Normal Products in Dimensional Regularization
Sep, 197430 pages
Published in:
- Nucl.Phys.B 92 (1975) 477-506
- Published: 1975
Report number:
- DAMTP-74-17
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Abstract: (Elsevier)
It is shown how to reformulate Zimmermann's normal product method for quantum field theory using dimensional regularization. The finite part operation we use is defined by the subtraction of pole parts of diagrams (and subdiagrams) at the physical space-time dimension n = 4. When applied to spontaneous symmetry breaking (SSB), at least of the Nambu-Goldstone type, the original method has complications caused by non-linearity in the Bogoliubov finite-part operation. We show how the method avoids such problems, the subtractions being always minimal. SSB is treated almost as easily as in the tree approximation, e.g. when proving Ward identities. Similar simplification should occur for gauge theories, though this is not demonstrated in this paper. The minimality of the subtractions means that anisotropic and oversubtracted normal products are not defined in the new method. Finally, certain properties of n-dimensional Feynman integrals are proved; the use of analytic regularization in rigorous proofs of Ward identities etc. is thus avoided.- FIELD THEORY: GAUGE
- RENORMALIZATION
- SYMMETRY: BROKEN
- PERTURBATION THEORY
- FEYNMAN GRAPH
- ANALYTIC PROPERTIES
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