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Coherent states in mathematical physics
About: Coherent states in mathematical physics is a research topic. Over the lifetime, 732 publications have been published within this topic receiving 32024 citations.
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01 Jan 2008
TL;DR: In this paper, a unified approach for finding coherent states of polynomially deformed algebras such as the quadratic and Higgs algeses is presented.
Abstract: We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general procedure to map these deformed algebras to appropriate Lie algebras. This is used , for the non compact cases, to obtain the annihilation operator coherent states, by finding the canonical conjugates of these operators. Generalized coherent states, in the Perelomov sense also follow from this construction. This allows us to explicitly construct coherent states associated with various quantum optical systems.
01 Jan 1995
TL;DR: In this paper, the authors studied q-quantum mechanics in one degree of freedom and discussed the holomorphic representation of the q-deformed Heisenberg-Weyl algebra and its realization by covariant Berezin symbols.
Abstract: We study q-quantum mechanics in one degree of freedom. Among other things, we discuss the holomorphic representation of the q-deformed Heisenberg-Weyl algebra and its realization by covariant Berezin symbols.
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TL;DR: In this article, the R-matrix method was used to generate a class of deformed fermionic-bosonic quantum Hopf algebras of type I--II, obtained by duality.
Abstract: Starting from a faithful five-dimensional matrix representation of the group of two independent oscillators and applying the R-matrix method we generate some classes of deformed fermionic-bosonic quantum Hopf algebras The corresponding Lie deformed superalgebras of type I--II, obtained by duality, are computed and a realization of generators of these deformed superalgebras are given in terms of the usual fermionic and bosonic creation and annihilation operators associated to the supersymmetric harmonic oscillator Then, a generalized deformed annihilator is construted and their eigenstates are computed giving a new class of deformed coherent states
19 Mar 2001
TL;DR: In this paper, the authors formulate a theory of generalized Fock spaces, which has a three tired structure consisting of Fock space, statistics and algebra, which unifies various forms of statistics and algebras, which were earlier considered to describe different systems.
Abstract: The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure This exercise becomes all the more important in order to provide a general classification scheme for various forms of statistics, and establish interconnections among them whenever it is possible We formulate a theory of generalized Fock spaces, which has a three tired structure consisting of Fock space, statistics and algebra This general formalism unifies various forms of statistics and algebras, which were earlier considered to describe different systems Besides, the formalism allows us to construct many new kinds of quantum statistics and the associated algebras of creation and destruction operators Some of these are: orthostatistics, null statistics or statistics of frozen order, quantum group based statistics and its many avatars, and ‘doubly-infinite’ statistics The emergence of new forms of quantum statistics for particles interacting with singular potential is also highlighted