arXiv subjects

Kimikazu Taniguchi

Publications and source records attributed to Kimikazu Taniguchi.

5 recordsLinked to original sources

arXiv2026

Proper derivation of subspace mapping from whole space mapping in boson expansion theory

The norm operator method, which was recently proposed as a new formulation of the boson expansion theory (BET), is used to show that the subspace mapping is properly derived from the whole space mapping. This derivation requires the appropriate renormalization of the contribution of phonons that are not adopted as boson excitations in the subspace mapping. This was impossible with conventional BETs (which ignore these contributions), and is only made possible for the first time by the norm operator method, which treats these contributions appropriately. We also correct the confusion in the claims of conventional BETs. Namely, contrary to conventional claims, we show that when the phonon excitations not adopted as boson excitations make no contribution at all, the subspace mapping is obtained simply by discarding those excitations. Furthermore, we demonstrate that the Park operator, which had been considered effective only in the whole space mapping, is also effective in the subspace mapping. These findings provide a clear criterion for verifying the applicability of the boson expansion theory to large-amplitude collective motions and offer a new perspective on a microscopic foundation of the interacting boson model (IBM).

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arXiv2025

On the mapping after and before truncation in the boson expansion theory

Using the norm operator method, which extends and corrects the conventional boson expansion theories, we investigate two boson mappings of the boson expansion theory, the so-called mapping after truncation and the mapping before truncation. The difference between them stems from the treatment of the phonon excitation modes; those not adopted as boson excitation modes in the former mapping are first all adopted as boson excitation modes and then truncated later in the latter mapping. If and only if the commutation relations among the phonon operators are closed among the excitation modes adopted as the boson excitation modes in the mapping after truncation, the mapping after and the mapping before truncation coincide, not depending on the types, Hermitian and non-Hermitian. We also investigate the Park operator, which judges whether a boson state vector is physical, and reveal that the conventional claim, which claims that it is applicable only when the mapping is that of the whole fermion space, is incorrect.

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arXiv2023

A new boson expansion theory utilizing a norm operator

We propose a new boson expansion method using a norm operator. The small parameter expansion, in which the boson approximation becomes the zeroth-order approximation, requires the double commutation relations between phonon operators that are not closed between the phonon excitation modes adopted as boson excitations. This results in an infinite expansion regardless of whether the type of the boson expansion is Hermitian or non-Hermitian. The small parameter expansion does not hold when the commutation relations are closed. The norm operator is expressed as a function of the number operator in the physical subspace, which enables us to obtain substantially a finite boson expansion regardless of the Hermitian or non-Hermitian type. We also point out the problems of the conventional boson expansion methods. The normal-ordered linked-cluster expansion theory has failed to refute Marshalek's claim that KT-1 and KT-2 are of chimerical boson expansion. The Dyson boson expansion theory does not have exceptional superiority over other types. Previous studies using the boson expansion methods should be re-examined.

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arXiv2022

Norm operator method for boson expansions

We propose a new boson expansion theory that does not premise the closed-algebra approximation, indispensable for formulation until now, as an extension of the conventional practical boson expansion methods that have tried to elucidate nuclear collective motion, which is a method that allows the closed-algebra approximation not to be used or to be used appropriately, enables us to obtain the boson expansion easier, and reproduces the fermion subspace onto the boson subspace more faithfully than the conventional practical methods. The two-phonon norm matrix composed of all the phonon excitation modes is investigated in detail, which reveals the mechanism, essential for the boson expansion methods, of how we should construct the fermion subspace to be mapped from the whole fermion space. The conventional practical boson expansion methods have applied the closed-algebra approximation improperly to strengthen the effect of the Pauli principle inappropriately, which should be replaced by those that do not use that approximation or use it properly.

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arXiv1998

On the Approximation in the Hermitian Treatment of Dyson Boson Expansion Theory

We discuss about the Hermitian treatment of Dyson-type boson expansion theory. We show that the basic assumption of the conventional treatment does not hold in general and the method is only approximately valid. We also show that the approximation is the same order as that of truncation of the expansion usually done in the Hermitian type boson expansion theory.

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