Related papers: Bogoliubov transformation for distinguishable part…

The behavior of the momentum transferred to a trapped Bose-Einstein condensate by a two-photon Bragg pulse reflects the structure of the underlying Bogoliubov spectrum. In elongated condensates, axial phonons with different number of radial…

We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or…

Time-dependent terms in Hamiltonians and equations of motion are rather important for a quantum-mechanical description of particles with arbitrary spins in nonstationary fields. We use the Foldy-Wouthuysen representation which allows one to…

We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit…

We present a new construction for Poisson transforms between vector bundle valued differential forms on homogeneous parabolic geometries and the corresponding Riemannian symmetric space, which can be described in terms of finite dimensional…

Modern relativistic theory of the second quantization of fermion and boson fields is based on the use of the mathematical apparatus of C*-algebras and Lie superalgebras. In this case, for fermions, the Lorentz transformations are considered…

Quantization of free Dirac fields is formulated in terms of a reducible representation of CAR. Similarly to the bosonic case we arrive at field operators which are indeed operators and not operator valued distributions. Observables such as…

To describe charged particles interacting with the quantized electromagnetic field, we point out the differences of working in the so-called generalized and the true Coulomb gauges. We find an explicit gauge transformation between them for…

A single real scalar field of spin zero obeying the Klein-Gordon equation in flat space-time under external conditions is considered in the context of the spin-statistics connection. An imposed accelerated boundary on the field is made to…

We show that the amount of particle production in an arbitrary cosmological background can be determined using only the late-time positive-frequency modes. We don't refer to modes at early times, so there is no need for a Bogolubov…

We consider differential operators on a supermanifold of dimension $1|1$. We define non-degenerate operators as those with an invertible top coefficient in the expansion in the "superderivative" $D$ (which is the square root of the shift…

We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on Fock space. Both the…

In this paper the explicit form of the operator of transformation of the vacuum states for the general two-mode Bogolubov transformation is found

There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of…

This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these…

All gauge bosons of a non-abelian gauge theory do not transform the same way under the discrete transformations of time-reversal and charge-conjugation. Moreover, the transformations rules depend on how the generators are chosen. We show…

This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first…

This paper introduces a generalization of the so-called space-fractional Poisson process by extending the difference operator acting on state space present in the associated difference-differential equations to a much more general form. It…

The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this.…

We analyze the consequences caused by a deformed dispersion relation, suggested in several quantum gravity models, upon a bosonic gas. Concerning the ground state of the Bogoliubov space of this system, we deduce the corrections in the…