Related papers: Quantum Mechanics in non-inertial reference frames…
Quantum reference frames are needed in quantum theory for much the same reasons that reference frames are in classical theories: to manifest invariance in line with fundamental relativity principles and to provide a basis for the definition…
We revisit the classifications of classical and quantum galilean particles: that is, we fully classify homogeneous symplectic manifolds and unitary irreducible projective representations of the Galilei group. Equivalently, these are…
A Newtonian mechanics model is essentially the model of a point body in an inertial reference frame. How to describe extended bodies in non-inertial (vibrational) reference frames with the random initial conditions? One of the most general…
In standard quantum mechanics, reference frames are treated as abstract entities. We can think of them as idealized, infinite-mass subsystems which decouple from the rest of the system. In nature, however, all reference frames are realized…
The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is…
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…
The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval --…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
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…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
We develop a formulation of particle mechanics in which the functional relation between force and kinetic energy is derived directly from local conservation mechanical energy $E$, rather than postulated through Newton's second law or a…
A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…