Related papers: Higher representations for extended operators
Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are important from a physical point of view…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the…
The definition of Q-conditional symmetry for one PDE is correctly generalized to a special case of systems of PDEs and involutive families of operators. The notion of equivalence of Q-conditional symmetries under a group of local…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…
World spinors are objects that transform w.r.t. double covering group $\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic mathematical results and the corresponding physical interpretation concerning these,…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
In this paper we study invertible extensions of a symmetric operator in a Hilbert space $H$. All such extensions are characterized by a parameter in the generalized Neumann's formulas. Generalized resolvents, which are generated by the…
Reducible representations of CAR and CCR are applied to second quantization of Dirac and Maxwell fields. The resulting field operators are indeed operators and not operator-valued distributions. Examples show that the formalism may lead to…
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible…
Let $\mathbb F$ be a finite field. Consider a direct sum $V$ of an infinite number of copies of $\mathbb F$, consider the dual space $V^\diamond$, i.~e., the direct product of an infinite number of copies of $\mathbb F$. Consider the direct…
To simulate a quantum system with continuous degrees of freedom on a quantum computer based on quantum digits, it is necessary to reduce continuous observables (primarily coordinates and momenta) to discrete observables. We consider this…
Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data…
We construct representations of the quantum algebras ~$U_{q{\bf q}}(gl(n))$ and ~$U_{q{\bf q}}(sl(n))$~ which are in duality with the multiparameter quantum groups ~$GL_{q{\bf q}}(n)$, ~$SL_{q{\bf q}}(n)$,~ respectively. These objects…
We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…
The representation theory of the generalized deformed oscillator algebras (GDOA's) is developed. GDOA's are generated by the four operators ${1,a,a^{\dag},N}$. Their commutators and Hermiticity properties are those of the boson oscillator…
We consider the consequences of global higher-spin symmetries in quantum field theories on a fixed de Sitter background of spacetime dimension $D \ge 3$. These symmetries enhance the symmetry group associated with the isometries of the de…