46 citations · 164 across the 19 of their papers we have counts for
14 papers · 1 filter
Holomorphic family of Dirac-Coulomb Hamiltonians in arbitrary dimension
Jan Dereziński, Błażej Ruba
We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_{ω,λ}:=\begin{bmatrix}-\frac{λ+ω}{x}&-\partial_x \\ \partial_x & -\fr…
On the domains of Bessel operators
Jan Dereziński, Vladimir Georgescu
We consider the Schrödinger operator on the halfline with the potential , often called the Bessel operator. We assume that is complex. We study the do…
Momentum approach to the potential as a toy model of the Wilsonian renormalization
Jan Dereziński, Oskar Grocholski
The Bessel operator, that is, the Schrödinger operator on the half-line with a potential proportional to , is analyzed in the momentum representation. Many features of this…
An Evolution Equation Approach to Linear Quantum Field Theory
Jan Dereziński, Daniel Siemssen
In the first part of our paper we analyze bisolutions and inverses of (non-autonomous) evolution equations. We are mostly interested in pseudo-unitary evolutions on Krein spaces, w…
An Evolution Equation Approach to the Klein-Gordon Operator on Curved Spacetime
Jan Dereziński, Daniel Siemssen
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows u…
Equations of hypergeometric type in the degenerate case
Jan Dereziński, Maciej Karczmarczyk
We consider the three most important equations of hypergeometric type, , and , in the so-called degenerate case. In this case one of the parameters, usu…
Quantization of Gaussians
Jan Dereziński, Maciej Karczmarczyk
Our paper is devoted to the oscillator semigroup, which can be defined as the set of operators whose kernels are centered Gaussian. Equivalently, they can be defined as the the Wey…
On the Weyl symbol of the resolvent of the harmonic oscillator
Jan Dereziński, Maciej Karczmarczyk
We compute the Weyl symbol of the resolvent of the harmonic oscillator and study its properties.
Feynman Propagators on Static Spacetimes
Jan Dereziński, Daniel Siemssen
We consider the Klein-Gordon equation on a static spacetime and minimally coupled to a static electromagnetic potential. We show that it is essentially self-adjoint on $C_{\mathrm{…
Bosonic quadratic Hamiltonians
Jan Dereziński
We discuss self-adjoint operators given formally by expressions quadratic in bosonic creation and annihilation operators. We give conditions when they can be defined as self-adjoin…
From Conformal Group to Symmetries of Hypergeometric Type Equations
Jan Dereziński, Przemysław Majewski
We show that properties of hypergeometric type equations become transparent if they are derived from appropriate 2nd order partial differential equations with constant coefficients…
Quantum fields with classical interactions
Jan Dereziński
We describe basic types of free fields (1) neutral scalar bosons; (2) massive vector bosons; (3) massless vector bosons; (4) charged scalar bosons; (5) Dirac fermions; (6) Majorana…
On the minimization of Hamiltonians over pure Gaussian states
Jan Dereziński, Marcin Napiórkowski, Jan Philip Solovej
A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian…
Quantum massless field in 1+1 dimensions
Jan Derezi{ń}ski, Krzysztof A. Meissner
We present a construction of the algebra of operators and the Hilbert space for a quantum massless field in 1+1 dimensions.