Recursive boson system in the Cuntz algebra O{sub {infinity}}
- College of Science and Engineering, Ritsumeikan University, 1-1-1 Noji Higashi, Kusatsu, Shiga 525-8577 (Japan)
Bosons and fermions are often written by elements of other algebras. Abe (private communication) gave a realization of bosons by formal infinite sums of the canonical generators of the Cuntz algebra O{sub {infinity}}. We show that such formal infinite sum always makes sense on a certain dense subspace of any permutative representation of O{sub {infinity}}. In this meaning, we can regard as if the algebra B of bosons was a unital *-subalgebra of O{sub {infinity}} on a given permutative representation. According to this relation, we compute branching laws arising from restrictions of representations of O{sub {infinity}} on B. For example, it is shown that the Fock representation of B is given as the restriction of the standard representation of O{sub {infinity}} on B.
- OSTI ID:
- 21013642
- Journal Information:
- Journal of Mathematical Physics, Vol. 48, Issue 9; Other Information: DOI: 10.1063/1.2759838; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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