相关论文: Time as an operator/observable in nonrelativistic …

The failure of conventional quantum theory to recognize time as an observable and to admit time operators is addressed. Instead of focusing on the existence of a time operator for a given Hamiltonian, we emphasize the role of the…

(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum…

We present a generic way of thinking about time machines from the view of a far away observer. In this model the universe consists of three (or more) regions: One containing the entrance of the time machine, another the exit and the…

We develop a general framework for the construction of probabilities for the time of arrival in quantum systems. The time of arrival is identified with the time instant when a transition in the detector's degrees of freedom takes place.…

Time-dependent terms in Hamiltonians and equations of motion are rather important for a quantum-mechanical description of particles with arbitrary spins in nonstationary fields. We use the Foldy-Wouthuysen representation which allows one to…

Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…

The simplest nonlinear Schrodinger equation that contains the time derivative of the probability density is investigated. This equation has the same stationary solutions as its linear counterpart, and these solutions are the eigenstates of…

Some precisions are given about the definition of the Hamiltonian operator H and its transformation properties, for a linear wave equation in a general spacetime. In the presence of time-dependent unitary gauge transformations, H as an…

Non-Hermitian systems have garnered significant attention due to the emergence of novel topology of complex spectra and skin modes. However, investigating transport phenomena in such systems faces obstacles stemming from the non-unitary…

A neutral particle with general spin and magnetic moment moving in an arbitrarily varying magnetic field is studied. The time evolution operator for the Schr\"odinger equation can be obtained if one can find a unit vector that satisfies the…

We develop a Heisenberg-picture \emph{kinematical} framework in which (i) time is treated as a quantum observable, admitting both a relational POVM construction for semibounded spectra and a fully self-adjoint realization on an enlarged…

A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of…

In high-energy physics, coordinate noncommutativity represents the core idea that space itself can be quantized, as expressed through the frameworks of string theory and noncommutative field theory. Influence of such a noncommutativity on…

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…

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…

A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…

Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…

Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schr\"odinger-Heisenberg formulation that utilizes states on spacelike…

Including the metric fluctuations of a realistic cosmological geometry we reconsider an earlier suggestion that measuring the relative time-of-flight of ultra-relativistic particles can provide interesting constraints on fundamental…

A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time…