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Communications in Theoretical Physics

Normal Product Expansion of Rotation Operators Gained by Coherent State Method

Fan Hang-yi

Published Mar 1, 1987• 6 citations
Publisher

Abstract

In Schwinger boson representation of angular momentum theory we derive new normal product expansion of rotation operators which can generate new operator identities in the Hilbert space to which SU 2 group maps, some properties and applications of them are presented.
DOI
10.1088/0253-6102/7/2/125

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By the properties of the coherent state and the technique of performing integrations within ordered products as in Ref. [1], we derive some new useful operator ordering identities. Their applications, especially in studying the Boglyubov transformations both in one and two dimensional cases, are presented. The explicit non-unitary operators which turn the coordinate or momentum eigen-state to the corresponding coherent state are also given. Moreover, by using the Schwinger angular momentum theory and the technique mentioned above we find the normal product form of the rotation operator, with which the coefficient of the rotation D-matrix can be easily obtained.
The various representations of rotations in physical space and Hilbert space are developed in detail. This leads to an in-depth treatment of the representation of states of well-defined spin and angular momentum in quantum systems. The peculiarities of the physics of spin— systems (spinors) is outlined. The tensorial character of representations is implicit in the treatment. The Schwinger and Bargmann representations are introduced in some detail; and this leads to SU(2) coherent states (which are important for more advanced group representation theory).