Related papers: Quantum Mechanics in non-inertial reference frames…
Dynamical evolution is described as a parallel section on an infinite dimensional Hilbert bundle over the base manifold of all frames of reference. The parallel section is defined by an operator-valued connection whose components are the…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata…
We study quantum equivalents of non-commutative operators in quantum mechanics. Any matrix "$B$" satisfying the non-commuting relation $[A,B]\neq 0$ with "$A$", can be used via $B^{-1} AB$ to reproduce eigenvalues of "$A$". This…
To investigate how quantum effects might modify special relativity, we will study a Lorentz transformation between classical and quantum reference frames and express it in terms of the four-dimensional (4D) momentum of the quantum reference…
In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and…
In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
The group E(3)=SO(3) *s T(3), that is the homogeneous subgroup of the Galilei group parameterized by rotation angles and velocities, defines the continuous group of transformations between the frames of inertial particles in Newtonian…
The current theories of quantum physics and general relativity on their own do not allow us to study situations in which the gravitational source is quantum. Here, we propose a strategy to determine the dynamics of objects in the presence…
Based on a recent relational formulation of quantum reference frame transformations, especially with a case of quantum spatial translations in particular, we analyzed how the `value' of an observable for a fixed state change. That is the…
Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…
We reinvestigate Bargmann's superselection rule for the overall mass of $n$ particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should…
It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a…
The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently, many attempts have been made to extend…