Sigenobu Sunakawa

Collective Description of a System of Interacting Bose Particles. I

BS>The collective behavior of the three-dimensional Bose system is investigated. The momentum density operator is modified: the modified momentum density operator is equivalent to the velocity operator of the quantum hydrodynamics. The Hamiltonian is described in terms of collective variables for irrotational motion. Results are compared with other theories. (auth)

The Formal Theory of Scattering

The time·dcpendent theory of scattering is reformulated. In § 1, it is developed on the basis of a Bew limiting process which is self.consistent, and the equivalence is shown of Heisenbergs S·matrix and Dysons one, when the total Hamiltonian permits the existence of bound states. In § 2, a theory of scattering of wave packet is proposed in conformity with the physical picture. The damping factor e-•111 is derived from the amplitude of the wave packet. In § 3, the rearrangement scatterini is treated on the basis of the wave packet formalism.

On the Velocity Operator in Many-Boson System

Garrison, Morrison and W ong,l> however, have recently shown that the commutation relation (1) is inconsistent with the nonnegative character of the density operator, and asserted that existence of the velocity operator which satisfies the relation (1) is not admissible. The point of their arguments is essentially equivalent to the wellknown theorem that canonical variables satisfying a canonical commutation relation have as eigenvalues all real numbers from + oo to oo (e.g. see reference 2)). Their assertion is quite correct if one introduces the velocity operator as a canonical conjugate of the density operator itself defined by p(x)=cf;*(x)c{;(x) or by p(x)=(1/N) X2]aJ(x-ra).3l It is however a hasty conclusion to assert non-existence of the velocity operator which satisfies the commutation relation (1). The interacting Bose system enclosed in a cubic box of volume Q is represented by the Hamiltonian h2 H= 2m itk2ak*ak

Quantum Electrodynamics with the Indefinite Metric : Non-Lorentz-Invariance of the Gupta Formalism

BS>Guptas quantum electrodynamics was investigated in several kinds of representation, and it was shown that the Gupta metric operator for the free field can be used even in the case of interacting fields. It was also shown that the Gupta theory is not invariant under the Lorentz transformation. (auth)

Theory of Scattering in Three-Particle System and Its Application to Electron-Exciton Scattering

The formulae in the theory of scattering in the three-particle system developed in a previous paper are transformed into those in the new coordinate systems which are appropriate to the practical application of the theory. On the basis of the general theory, the cross section of electron-exciton scattering which has recently been measured by Otsuka and his coworkers is evaluated in the low-energy limit of incident electron. It has been found that the theoretical result is consistent with their experimental ones.

On the Phonon-Phonon Interaction in a System of Bose Particles

The definite expression of the phonon-phonon interaction in a Bose

Energy Spectrum of the Excitations in Liquid Helium II

ystem is derived up to the order of N-1 in terms of the density operator and its exact canonical conjugate which was introduced in the previous papers. We find some mathematical ambiguity in the course of calculation, and clarify the reason why the different results were obtained so far. The validity of our formalism is discussed from the physical point of view.