Related papers: Nonperturbative quantization approach for QED on t…
Dirac's approach to the canonical quantization of constrained systems is applied to $N = 1$ supergravity, with or without gauged supermatter. Two alternative types of boundary condition applicable to quantum field theory or quantum gravity…
We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form $x_\mu x^\mu = \tau^2$. This choice of quantization surface implies that all components of the 4-momentum…
Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock…
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
The irreducible *-representations of the polynomial algebra O(S^3_{pq}) of the quantum 3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C*-algebra are shown to coincide with their classical…
We investigate the semiclassical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the $\alpha$ matrices to the spin-$S$ matrices and doing a certain scaling, we…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…
The space of continuous states of perturbative interacting quantum field theories in globally hyperbolic curved spacetimes is determined. Following Brunetti and Fredenhagen, we first define an abstract algebra of observables which contains…
Starting from the relativistic gauge-invariant quark-antiquark Green function we obtain the relevant interaction in the one-body limit, which can be interpreted as the kernel of a non-perturbative Dirac equation. We study this kernel in…
We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
Superconducting circuits are an extremely versatile platform to realize quantum information hardware and to emulate topological materials. We here show how a simple arrangement of capacitors and conventional…
Noncommutative geometry of quantised contact spheres introduced by Omori, Maeda, Miyazaki and Yoshioka is studied. In particular it is proven that these spheres form a noncommutative Hopf fibration in the sense of Hopf-Galois extensions.…
We study Maxwell's equation as a theory for smooth $k$-forms on globally hyperbolic spacetimes with timelike boundary as defined by Ak\'e, Flores and Sanchez. In particular we start by investigating on these backgrounds the D'Alembert - de…
We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative…
The Weyl-Wigner-Moyal formalism for Dirac second class constrained systems has been proposed recently as the deformation quantization of Dirac bracket. In this paper, after a brief review of this formalism, it is applied to the case of the…
This paper develops a weighted $L^2$-method for the (half) Dirac equation. For Dirac bundles over closed Riemann surfaces, we give a sufficient condition for the solvability of the (half) Dirac equation in terms of a curvature integral.…
The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged…
For a linear Dirac field on a globally hyperbolic static space-time the analytic continuation of its Wightman functions (Green functions) to Schwinger functions and back at zero and finite temperature is shown.