相关论文: Bypassing Pauli's theorem
We reconsider the generalization of standard quantum mechanics in which the position operators do not commute. We argue that the standard formalism found in the literature leads to theories that do not share the symmetries present in the…
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution…
Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory…
In light of the transformation defined in the current quantum field theory, electromagnetic interaction is unchanged under time reversal. However, this kind of time reversal only lets in the Hamiltonian of the coordinate space, without…
We construct concrete examples of time operators for both continuous and discrete-time homogeneous quantum walks, and we determine their deficiency indices and spectra. For a discrete-time quantum walk, the time operator can be self-adjoint…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Relations between integrals of time-ordered product of operators, and their representation in terms of energy-ordered products are studied. Both can be decomposed into irreducible factors and these relations are discussed as well. The…
The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a…
The correspondence between classical and quantum invariants is established. The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase…
It is well-known that the 4-rotation in the 4-dimensional space-time is equivalent to the CPT-transformation (C is the charge conjugation, P is the space inversion and T is the time-reversal). The standard definition of the T-reversal…
The time operator canonically conjugated to the Hamiltonian of $N$ interacting particles on the line is constructed using SU(1,1) as a dynamical symmetry. This hidden conformal symmetry enables us to make a group theoretic analysis of the…
The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the…
We consider the conditioning of the timeless solution to the Wheeler-DeWitt equation by a predefined matter clock state in the simple scenario of de Sitter universe. The resulting evolution of the geometrodynamical degree of freedom with…
We address various aspects of a widely used tool in quantum information theory: the Choi-Jamiolkowski isomorphism [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. We review different versions of the isomorphism, their properties and…
The polarized Gowdy ${\bf T}^3$ vacuum spacetimes are characterized, modulo gauge, by a ``point particle'' degree of freedom and a function $\phi$ that satisfies a linear field equation and a non-linear constraint. The quantum Gowdy model…
For classical dynamical systems time operators are introduced as selfadjoint operators satisfying the so called weak Weyl relation with the unitary groups of time evolution. Dynamical systems with time operators are intrinsically…
Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…