Related papers: Quantization of the Relativistic Particle
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
We address a conceptual issue of reconciling the traditional canonical quantization framework of quantum theory with the spatially restricted quantum dynamics and the related spectral problems for confined and global observables of the…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation $[q,p]={\rm i}\hbar$. We present some new results concerning relativistic…
For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for…
It is often said that in relativistic quantum physics, a fundamental particle ontology is not viable. However, previous works have shown that certain relativistic quantum field theories can be reformulated as path integrals over particle…
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of the contemporary theory. The result is a fully…
The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees…
We present a formulation of quantum circuits where the focus is set on whether a given circuit (made of unitary operators and projective measurements with definite outcomes) does reflect an actually realizable physical experiment. In order…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…