Applications of the Coherent State Representation in the Theory of Magnetism .

V. V. Dodonov

Hisanao Ogura

Abstract By an analogy between the theories of the Wiener functional and photon quantum field, such as the Wiener‐Itô expansion and the Fock‐space representation, a “coherent‐state” representation is introduced as a functional integral of nonorthogonal, overcomplete basis, corresponding to the coherent‐state representation of a photon field. A discrete‐state version is given to the “coherent‐state” representation in a form convenient for practical application. Analogously, a “coherent‐state” representation is established for functional of the Poisson process, where a remarkable analogy exists between the two. The Wiener‐Itô representation is derived from the coherent‐state representation by interpreting the coherent state as a generating functional of the orthogonal functionals.

DAVID J. ROWE

The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

Oluf Danielsen, Per-Anker Lindgård

D. C. Cabra, Pierre Pujol