A Class of New Nonlinear Bogoliubov Transformations

2002 ◽  
Vol 19 (11) ◽  
pp. 1625-1627 ◽  
Author(s):  
Yang Xiao-Xue ◽  
Wu Ying
Keyword(s):  
Bogoliubov Transformations

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

scholarly journals Canonical transformations for fermions in superanalysis

2014 ◽  
Vol 26 (06) ◽  
pp. 1450009
Author(s):  
Joachim Kupsch
Keyword(s):  
Infinite Number ◽  
Orthogonal Group ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Continuous Representation ◽  
Canonical Transformations ◽  
Module Extension ◽  
Bogoliubov Transformations

Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a Grassmann module extension of the Fock space. The pull-back of these operators to the Fock space yields a unitary ray representation of the group that implements the Bogoliubov transformations.

ν − ν interactions in supernovae environments as a function of density and temperature

2021 ◽  
Vol 30 (03) ◽  
pp. 2150018
Author(s):  
M. P. Colombi ◽  
O. Civitarese ◽  
A. V. Penacchioni
Keyword(s):  
Density Dependence ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Neutrino Energy ◽  
Phase Approximation ◽  
Temperature Dependent ◽  
Energy Distributions ◽  
Quasi Particle ◽  
Collective Response ◽  
Bogoliubov Transformations

Neutrinos in astrophysical environments, such as Supernovae (SNe), may interact through pair interactions. These interactions are density and temperature-dependent. Under certain conditions, a neutrino-condensate may form. In this work, we have adapted the separable nonlocal pairing interactions to the SN conditions and studied the temperature and density dependence of the pairing gap as well as the collective response with respect to these variables. We have applied the Bogoliubov transformations and solved the Bardeen, Cooper and Schrieffer (BCS) equations to construct the free quasi-particle sector of the Hamiltonian. The residual two-quasi-particle terms have been treated by applying the Tamm–Dancoff approximation (TDA) and random-phase approximation (RPA), suited to the extended neutrino media. With this, we have constructed neutrino energy distributions both in the superfluid and normal regimes and extracted critical values of the density and temperature.

scholarly journals A q -deformation of the Bogoliubov transformations

2018 ◽  
Vol 382 (7) ◽  
pp. 464-466 ◽  
Author(s):  
Ivan Arraut ◽  
Carlos Segovia
Keyword(s):  
Bogoliubov Transformations

scholarly journals Conformal Symmetry and Supersymmetry in Rindler Space

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 144
Author(s):  
Jan-Willem van Holten
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Extended Space ◽  
Rindler Space ◽  
Dimensional Space Time ◽  
Critical Spectrum ◽  
Infinite Strings ◽  
Bogoliubov Transformations

This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional space-time. Generically, in addition to a conformal co-ordinate transformation, the transformation of fields from Minkowski to Rindler space is accompanied by local conformal and Lorentz transformations of the components, which also affect the Bogoliubov transformations between the associated Fock spaces. I construct these transformations for massless scalars and spinors, as well as for the ghost and super-ghost fields necessary in theories with local conformal and supersymmetries, as arising from coupling to two-dimensional (2-D) gravity or supergravity. Cancellation of the anomalies in Minkowski and in Rindler space requires theories with the well-known critical spectrum of particles that arise in string theory in the limit of infinite strings, and it is relevant for the equivalence of Minkowski and Rindler frame theories.

From the particle pair production to the Hawking–Unruh radiation in the maximal acceleration hypothesis

2019 ◽  
Vol 34 (26) ◽  
pp. 1950209
Author(s):  
Antonio Feoli
Keyword(s):  
Black Hole ◽  
Pair Production ◽  
Scalar Fields ◽  
Point Of View ◽  
Unruh Effect ◽  
Particle Pair ◽  
Maximal Acceleration ◽  
Standard Scenario ◽  
Nonstandard Approach ◽  
Bogoliubov Transformations

Starting from a nonstandard approach to the Unruh effect, we present a description of the emission of radiation from a black hole that avoids quantization of scalar fields and Bogoliubov transformations, but assumes the existence of a maximal acceleration. In this framework, the description appears closer to the original heuristic Hawking’s point of view, with respect to the standard scenario.

scholarly journals Bogoliubov Hamiltonians and one-parameter groups of Bogoliubov transformations

2007 ◽  
Vol 48 (2) ◽  
pp. 022101 ◽  
Author(s):  
Laurent Bruneau ◽  
Jan Dereziński
Keyword(s):  
Bogoliubov Transformations

TIME-DEPENDENT BOGOLIUBOV TRANSFORMATIONS AND THE DAMPED HARMONIC OSCILLATOR

1993 ◽  
Vol 08 (21) ◽  
pp. 1999-2009
Author(s):  
P. SHANTA ◽  
S. CHATURVEDI ◽  
V. SRINIVASAN ◽  
F. MANCINI
Keyword(s):  
Harmonic Oscillator ◽  
Master Equation ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Bogoliubov Transformations ◽  
Non Equilibrium

We derive the master equation for a damped harmonic oscillator, for any α, using time-dependent Bogoliubov transformations of non-equilibrium thermofield dynamics. This investigation naturally leads us to a physically and mathematically meaningful parametrization of the Bogoliubov matrix.

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