Related papers: Proper time derivatives in quantum mechanics
With many Hamiltonians one can naturally associate a |Psi|^2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field…
The paper is devoted to the description a measurable time-interval (``proper time'') in the Hamiltonian version of general relativity with the Dirac-ADM metric. To separate the dynamical parameter of evolution from the space metric we use…
The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
We consider the Hamiltonian and Lagrangian formalism describing free \k-relativistic particles with their four-momenta constrained to the \k-deformed mass shell. We study the modifications of the formalism which follow from the introduction…
Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
We develop a new concept of quantum mechanics which is based on a generalized space-time and on an action vector space similar to it. Both spaces are provided by algebraic properties. This allows to calculate the Dirac matrixes and to…
Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked…
We consider the quantum mechanics of a charged particle in the presence of Dirac's magnetic monopole. Wave functions are sections of a complex line bundle and the magnetic potential is a connection on the bundle. We use a continuum…
The purpose of this paper is to show that: when a single particle moving under 3-proper time (three-dimensional time), the trajectories of a classical particle are equivalent to a quantum field with spin. Three-proper time models are built…
In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a…
This work discloses some inconsistencies of quantum mechanics (QM) in two different contexts. On the one hand the equivalence principle in his two formulations is the starting point of all gravitational theories; yet there is no way to make…
Based on 1) the spectral resolution of the energy operator; 2) the linearity of correspondence between physical observables and quantum Hermitian operators; 3) the definition of conjugate coordinate-momentum variables in classical…
Finite dimensional models that mimic the constraint structure of Einstein's General Relativity are quantized in the framework of BRST and Dirac's canonical formalisms. The first system to be studied is one featuring a constraint quadratic…
We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
The space time that is used in relativistic Quantum Mechanics and Quantum Field Theory is the Minkowski space time. Yet, as pointed out by several scholars this classical space time is incompatible with the Heisenberg Uncertainity…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…