Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2012.05092 · International Journal of Modern Physics E

New results about the canonical transformation for boson operators

C. M. Raduta, A. A. Raduta

Published Feb 10, 2021• 0 citations
arXivHTMLPDF

Abstract

The Bogoliubov transformation for a monopole boson induces a unitary transformation connecting the Fock spaces of initial and correlated bosons. Here, we provide a very simple method for deriving the analytical expression for the overlap matrix of the basis states generating the two boson spaces.
DOI
10.1142/s0218301321500191

Related papers

The explicit determination of the linear boson transformation coefficients

K. Tanabe

The problem of determining the wavefunction is solved for the boson Bogoliubov transformation. The method of series expansion is applied to derive the general expression for the coefficients which connect the new Fock states of an arbitrary number of quasiparticles with the states before the transformation.

Journal of Mathematical Physics•May 1, 1973•25 citations

Linear boson transformation coefficients

Arvind Narayan Vaidya

A simple expression for the coefficients which connect a Fock state containing an arbitrary number of quasiparticles with its tranformed state under a boson Bogoliubov transformation is obtained.

Journal of Mathematical Physics•Jun 1, 1976•0 citations

Recursive Construction of the Bosonic Bogoliubov Vacuum State

D. Portes, Marcos O Pinho, Hilário Rodrigues

Abstract: In this work we derive a novel procedure for obtaining the bosonic Bogoliubov vacuum states by using a recursive scheme. The vacuum state for the new creation and annihilation operators is explicitly constructed in terms of the number states of the old operators, which are connected by a Bogoliubov transformation. The coefficients of the ground state in Fock basis are thus obtained as exclusive functions of the parameters of the Bogoliubov transformations.

Quantum Physics Letters•Apr 1, 2013•1 citation

Bogoliubov Hamiltonians and one parameter groups of Bogoliubov transformations

Laurent Bruneau, Jan Dereziński

On the bosonic Fock space, a family of Bogoliubov transformations corresponding to a strongly continuous one-parameter group of symplectic maps R(t) is considered. Under suitable assumptions on the generator A of this group, which guarantee that the induced representations of CCR are unitarily equivalent for all time t, it is known that the unitary operator U_{nat}(t) which implement this transformation gives a prjective unitary representation of R(t). Under rather general assumptions on the generator A, we prove that the corresponding Bogoliubov transformations can be implemented by a one-parameter group U(t) of unitary operators. The generator of U(t) will be called a Bogoliubov Hamiltonian. We will introduce two kinds of Bogoliubov Hamiltonians (type I and II) and give conditions so that they are well defined.

arXiv:math-ph/0511069•Nov 22, 2005•0 citations

A simple derivation of a closed formula for Bogoliubov boson transformations

Apolodor Aristotel Raduta, M. Badea, E. Badralexe

Considering the states with an arbitrary number of bosons and their transformed states under Bogoliubov transformations as wavefunctions of an oscillator type, a very simple derivation for the matrix elements of the Bogoliubov transformations is given.

Journal of Mathematical Physics•Apr 1, 1977•7 citations

Group-theoretical method for calculating overlaps of HFB states

Heinz Günter Becker

Overlaps of Hartree- Fock- Bogoljubov states occurring in modified HFB theories (e.g., projected HFB) are calculated using group theoretical methods. For this purpose the BogoliubovValatin transformation is generalized. The resulting nonunitary transformation leaves the Fermi commutation relations invariant, but the characteristic property of the creation and annihilation operators, namely that they are hermitean conjugate to each other, is lost. A suitable factorization of the new transformation is derived, which also applies to the unitary Bogoliubov- Valatin transformation but the structure of which is completely different from the well known Bloch-- Messiah decomposition. Furthermore, the relation between various representations of the HFB state vector is clarified. (GE)

•Jan 1, 1973•0 citations
On the bosonic Fock space, a family of Bogoliubov transformations corresponding to a strongly continuous one-parameter group of symplectic maps R(t) is considered. Under suitable assumptions on the generator A of this group, which guarantee that the induced representations of CCR are unitarily equivalent for all time t, it is known that the unitary operator U_{nat}(t) which implement this transformation gives a prjective unitary representation of R(t). Under rather general assumptions on the generator A, we prove that the corresponding Bogoliubov transformations can be implemented by a one-parameter group U(t) of unitary operators. The generator of U(t) will be called a Bogoliubov Hamiltonian. We will introduce two kinds of Bogoliubov Hamiltonians (type I and II) and give conditions so that they are well defined.
Overlaps of Hartree- Fock- Bogoljubov states occurring in modified HFB theories (e.g., projected HFB) are calculated using group theoretical methods. For this purpose the BogoliubovValatin transformation is generalized. The resulting nonunitary transformation leaves the Fermi commutation relations invariant, but the characteristic property of the creation and annihilation operators, namely that they are hermitean conjugate to each other, is lost. A suitable factorization of the new transformation is derived, which also applies to the unitary Bogoliubov- Valatin transformation but the structure of which is completely different from the well known Bloch-- Messiah decomposition. Furthermore, the relation between various representations of the HFB state vector is clarified. (GE)