Related papers: Metric approach to quantum constraints
In this contribution, we propose a new model for studying the confinement of a spin-half particle to a two-dimensional quantum ring in systems described by the Dirac equation by introducing a new minimal coupling into the Dirac equation. We…
The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets…
A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form…
Quantum metrology makes use of coherent superpositions to detect weak signals. While in principle the sensitivity can be improved by increasing the density of sensing particles, in practice this improvement is severely hindered by…
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.…
We introduce the analogue of the metric tensor in case of $q$-deformed differential calculus. We analyse the consequences of the existence of such metric, showing that this enforces severe restrictions on the parameters of the theory. We…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first…
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
We study the Dirac equation minimally coupled to general relativity using quantum field theory and the semiclassical gravity approximation. Previous studies of the Einstein-Dirac system did not quantize the Dirac field and required multiple…
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
The relativistic Wigner function for spin 1/2 particles is the subject of active research due to diverse applications. However, further progress is hindered by the fabulous complexity of the integro-differential equations of motion. We…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
It has been established that endowing classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In this letter we argue that, while sufficient, the above condition is certainly not necessary in passing…
Weighted model counting (WMC) has proven effective at a range of tasks within computer science, physics, and beyond. However, existing approaches for using WMC in quantum physics only target specific problem instances, lacking a general…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
The dynamics of a massive, relativistic spinning particle could be described either by the Dirac equation or by the Kerr solution of Einstein equations. However, one does not know a priori as to which of the two systems of equations should…
In the Dirac approach to the generalized Hamiltonian formalism, dynamical systems with first- and second-class constraints are investigated. The classification and separation of constraints into the first- and second-class ones are…
A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and…