Related papers: A New Formulation of Quantum Mechanics
In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr\"odinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
It is demonstrated how quantum mechanics emerges from the stochastic dynamics of force-carriers. It is shown that the quantum Moyal equation corresponds to some dynamic correlations between the momentum of a real particle and the position…
In this study, we describe a novel approach to quantum phenomena of the generalized electromagnetic fields of dyons with quaternionic analysis. Starting with quaternionic quantum wave equations, we have established a quantized condition for…
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schroedinger equations (SE). Despite the success of this representation of the quantum…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle…
We develop the quantum field theory of fermion mixing in curved spacetime and discuss the role of unitarily inequivalent representations in the particle interpretation of the theory. We derive general oscillation formulae and apply them to…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…