Related papers: Implementing Bogoliubov Transformations Beyond the…
We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to…
Open quantum systems that interact with a Markovian environment can be described by a Lindblad master equation. The generator of time-translation is given by a Liouvillian superoperator $\mathcal{L}$ acting on the density matrix of the…
We present an exhaustive BRST lagrangian description of partially massless bosonic fields in four-dimensional space. The basic fields are formulated in terms of two-component spin-tensors in (A)dS space where the tracelessness conditions…
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…
Hamiltonian quantum simulation of bosons on digital quantum computers requires truncating the Hilbert space to finite dimensions. The method of truncation and the choice of basis states can significantly impact the complexity of the quantum…
Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational…
The paper presents the bosonic and fermionic supersymmetric extensions of the structural equations describing conformally parametrized surfaces immersed in a Grasmann superspace, based on the authors' earlier results. A detailed analysis of…
We consider extensions of Anosov diffeomorphisms of an infranilmanifold by the real vector space R^{\omega}. Our main result, based on the analogous theorem in finite dimensions proven by Nitica and Pollicott, is that any Holder cocycle…
We introduce a functional realization of the Hamiltonian structure on the moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup in SL_n. We also introduce a construction of the corresponding quantum algebras.
An approach for $q$-deformed Bogoliubov transformations is presented. Assuming a left-right module action together with an *-operation and deformed commutation relations, we construct a q-deformation of the nonlinear Bogoliubov…
We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…
The extended Falicov-Kimball model, with both an on-site hybridization potential and dispersive narrow band, is examined within the saddle-point approximation to the Kotliar-Ruckenstein slave boson theory. We first set the hybridization…
We suggest necessary conditions of soficness of multidimensional shifts formulated in termsof resource-bounded Kolmogorov complexity. Using this technique we provide examples ofeffective and non-sofic shifts on $\mathbb{Z}^2$ with very low…
We consider the quantum dynamics of a massless scalar field in de Sitter space-time. The classical evolution is represented by a canonical transformation on the phase space for the field theory. By studying the corresponding Bogoliubov…
As an aid to understanding the {\it displacement operator} definition of squeezed states for arbitrary systems, we investigate the properties of systems where there is a Holstein-Primakoff or Bogoliubov transformation. In these cases the…
In many Lagrangian field theories one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different…
One of the methods used to extend two-dimensional bosonization to four space-time dimensions involves a transformation to new spatial variables so that only one of them appears kinematically. The problem is then reduced to an Abelian…
We address the issue of inequivalent Fock representations in Quantum Field Theory in a curved homogenous and anisotropic background, namely Kantowski-Sachs spacetime. A family of unitarily equivalent Fock representations that are invariant…
A class of gravity theories respecting spatial covariance and in the presence of non-dynamical auxiliary scalar fields with only spatial derivatives is investigated. Generally, without higher temporal derivatives in the metric sector, there…
The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically…