Related papers: Proper time operator and its uncertainty relation
A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy…
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a ``clock''. Conditional probabilities are…
A model one-dimensional self consistent steady state collisionless self-gravitating system in which all the particles have the same energy is presented. This has the remarkable property that the position and velocity of the particles…
We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this…
The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of…
The most realistic situations in quantum mechanics involve the interaction between two or more systems. In the most of reliable models, the form and structure of the interactions generate differential equations which are, in the most of…
We consider a spin half particle in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction. We find that the energy eigenvalues for this system are real even though the interaction is…
In this paper, we study some interesting properties of a spherically symmetric oscillating soliton star made of a real time-dependent scalar field which is called an oscillaton. The known final configuration of an oscillaton consists of a…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
New applications of Feynman disentangling method in quantum mechanics are studied and the time-dependent singular oscillator problem is solved in this approach. The important role of representation group theory is discussed in this context.
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…
Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to…
(A) The momentum density conjugate to a bosonic quantum field splits naturally into the sum of a classical component and a nonclassical component. It is shown that the field and the nonclassical component of the momentum density satisfy…
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through…
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is…
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
Time continues to be an intriguing physical property in the modern era. On the one hand, we have the Classical and Relativistic notion of time, where space and time have the same hierarchy, which is essential in describing events in…
We discuss a mechanism of spin decoherence in gravitation within the framework of general relativity. The spin state of a particle moving in a gravitational field is shown to decohere due to the curvature of spacetime. As an example, we…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…