman rules for its calculation are given. The resultant renormalization group equation is solved by a formal solution which is exhibited explicitly. Simple, explicit calculations are performed which verify Mueller's conjecture for the recovery of the usual parton model results for the Drell-Yan cross-section. The approach developed in this work offers a general framework to analyze the role played by the group factors in the cancellation of the soft divergences, and study their influence on the asymptotic behavior. Part II deals with factorization properties of the Green functions in position space. In this part, a Landau equation analysis is carried out for the singularities of the position space Green fucntions, in perturbation theory with the theta/sup 4/ interaction Lagrangian. A physical picture interpretation is given for the corresponding Landau equations. It is used to suggest a light-cone expansion. Using a power counting method, a formal derivation of the light-cone expansion for the two point function, the three point function and a product of two currents, is given without assuming a short distance expansion. Possible extensions to other theories is also considered.
- Research Organization:
- State Univ. of New York, Stony Brook (USA)
- OSTI ID:
- 6740059
- Country of Publication:
- United States
- Language:
- English
Similar Records
Dimensional renormalization in {phi}{sup 3} theory: Ladders and rainbows
Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of {lambda}{phi}{sup 4} field theory
Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANOMALOUS DIMENSION
ASYMPTOTIC SOLUTIONS
CROSS SECTIONS
DRELL MODEL
FACTORIZATION
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
LIGHT CONE
PERTURBATION THEORY
PHI4-FIELD THEORY
QUANTUM FIELD THEORY
RENORMALIZATION
SCALE DIMENSION
SINGULARITY
SPACE-TIME