Showing papers on "Coherent states in mathematical physics published in 1981"
TL;DR: In this article, it is shown that the use of coherent meson-pair states simplifies and improves calculations in static-source theories with complicated algebras and improves the performance.
Abstract: It is shown that the use of coherent meson-pair states simplifies and improves calculations in static-source theories with complicated algebras.
8 citations
TL;DR: Fermionic coherent states (FCS) were constructed via the Weyl supergroup of isometries of a Fock superspace as mentioned in this paper, and their properties were derived and the connection with pseudomechanics formalism was pointed out.
Abstract: Fermionic coherent states (FCS) are constructed via the Weyl supergroup of isometries of a Fock superspace. Their properties are derived and the connection with the pseudomechanics formalism is pointed out.
6 citations
TL;DR: In this paper, a new set of coherent angular momentum states for the oscillator was proposed by diagonalizing v and λ. They are shown to be minimum-uncertainty states for variables v, v + λ, and ǫ+ and provide a new quasiclassical description of the oscillators.
Abstract: The Hamiltonian for the oscillator has earlier been written in the form H=ℏω(2v+v+λ+·λ+3/2), where v+ and v are raising and lowering operators for v+v, which has eigenvalues k (the "radial" quantum number), and λ+ and λ are raising and lowering 3-vector operators for λ+·λ, which has eigenvalues l (the total angular momentum quantum number). A new set of coherent states for the oscillator is now denned by diagonalizing v and λ. These states bear a similar relation to the commuting operators H, L2, and L3 (where L is the angular momentum of the system) as the usual coherent states do to the commuting number operators N1, N2, and N 3. It is proposed to call them coherent angular momentum states. They are shown to be minimum-uncertainty states for the variables v, v +λ, and λ+ and to provide a new quasiclassical description of the oscillator. This description coincides with that provided by the usual coherent states only in the special case that the corresponding classical motion is circular, rather than elliptical; and, in general, the uncertainty in the angular momentum of the system is smaller in the new description. The probabilities of obtaining particular values for k and l in one of the new states follow independent Poisson distributions. The new states are overcomplete, and lead to a new representation of the Hilbert space for the oscillator, in terms of analytic functions on C×K3, where K3 is the three-dimensional complex cone. This space is related to one introduced recently by Bargmann and Todorov, and carries a very simple realization of all the representations of the rotation group.
5 citations
TL;DR: In this paper, it was shown that the transition probability between the first excited and ground states is proportional to the square of the number of nucleons, representing a cooperativity of the super-radiant type.
Abstract: It is shown that the Bloch or angular momentum coherent states furnish a particularly efficacious basis for a discussion of various aspects of the Lipkin model of the ’’nucleus.’’ The Hartree–Fock description (as well as its projected version) is elegantly obtained in this framework. It is demonstrated that the ’’transition probability’’ between the first excited and ground states is proportional to the square of the number of ’’nucleons,’’ representing (in contrast to what obtains in the random phase approximation) a cooperativity of the ’’super‐radiant’’ type. The extension of the model through the introduction of bosons permits, with the use of Bloch and Glauber coherent states, a succinct description of the phenomenon of boson condensation.
1 citations