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Wick products of the CAR algebra

Author: E. R. Negrin
Journal: Proc. Amer. Math. Soc. 126 (1998), 3639-3645
MSC (1991): Primary 81T08
MathSciNet review: 1623044
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Abstract: The purpose of this paper is to put in a precise mathematical (algebraic) form the Wick products of the CAR algebra. We state in detail the reduction of the ordinary product of Fermi fields in terms of a finite sum of monomials in the creation and annihilation operators in which all creation operators occur to the left of all annihilation operators (Wick-ordered) and the Fock (vacuum) state of the former.

References [Enhancements On Off] (What's this?)

  • 1. J. C. Baez, I. E. Segal and Z. Zhou, ``Introduction to Algebraic and Constructive Quantum Field Theory", Princeton Univ. Press, Princeton, NJ, 1992.
  • 2. J. D. Bjorken and S. D. Drell, ``Relativistic Quantum Fields", McGraw-Hill, NY, 1965. MR 32:5092
  • 3. N. N. Bogoliubov and D. V. Shirkov, ``Quantum Fields", Benjamin/Cummings Pub. Co., Reading, MA, 1983. MR 85g:81096
  • 4. F. J. Dyson, The Radiation Theories of Tomonaga, Schwinger, and Feynman, Phys. Rev. (3) 75 (1949), 486-502. MR 10:418a
  • 5. C. Itzykson and J.-B. Zuber, ``Quantum Field Theory", McGraw-Hill, NY, 1980. MR 82h:81002
  • 6. P. E. T. Jorgensen and G. L. Price, Index Theory and Second Quantization of Boundary Value Problems, J. Funct. Anal. 104 (1992), 243-290.
  • 7. I. E. Segal, Quantized Differential Forms, Topology 7 (1968), 147-172. MR 38:1113
  • 8. I. E. Segal, Nonlinear Functions of Weak Processes I, J. Funct. Anal. 4 (1969), 404-456. MR 40:2309
  • 9. G. C. Wick, The evaluation of the collision matrix, Phys. Rev. (2) 80 (1950), 268-272. MR 12:380d

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Additional Information

E. R. Negrin
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 Canary Islands, Spain

Keywords: Wick-ordered, vacuum state, Fermi field, CAR algebra
Received by editor(s): November 19, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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