Related papers: Dirac versus reduced phase space quantization
A quantum Dirac field theory with no divergences of vacuum energy is presented. The vacuum energy divergence is eliminated by removing a extra degree of freedom of the Dirac fields. The conditions for removing the extra degree of freedom,…
The main goal of this work is to study the Dirac oscillator as a quantum field using the canonical formalism of quantum field theory and to develop the canonical quantization procedure for this system in $(1+1)$ and $(3+1)$ dimensions. This…
The necessary and sufficient conditions are established for the second-class constraint surface to be (an almost) K\"ahler manifold. The deformation quantisation for such systems is scetched resulting in the Wick-type symbols for the…
Quantization of free Dirac fields is formulated in terms of a reducible representation of CAR. Similarly to the bosonic case we arrive at field operators which are indeed operators and not operator valued distributions. Observables such as…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
There are several mathematical and physical reasons why Dirac's quantization must hold. How far one can go without it remains an open problem. The present work outlines a few steps in this direction.
It is shown that the Lagrangian reduction, in which solutions of equations of motion that do not involve time derivatives are used to eliminate variables, leads to results quite different from the standard Dirac treatment of the first order…
We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
Geometrical interpretation on U(1) gage theory of Dirac monopole, introduced here from the line integral\cite{Brandt} form of vector potentials, shows the gauge representation be multi-valued. In this paper, we construct Euclidean form of…
When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…
The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
The Jackiw-Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac…
In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
Last years a certain attention was attracted to the statement that Hamiltonian formulations of General Relativity, in which different parametrizations of gravitational variables were used, may not be related by a canonical transformation.…
It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and $R^2$-Gravity are {\em embedded} in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above…