Ultralocal Quantum Field Theory
These notes cover lecture material presented at two 1971 Winter Schools.
A special class of model field theories, differing from relativistic theories by the absence of the spatial gradient in the Hamiltonian, is discussed. Simple operator solutions are constructed which circumvent the infinite mass renormalization, infinite coupling constant renormalization and infinite field strength renormalization inherent in a perturbation approach. A number of properties of these solutions are analyzed including the spectrum of the Hamiltonian. Compared to free field theories, the ultralocal models discussed herein may, conceivably, provide an alternate starting point to attack covariant field theories.
KeywordsField Operator Coherent State Model Function Local Operator Free Theory
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- 1.See, e.g., J. Glimm and A. Jaffe in:Statistical Mechanics and Field Theory; C. DeWitt and R. Stora eds. (Gordon and Breach Science Publishers, Inc., New York and London, 1971 ).Google Scholar
- 3.G. Wentzel, Heiv. Phys. Acta 13, 269 (1940)Google Scholar
- A. Araki, Princeton thesis, 1960, Chap. VGoogle Scholar
- R. F. Streater, Lectures at the 1968 Karpacz Winter School.Google Scholar
- 4.I. M. Gel’fand and N. Ya Vilenkin, Generalized Functions, Vol. 4: Applications of Harmonic Analysis, translated by A. Feinstein (Academic Press, New York, 1964 ), Chap. III.Google Scholar
- 5.G. Szego, Orthogonal Polynomials (American Mathematical Society, New York, 1959 ), pg. 99, 377.Google Scholar
- J. R. Klauder, Relativity, Carmeli et al. eds. ( Penum, New York, 1970 ), pg. 1.Google Scholar
- 7.C. Newman, Princeton thesis (in preparation).Google Scholar