Hiroshi Kuratsuji

Path integral in the representation of SU(2) coherent state and classical dynamics in a generalized phase space

Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two‐dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.

Path integral approach to many-nucleon systems and time-dependent Hartree-Fock

Abstract The quantum mechanical treatment of many-nucleon systems is investigated by using the path integrals in the representation of the generalized coherent state for the unitary group. Utilizing the completeness relation of the coherent state, we derive a path integral representation for the transition amplitude which joins arbitrary initial and final states; thereby the time-dependent Hartree-Fock is naturally obtained as a classical limit.

A semiclassical treatment of path integrals for the spin system

Starting with path integrals in the SU(2) coherent state representation, the semiclassical approximation of the propagator for the spin system is investigated. By extending the idea of the semiclassical expansion method, which was developed in the usual phase‐space path integrals, to the path integrals in the curved phase space, which is characteristic of the SU(2) coherent states, we obtain a closed form for the semiclassical propagator. As an application, we discuss the semiclassical quantization condition for the spin system.

Semiclassical quantization with a quantum adiabatic phase

Abstract By applying the path integral method to two interacting systems, we derive a novel form of the semiclassical quantization rule including the topological phase which was recently found in certain quantum adiabatic processes.

A Path Integral Formalism of Collective Motion

A Quantum mechanical formalism of collective motion is proposed by using the idea of path integral method. Time evolution of many· body system is described by the propagator which joins the many-body state vectors parametrized by complex collective parameters. A general form of path integral representation for the propagator is derived in the complex parameter space. In particular the case of the coherent state representation is discussed in detail. It is pointed out that the time-dependent variation principle and especially the time dependent Hartree-Fock are naturally obtained as a classical limit.

Semiclassical asymptotics for fermion systems based on the coherent-state path integral

Abstract With use of the path integrration in the coherent-state representation, a semiclassical asymptotics is developed for the bound state quantization of fermion systems. The quantum correspondence is given for the stability and instability of the periodic classical solutions in the generalized phase space, which are governed by the stability equation deduced from the second variation of action. The complex exponents corresponding to the unstable solutions are shown to result in a broadening of the quantized resonances.

Classical quantization of time-dependent Hartree-Fock solutions by coherent-state path integrals

Abstract We investigate a classical (Bohr-Sommerfeld like) quantization for the time-dependent Hartree-Fock solutions by extending the idea of the quantized periodic-orbit theory developed by Gutzwiller and Dashen et al. to path integrals in the representation of the coherent state for unitary groups. We consider the n -level model as an example.

Classical quantization condition in the generalized coherent-state representation with application to many-body systems

Abstract On the basis of the ansatz of the single-valuedness for the classically approximated wave function, a classical quantization rule is derived for a dynamical system described by a general class of coherent states. The classical wave function, which is defined on the manifold parametrizing the coherent states, is constructed by an application of the stationary phase approximation to the coherent-state path integral. The general form of the quantization rule for the time-dependent Hartree-Fock solutions is obtained as a particular case.

Semiclassical quantization of a spin system by coherent state path integrals

Abstract By using the path integral in the SU(2) coherent state representation, we investigate the semiclassical quantization for an interacting spin system. We arrive at the Bohr-Sommerfeld like quantization rule in curved phase space.

Collective dynamics for the bag: Semiclassical approach to the breathing motion

Starting from the bag Lagrangian, we derive a collective Lagrangian which describes the breathing motion of the bag in a microscopic manner. The essential point of our procedure is to adopt a parametrized quark wave function promoted by the local Lorentz-boost so that the linear boundary condition of the bag model is exactly satisfied. After evaluating the mass parameter and the potential energy, we calculate quantized spectra of the breathing mode of nucleon and delta by using the semiclassical quantization scheme. The calculated mass of Roper resonance is comparable to the recent estimate by using the Skyrme model.