Related papers: Pauli-Jordan Function and Scalar Field Quantizatio…
Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position…
In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of…
We propose a new Doubly Special Relativity theory based on the generalization of the $\kappa$-deformation of the Poincar\'e algebra acting along one of the null directions. We recall the quantum Hopf structure of such deformed Poincar\'e…
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation…
In this paper, we investigate the quantum field theory in Klein space that has two time directions. To study the canonical quantization, we select the ``length of time" $q$ as the evolution direction of the system. In our novel…
In this paper we will analyse a scalar field theory on a spacetime with noncommutative and non-anticommutative coordinates. This will be done using supermanifold formalism. We will also analyse its quantization in path integral formalism.
We construct a scalar field theory on the Snyder non-commutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincar\'e algebra is undeformed. The Lorentz sector is…
A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this algebra are hermitean and can be identified…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ \Gamma_{D}^{d}=(\mathbb{S}^{1})^{d}\times \mathbb{M}^{D-d}$. The modular operator is…
Derivation of $\kappa$-Poincare bicovariant commutation relations between coordinates and 1-forms on $\kappa$-Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U(1) gauge theory and appearance of an…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection…
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach…
We develop a noncommutative invariant theory for ordinary linear differential operators on Riemann surfaces. For a monic binomially normalized operator $L=\sum_{k=0}^n {n\choose k}a_kD^{\,n-k}$, $a_0=1$, with coefficients in an associative…
We study the cosmology of an extended version of Horndeski theories with second-order equations of motion on the flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background. In addition to a dark energy field $\chi$ associated with the…
A four-dimensional photon polarization space, such that gives a different interpretation of the ladder operators for the time-like degree comparing to the Gupta-Bleuler formulation is presented. This interpretation, coming from the…
The space of time-like geodesics on Minkowski spacetime is constructed as a coset space of the Poincar\'e group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson…
The quantized free Dirac field is considered on Minkowski spacetime (of general dimension). The Dirac field is coupled to an external scalar potential whose support is finite in time and which acts by a Moyal-deformed multiplication with…
Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This…