Related papers: Representations for creation and annihilation oper…
Using the formalism of Maya diagrams and ladder operators, we describe the algebra of annihilating operators for the class of rational extensions of the harmonic oscillators. This allows us to construct the corresponding coherent state in…
The paper concerns algebras of almost periodic pseudodifferential operators on $\mathbb R^d$ with symbols in H\"ormander classes. We study three representations of such algebras, one of which was introduced by Coburn, Moyer and Singer and…
We define co-Toeplitz operators, a new class of Hilbert space operators, in order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz quantization scheme introduced by the author in the setting of symbols that come from…
Exploiting the SU(2) Skyrmion Lagrangian with second-class constraints associated with Lagrange multiplier and collective coordinates, we convert the second-class system into the first-class one in the Batalin-Fradkin-Tyutin embedding…
Using the results obtained by Staruszkiewicz in Acta Phys. Pol. B 23, 591 (1992) and in Acta Phys. Pol. B 23, 927 (1992) we show that the representations acting in the eigenspaces of the total charge operator corresponding to the…
In this article we unveil a new structure in the space of operators of the XXZ chain. We consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the…
We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…
It is shown how to introduce a geometric description of the algebraic approach to the non-relativistic quantum mechanics. It turns out that the GNS representation provides not only symplectic but also Hermitian realization of a `quantum…
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
The Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…
Both algebras, Clifford and Grassmann, offer "basis vectors" for describing the internal degrees of freedom of fermions. The oddness of the "basis vectors", transferred to the creation operators, which are tensor products of the finite…
We give a complete description of the representation of $SL(2,\mathbb{C})$ acting in the Hilbert space of the quantum Coulomb field and a constructive consistency proof of the axioms of the quantum theory of the Coulomb field.
A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
We initiate a mathematically rigorous study of Klein-Gordon position operators in single-particle relativistic quantum mechanics. Although not self-adjoint, these operators have real spectrum and enjoy a limited form of spectral…
We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…
We obtain some $L^2$ results for the Cauchy-Riemann operator on forms that vanish to high order near the singular set of a complex space.
The commutation relations for bosons are field independent, and can be reliably inferred from the definition of creation and annihilation operators. Here, the commutation relations are assumed known, and the quantum electrodynamics…