Showing papers on "Coherent states in mathematical physics published in 1977"
TL;DR: In this paper, a review of definite overcomplete non-orthogonal state systems that are connected with irreducible representations of Lie groups is presented, which are called systems of generalized coherent states.
Abstract: The review is devoted to an analysis of definite overcomplete non-orthogonal state systems that are connected with irreducible representations of Lie groups–the so called systems of generalized coherent states. These systems, which the author is the first to propose, are generalizations of Glauber's coherentstate system and arise in natural fashion in physical problems that have dynamic symmetry. They permit a considerable simplification of the solution of the quantum problem by reducing it to a simpler "classical" problem. The review deals with the properties of generalized-coherent-state systems connected with the simplest Lie groups.
241 citations
TL;DR: In this paper, a generalization of the notion of coherent states is given, and one-to-one correspondences between covariant overcomplete systems of coherent state and a class of covariant semi-spectral measures are shown.
Abstract: A generalization of the notion of coherent states is given. The following one-to-one correspondences are pointed out: (1) between covariant overcomplete systems of coherent states and a class of covariant semi-spectral measures; (2) between covariant semispectral measures and unitary irreducible subrepresentations of induced representations of Lie groups; (3) between unitary irreducible representations of Lie groups with covariant overcomplete systems of coherent states and unitary irreducible subrepresentations of induced representations, whose representation spaces are reproducing kernel Hilbert spaces.
33 citations
TL;DR: In this paper, a unified algebraic approach for the coherent states associated with a continuous spectrum of the noncompact group SU(1,1) was proposed, based on a simple and unified approach.
Abstract: A new, explicit formula is obtained for the coherent states associated with a continuous spectrum of the noncompact group SU(1,1). The method is based on a simple and unified algebraic approach. We briefly discuss its relations to the generalized coherent states of Barut and Girardello, and of Perelomov.
15 citations
TL;DR: In this article, the time evolution of a coherent state is discussed using the evolution operator of the underlying Hamiltonian, which is a special case of the Hamiltonian evolution operator used in this paper.
8 citations
5 citations
2 citations
01 Jan 1977
TL;DR: In this paper, the difference between three important sets of states related to the SU(2) algebra and describes the properties of the Heisenberg uncertainty relation associated with the elements of this algebra are discussed.
Abstract: Publisher Summary This chapter discusses the difference between three important sets of states related to the SU(2) algebra and describes the properties of the Heisenberg uncertainty relation associated with the elements of this algebra. These states can be classified into minimum uncertainty states, Bloch states, which are atomic or coherent spin states, and intelligent spin states. The chapter discusses the dynamical properties associated with the intelligent spin states. The set of all generalized intelligent spin (G.I.S.S) states contains the Bloch states; therefore, {G.I.S.S} can be called a refinement of them. The G.I.S.S. do not necessarily satisfy the Heisenberg equality. The chapter further illustrates the time evolution of a nonrelativistic system of spin j having a magnetic moment γ, with the help of certain equations.
TL;DR: In this article, it was shown that the possibility of representing every operator, acting on a vector space, irreducible under SU(2), in the form f|Ω>G(Ω) } is a set of Bloch coherent states, can be generalized to compact semi-simple Lie groups.
Abstract: It is shown that the possibility of representing every operator, acting on a vector space, irreducible under SU(2), in the form f|Ω>G(Ω) } is a set of Bloch (atomic) coherent states, can be generalized to compact semi-simple Lie groups.