Representations of the CCR in the (φ4)3 model: Independence of space cutoff

作者: Jean-Pierre Eckmann

DOI: 10.1007/BF01877586

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摘要: The algebra of observables for the renormalized φ4 interaction in 3-dimensional space-time is constructed. It shown that von Neumann algebras associated with a bounded regionB are independent space cutoff which used construction Hamiltonian this interaction. This result to be useful translation invariant theory three dimensions. also gives physical criterion equivalence non-Fock representations canonical commutation relations.

参考文章(19)
K. Osterwalder, J. Eckmann, UNIQUENESS OF THE HAMILTONIAN AND OF THE REPRESENTATION OF THE CCR FOR THE QUARTIC BOSON INTERACTION IN THREE DIMENSIONS. Helv. Phys. Acta 44: No. 7, 884-909(31 Dec 1971).. ,(1971)
T. A. A. B., A. Erdelyi, Tables of Integral Transforms. I The Mathematical Gazette. ,vol. 39, pp. 337- ,(1955) , 10.2307/3608613
J. v. Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren Mathematische Annalen. ,vol. 104, pp. 570- 578 ,(1931) , 10.1007/BF01457956
I. Segal, Notes toward the construction of nonlinear relativistic quantum fields, I. The hamiltonian in two space-time dimensions as the generator of a C-automorphism group. Proceedings of the National Academy of Sciences of the United States of America. ,vol. 57, pp. 1178- 1183 ,(1967) , 10.1073/PNAS.57.5.1178
Klaus Hepp, Théorie de la renormalisation Lecture Notes in Physics. ,vol. 2, pp. 1- 201 ,(1969) , 10.1007/BFB0108958
Steven Weinberg, High-Energy Behavior in Quantum Field Theory Physical Review. ,vol. 118, pp. 838- 849 ,(1960) , 10.1103/PHYSREV.118.838
A. Van Daele, A. Verbeure, Unitary equivalence of Fock representations on the Weyl algebra Communications in Mathematical Physics. ,vol. 20, pp. 268- 278 ,(1971) , 10.1007/BF01646623