Collective Description of a System of Interacting Bose Particles. II

1998

Int. J. Mod. Phys. A

The collective field formalism by Jevicki and Sakita is a useful approach to the problem of treating general planar diagrams involved in an SU(N ) symmetric quantum system. To approach this problem, standing on the Tomonaga spirit we also previously developed a collective description of an SU(N ) symmetric Hamiltonian. However, this description has the following difficulties: (i) Collective momenta associated with the time derivatives of collective variables are not exact canonically conjugate to the collective variables; (ii) The collective momenta are not independent of each other. We propose exact canonically conjugate momenta to the collective variables with the aid of the integral equation method developed by Sunakawa et al. A set of exact canonical variables which are derived by the first quantized language is regarded as a natural extension of the Sunakawa et al.'s to the case for the SU(N ) symmetric quantum system. A collective Hamiltonian is represented in terms of the exact canonical variables up to the order of 1 N . * This work extends the approximation given by the previous talk which has been presented in 5535 Int. J. Mod. Phys. A 1998.13:5535-5556. Downloaded from www.worldscientific.com by UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN on 03/11/15. For personal use only.

“…5 As is shown from the above, the right-hand side of the second line does not take the value −i δ kk and the third one does not vanish. Detailed calculations for them are given in App.…”

Section: Collective Variables and The Associated Relationsmentioning

confidence: 87%

“…5,11 Consider the case that the collective variables φ k introduced by Eq. (2.7) are constructed from the Abelian commuting generators.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

EXACT CANONICALLY CONJUGATE MOMENTA APPROACH TO AN SU(N) QUANTUM SYSTEM

1998

Int. J. Mod. Phys. A

“…In this context, a new field of exploration of elementary excitations of a one-dimensional Fermi system, which is intended to be presented elsewhere, may be opened. Finally, we emphasize the possibility of extending the present exact canonical momenta approach to the three-dimensional case which would lead to the isospin T = 0 quantum hydrodynamics, by introducing the velocity operator v k instead of canonical conjugate momentum Π k as has been done by Sunakawa [33,34]. …”

Section: Calculation Of the Constant Termmentioning

confidence: 99%

Exact canonically conjugate momenta approach to a one-dimensional neutron–proton system, I

Providência

2015

Int. J. Mod. Phys. E

Introducing collective variables, a collective description of nuclear surface oscillations has been developed with the first quantized language, contrary to the second quantized one in Sunakawa's approach for a Bose system. It overcomes difficulties remaining in the traditional theories of nuclear collective motions: Collective momenta are not exact canonically conjugate to collective coordinates and are not independent. On the contrary to such a description, Tomonaga first gave the basic idea to approach elementary excitations in a one-dimensional Fermi system. The Sunakawa's approach for a Fermi system is also expected to work well for such a problem. In this paper, on the isospin space, we define a density operator and further following Tomonaga, introduce a collective momentum. We propose an exact canonically momenta approach to a one-dimensional neutron-proton (N-P) system under the use of the Grassmann variables.

“…proposed an exact canonically conjugate momenta approach to a SU(N) quantum system and derived a collective Hamiltonian in terms of the exact canonical variables up to the order of 1 N . Applying the Tomonaga's basic idea in his collective motion theory [8,9], to nuclei with the aid of the Sunakawa's integral equation method [10], one of the present authors (S.N.) developed a collective description of surface oscillations of nuclei [11].…”

Section: Introductionmentioning

confidence: 99%

Exact canonically conjugate momenta to quadrupole-type collective coordinates and derivation of nuclear quadrupole-type collective Hamiltonian

Providência

2014

Nuclear Physics A

Exact canonically conjugate momenta Π 2µ in quadrupole nuclear collective motions are proposed. The basic idea lies in the introduction of a discrete integral equation for the strict definition of canonically conjugate momenta to collective variables φ 2µ . A part of our collective Hamiltonian, the Π 2µ -dependence of the kinetic part of the Hamiltonian, is given exactly. Further, φ 2µ -dependence of the kinetic part of the Hamiltonian is also given.