Axiomatic derivation of Feynman rules and related topics
Previous results in axiomatic field theory by Steinmann and Epstein-Glaser establish the existence of the retarded and time ordered Green's functions in every order of perturbation. To connect these Green's functions with the ones calculated in canonical field theories via the Feynman rules, one has to consistently build them not just for every order of perturbation but for each specific graph. ([open quotes]Consisently[close quotes] means here that the Green functions associated with two [open quotes]small[close quotes] graphs build up to the Green's functions of the [open quotes]big[close quotes] graph formed by connecting the two [open quotes]small[close quotes] ones). This paper shows that this can indeed be done; that in this sense the Feynman rules of perturbative Lagrangian field theory can be derived from the abstract, but physically very basic, principles of axiomatic field theory. All results hold only for massive field theories. The LSZ formalism, to the best knowledge of the author, has so far not been modified to admit mass zero fields. To make the representation simpler and more transparent, the author restricts the discussion to a single component, scalar [Phi][sup 4] interaction which is a part of the Standard Model of Particle Physics. Motivated by its role in particle physics, the author complements the perturbative study of [Phi][sup 4]-theory by reviewing the status of non-perturbative solutions to the theory in the final chapter.
- Research Organization:
- Kansas Univ., Lawrence, KS (United States)
- OSTI ID:
- 7161672
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
The signed permutation group on Feynman graphs
The Epstein-Glaser approach to perturbative quantum field theory: graphs and Hopf algebras
Related Subjects
FEYNMAN PATH INTEGRAL
AXIOMATIC FIELD THEORY
PHI4-FIELD THEORY
PERTURBATION THEORY
GREEN FUNCTION
SU-2 GROUPS
FIELD THEORIES
FUNCTIONS
INTEGRALS
LIE GROUPS
QUANTUM FIELD THEORY
SU GROUPS
SYMMETRY GROUPS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)