Related papers: Wick calculus for noncommutative white noise corre…
We study the representation theory and enveloping $C^*$-algebras for Wick analogues of CAR and twisted CAR algebras. The realization of the $C^*$-algebras under consideration as algebras of continuous matrix-functions satisfying certain…
We prove that the Moyal product is covariant under linear affine spacetime transformations. From the covariance law, by introducing an $(x,\Theta)$-space where the spacetime coordinates and the noncommutativity matrix components are on the…
We discuss the notion of spectral synthesis for the setting of Quantum Harmonic Analysis. Using these concepts, we study subalgebras of the full Toeplitz algebra with certain invariant symbols and their commutators. In particular, we find a…
In this paper we present explicit formulas for the *-product on quantum spaces which are of particular importance in physics, i.e., the q-deformed Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions, respectively. Our…
This paper is a sequel to our previous work, where we proved the ``modularity theorem'' for algebraic Witt vectors over imaginary quadratic fields. This theorem states that, in the case of imaginary quadratic fields $K$, the algebraic Witt…
We define a canonical basis of the $q$-deformed Fock space representation of the affine Lie algebra $\glchap_n$. We conjecture that the entries of the transition matrix between this basis and the natural basis of the Fock space are…
We study the noncommutative scalar field theory in the presence of the Wick-Voros product (or normally ordered product), a variant of the more studied Moyal product. We discuss both the classical and the quantum field theory in the quartic…
Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida's white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the…
We consider the general framework of perturbative quantum field theory for the pure Yang-Mills model. We give a more precise version of the Wick theorem using Hopf algebra notations for chronological products and not for Feynman graphs.…
In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the…
We show that for all q in the interval (-1,1), the Fock representation of the q-commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In particular, this implies that the C*-algebra…
We investigate commutative analogues of Clifford algebras -- algebras whose generators square to $\pm1$ but commute, instead of anti-commuting as they do in Clifford algebras. We observe that commutativity allows for elegant results. We…
We consider non-commutative deformations of sheaves on algebraic varieties. We develop some tools to determine parameter algebras of versal non-commutative deformations for partial simple collections and the structure sheaves of smooth…
We construct $q$-deformations of quantum $\mathcal{W}_N$ algebras with elliptic structure functions. Their spin $k+1$ generators are built from $2k$ products of the Lax matrix generators of ${\mathcal{A}_{q,p}(\widehat{gl}(N)_c)}$). The…
We propose a type of non-anticommutative superspace, with the interesting property of relating to Lee-Wick type of higher derivatives theories, which are known for their interesting properties, and have lead to proposals of…
In this paper we present the groundwork for an It\^o/Malliavin stochastic calculus and Hida's white noise analysis in the context of a supersymmentry with Z3-graded algebras. To this end we establish a ternary Fock space and the…
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to…
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…
We develop a formalism to realize algebras defined by relations on function spaces. For this porpose we construct the Weyl-ordered star-product and present a method how to calculate star-products with the help of commuting vector fields.…
The gauge connections corresponding to electromagnetism, Yang-Mills theory and Einstein gravity can be derived by assuming specific commutation relations between the phase-space variables of a first quantized theory. Extending the procedure…