Related papers: Dirac operator on the quantum fuzzy four-sphere $ …
We show that an infinite set of q-deformed relevant operators close a partial q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The dynamics is described by the multicommutator: [H,..., [H, O]...], that follows a power…
The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincare or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita…
Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy analog($S^2_F$) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is…
We study the decomposition into irreducibles of the kernel of noncubic Dirac operators attached to finite-dimensional modules. We compare this decomposition with features of Kostant's cubic Dirac operator. In particular, we show that the…
We discuss a discrete analogue of the Dirac-K\"{a}hler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of…
We develop a general approach to the calculation of target mass and finite t=(p'-p)^2 corrections in hard processes which can be studied in the framework of the operator product expansion and involve momentum transfer from the initial to…
We study quantum analogs of the Dirac type operator $-2\bar{z}\frac{\partial}{\partial\bar{z}}$ on the punctured disk, subject to the Atiyah-Patodi-Singer boundary conditions. We construct a parametrix of the quantum operator and show that…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
We demonstrate how chiral oscillations of a massive Dirac field can be described within quantum field theory using a finite-time interaction picture approach, where the mass term in the Lagrangian is treated as a perturbative coupling…
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
Quadratic operators are used in transforming the model Hamiltonian (H) of one correlated and dispersive band in an unique positive semidefinite form coopting both the kinetic and interacting part of H. The expression is used in deducing…
We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition,…
We consider the $3-D$ Dirac operator $\mathfrak{D}_{\boldsymbol{A},\Phi ,Q_{\sin }}$ with variable regular magnetic and electrostatic potentials $ \boldsymbol{A}$,$\Phi $ and with singular potentials $Q_{\sin }$ with support on a smooth…
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…
We present a universal Dirac operator for noncommutative spin and spin^c bundles over fuzzy complex projective spaces. We give an explicit construction of these bundles, which are described in terms of finite dimensional matrices, calculate…
We study the basic quantum mechanics for a fully general set of Dirac matrices in a curved spacetime by extending Pauli's method. We further extend this study to three versions of the Dirac equation: the standard (Dirac-Fock-Weyl or DFW)…
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…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
The fixed point Dirac operator on the lattice has exact chiral zero modes on topologically non-trivial gauge field configurations independently whether these configurations are smooth, or coarse. The relation $n_L-n_R = Q^{FP}$, where $n_L$…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…