Prog. Theor. Phys. Supplement No.141 (2001) pp. 243-284
Canonical Formulation of Mixed State and Irreducible Representation of u(M) Algebra
Faculty of Engineering, Kansai University, Suita 564-86800, Japan
*Departamento de Fisica, Universidade de Coimbra, P 3000 Coimbra, Portugal
(Received July 31, 2000)
In order to get an irreducible representation of u(M)
algebra, we develop a canonical theory of mixed state and discuss the
dual property of mutually commutable u(M) algebras which have
the Casimir operators in common. With the aid of this dual property,
we can obtain an irreducible representation of u(M) algebra
which is useful for investigations of nuclear dynamics, where
generators of u(M) algebra given by one-body operators of
fermion are expressed in terms of bosons. As an example, we derive
the Holstein-Primakoff representation of u(M) generators.
We also derive the irreducible representation of su(3) algebra.
DOI : 10.1143/PTPS.141.243
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