Related papers: Metric approach to quantum constraints
Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
We present a novel framework for quantizing constrained quantum systems in which the processes of quantization and constraint enforcement are performed simultaneously. The approach is based on an extension of the stationary action…
The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical…
This paper describes a tentative relativistic quantum mechanics approach inspired by Dirac's point-form, which is based on the physics description on a hyperboloid surface. It is mainly characterized by a non-standard relation of the…
The Dirac equation provides a description of spin 1/2 particles, consistent with both the principles of quantum mechanics and of special relativity. Often its presentation to students is based on mathematical propositions that may hide the…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems dynamics is equivalent to the choice of the corresponding metric…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
We investigate the role of external constraints in quantum field theory using the path integral formalism. We begin by reviewing the quantization of constrained systems and extend the analysis to cases where constraints are added to the…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
The semiclassical solution of quantum Dirac constraints in generic constrained system is obtained by directly calculating in the one-loop approximation the gauge field path integral with relativistic gauge fixing procedure. The gauge…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary…
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…
We compare different treatments of the constraints in canonical quantum gravity. The standard approach on the superspace of 3--geometries treats the constraints as the sole carriers of the dynamic content of the theory, thus rendering the…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…