Related papers: Solution of quantum Dirac constraints via path int…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
Systems with constraints pose problems when they are quantized. Moreover, the Dirac procedure of quantization prior to reduction is preferred. The projection operator method of quantization, which can be most conveniently described by…
Exact procedures that follow Dirac's constraint quantization of gauge theories are usually technically involved and often difficult to implement in practice. We overview an "effective" scheme for obtaining the leading order semiclassical…
The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation and discuss gauge freedom and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it…
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…
The space of the solutions of Dirac's quantum constraints cannot be constructed factoring the quantum state space by the ``simple'' gauge transformations generated by the constraints. However, we show here that it can be constructed by…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give…
Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…
A pure Dirac's canonical analysis, defined in the full phase space for the Husain-Kuchar model is discussed in detail. This approach allows us to determine the extended action, the extended Hamiltonian, the complete constraint algebra and…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
We study the problem of gauge-invariance and gauge-dependence in one-loop quantum cosmology. We formulate some requirements which should be satisfied by boundary conditions in order to give gauge-independent path integral. The case of QED…
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…
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
Quantum cellular automata have been recently considered as a fundamental approach to quantum field theory, resorting to a precise automaton, linear in the field, for the Dirac equation in one dimension. In such linear case a quantum…
The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In…
We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological…