Related papers: Representations of Spacetime Alternatives and Thei…
Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible,…
In a way paralleling the recently accepted non-Hermitian version of quantum mechanics in its Schr\"{o}dinger representation (working often with the innovative and heuristically productive concept of ${\cal PT}-$symmetry), it is demonstrated…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
Starting from a real scalar quantum field theory with quartic self-interactions and non-minimal coupling to classical gravity, we define four equal-time, spatially covariant phase-space operators through a Wigner transformation of spatially…
While quantum correlations between two spacelike-separated systems are fully encoded by the bipartite density operator associated with the joint system, there does not exist an analogous operator representing general quantum correlations…
The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise…
Koopman-von Neumann in the 30's gave an operatorial formululation of Classical Mechanics. It was shown later on that this formulation could also be written in a path-integral form. We will label this functional approach as CPI (for…
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free field Hamiltonian and its Fourier…
The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time"…
Starting from generalized position operators, we derive complex and quaternionic angular momentum operators along with their commutation algebra as well. These algebras differ from the standard Hermitian ones, especially in terms of…
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
The classical Coriolis force finds its quantum analogue in the difference $\Sigma(t)=H(t)-G(t)$ where the ``true'', observable Hamiltonian $H(t)$ represents the instantaneous energy. The other, ``false'' Hamiltonian $G(t)$ generates the…
The definition of the Hamiltonian operator H for a general wave equa-tion in a general spacetime is discussed. We recall that H depends on the coordinate system merely through the corresponding reference frame. When the wave equation…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…