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Physica A Statistical Mechanics and its Applications

General glauber coherent states on the Weyl algebra and their phase integrals

Reinhard Honegger, Armin Rapp

Published Sep 1, 1990• 24 citations
Publisher
DOI
10.1016/0378-4371(90)90301-8

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Specifying their (normally ordered) characteristic functions we determine all states of the boson C *-Weyl algebra which satisfy Glauber's coherence condition and are not realizable as density operators in Fock space. The pure ones are shown to be just the eigenstates of the annihilation operators in their GNS-representations (in contrast to the Fock case) and are characterized in many equivalent manners. The central decomposition of an arbitrary coherent state has the macroscopic phase variable as parameter and is supported by the pure coherent states, which is in fact the only way for a maximal decomposition. The set of all coherent states with the same absolute factorizing function is proven to be a Bauer simplex. The appearence of a classical coherent field part is studied in detail in the GNS-representations and shown to correspond to an enlargement of the set of one boson states by just one additional mode.
The Glauber minimum-uncertainty coherent states with two variables for Landau levels, based on the representation of Weyl-Heisenberg algebra by two different modes, have been studied about four decades ago. Here, we introduce new two-variable coherent states with minimum uncertainty relationship for Landau levels in three different methods: the infinite unitary representation of su(1, 1) is realized in two different methods, first, by consecutive levels with the same energy gaps and also with the same value for z-angular momentum quantum number, then, by shifting z-angular momentum mode number by two units while the energy level remaining the same. Besides, for su(2), whether by lowest Landau levels or Landau levels with lowest z-angular momentum, just one finite unitary representation is introduced. Having constructed the generalized Klauder-Perelomov coherent states, for any of the three representations, we obtain their Glauber coherency by displacement operator of Weyl-Heisenberg algebra.