Related papers: Building a frame and gauge free formulation of qua…
We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously, using the…
Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered.…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing…
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism.…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
Starting from the observation that in Yang-Mills theory the Schroedinger state functional in the momentum representation is not gauge invariant, we investigate the reversed question: Which are the representations for the operators of a…
Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory.…
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
The classical counterpart of noncommutative quantum mechanics is a constrained system containing only second class constraints. The embedding procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to transform this system…
The quantization of gravity coupled to a perfect fluid model leads to a Schr\"odinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…