Related papers: The Noncommutative Doplicher-Fredenhagen-Roberts-A…
We introduce a new formalism of differential operators for a general associative algebra A. It replaces Grothendieck's notion of differential operator on a commutative algebra in such a way that derivations of the commutative algebra are…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
As a tool to carry out the quantization of gauge theory on a noncommutative space, we present a Dirac operator that behaves as a line element of the canonical noncommutative space. Utilizing this operator, we construct the Dixmier trace,…
We propose a minimal extension of the Newtonian action by introducing a time-dependent fractional kernel characterized by a single deformation parameter $\alpha$. This kernel admits a natural interpretation as a nontrivial temporal…
Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…
Noncommutative field theory on Yang's quantized space-time algebra (YSTA) is studied. It gives a theoretical framework to reformulate the matrix model as quantum mechanics of $D_0$ branes in a Lorentz-covariant form. The so-called kinetic…
In this paper we have studied a new form of Non-Commutative (NC) phase space with an operatorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an "{\it{internal}}" magnetic field, that is…
In this paper, we present a formulation of the classical theory of Fermionic (anticommuting) fields, which fits into the general framework proposed by K.Fredenhagen, M.Duetsch and R.Brunetti. It was inspired by the recent developments in…
The homogeneous Friedman-Lema\^\i tre-Robertson-Walker (FLRW) cosmology of a free scalar field with vanishing cosmological constant was recently shown to be invariant under the one-dimensional conformal group $\textrm{SL}(2,\mathbb{R})$…
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…
In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a…
We develop relativistic wave equations in the framework of the new non-hermitian ${\cal PT}$ quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of ${\cal…
We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra ${\cal A}$ on a transformation groupoid $\Gamma = E \times G$ where $E$ is the total space of a principal fibre bundle over…
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…
Actions for noncommutative (NC) gauge field theories can be expanded perturbatively in powers of the noncommutativity parameter $\theta$ using the Seiberg-Witten map between ordinary classical fields and their NC counterparts. The leading…
We use the Seiberg-Witten map (SW map) to expand noncommutative gravity coupled to fermions in terms of ordinary commuting fields. The action is invariant under general coordinate transformations and local Lorentz rotations, and has the…
We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We a\-chieved the task in the following steps: ($i$) determining the unitary realizations of the…
As a sequel to our previous work\cite{Feng2020}, we propose in this paper a quantization scheme for Dirac field in de Sitter spacetime. Our scheme is covariant under both general transformations and Lorentz transformations. We first present…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
There is increased interest in time-dependent (non-autonomous) Hamiltonians, stemming in part from the active field of Floquet quantum materials. Despite this, dispersive time-decay bounds, which reflect energy transport in such systems,…