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Teoreticheskaya i Matematicheskaya Fizika, 1978, Volume 36, Number 2, Pages 166–182
(Mi tmf4298)
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This article is cited in 1 scientific paper (total in 1 paper)
Algebras of observables of the free Dirac field
K. Yu. Dadashyan, S. S. Horuzhy
Abstract:
A net of algebras of local observables of the free Dirac field satisfying the
Haag–Araki axioms is constructed and investigated. It is shown that because of the $C$-number nature of the commutation relations the model also satisfies the axiom of weak additivity, in contrast to fermion systems of general form. A new representation for a spinor field is constructed that is unitarily equivalent to the usual one and taken as a basis for constructing a net of algebras of observables of threedimensional regions on the $t=0$ hyperplane of Minkowski space. It is shown that the algebra of observables of a three-dimensional region $B$ coincides with that of the four-dimensional double cone $C(B)$ with base $B$. This correspondence is used to prove structure theorems for the algebras of observables of the regions $C(B)$ and $C(B)'$. The methods of Tomita–Takesaki theory are used to show that these algebras are type III factors after restriction to coherent superselection sections and satisfy the duality condition.
Received: 25.11.1977
Citation:
K. Yu. Dadashyan, S. S. Horuzhy, “Algebras of observables of the free Dirac field”, TMF, 36:2 (1978), 166–182; Theoret. and Math. Phys., 36:2 (1978), 665–675
Linking options:
https://www.mathnet.ru/eng/tmf4298 https://www.mathnet.ru/eng/tmf/v36/i2/p166
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Abstract page: | 257 | Full-text PDF : | 101 | References: | 44 | First page: | 2 |
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