46 citations · 164 across the 19 of their papers we have counts for
19 papers
Perturbed Bessel operators
Jan Dereziński, Jérémy Faupin
We study perturbed Bessel operators on , where and is a complex locally integra…
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…
From Heun Class Equations to Painlevé Equations
Jan Dereziński, Artur Ishkhanyan, Adam Latosiński
In the first part of our paper we discuss linear 2nd order differential equations in the complex domain, especially Heun class equations, that is, the Heun equation and its conflue…
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…
On the derivatives of the Heun functions
G. Filipuk, A. Ishkhanyan, J. Dereziński
The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions…
Group-theoretical origin of symmetries of hypergeometric class equations and functions
Jan Dereziński
We show that properties of hypergeometric class equations and functions become transparent if we derive them from appropriate 2nd order differential equations with constant coeffic…
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…
Continuous and holomorphic functions with values in closed operators
Jan Dereziński, Michał Wrochna
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set.…
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.