Related papers: Special Relativity in Quantum Phase Space
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
The root of the divergence problem in the current quantum field theory seems to be in the special theory of relativity. Here we propose a modified special relativity theory by introducing the primed inertial coordinate system, in addition…
We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal…
The concept of quantum phase space offers a view on quantum mechanics, which is different from the standard Hilbert space approach, but which more closely resembles the classical phase space. Due to the properties of quantum mechanics there…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…
We present a rigorous study of quantum diffusion of a relativistic particle subjected to a time-dependent random potential with $\delta$ correlation in time. We find that in the asymptotic time limit the particle wave packet spreads…
The phenomenon of linearisation instability is identified in models of quantum cosmology that are perturbations of mini-superspace models. In particular, constraints that are second order in the perturbations must be imposed on wave…
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can,…
Does the measurement of a quantum system necessarily break Lorentz invariance? We present a simple model of a detector that measures the spacetime localization of a relativistic particle in a Lorentz invariant manner. The detector does not…
A local conception is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties --- as e.g. vacuum catastrophe --- of the global approach.
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former…
The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D,…
The purpose of this paper is twofold: On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational…
The phase space of a classical particle in DSR contains de Sitter space as the space of momenta. We start from the standard relativistic particle in five dimensions with an extra constraint and reduce it to four dimensional DSR by imposing…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…
A derivation of the relative velocity used in the definition of the relativistic cross-section is given in terms of manifestly Lorentz invariant quantities. Along the way we find that there is a certain arbitrariness in the usual definition…
After analyzing the implication of investigations on the C, P and T transformations since 1956, we propose that there is a basic symmetry in particle physics. The combined space-time inversion is equivalent to particle-antiparticle…
Application of the so-called refined algebraic quantization scheme for constrained systems to the relativistic particle provides an inner product that defines a unique Fock representation for a scalar field in curved space-time. The…