Related papers: Symmetries and time operators
We consider a number of aspects of the problem of defining time observables in quantum theory. Time observables are interesting quantities in quantum theory because they often cannot be associated with self-adjoint operators. Their…
We formulate incomplete classical statistics for situations where the knowledge about the probability distribution outside a local region is limited. The information needed to compute expectation values of local observables can be collected…
Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic…
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.…
We extend previous work on the arrival time problem in quantum mechanics, in the framework of decoherent histories, to the case of a particle coupled to an environment. The usual arrival time probabilities are related to the probability…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the…
We give full account of our recent report in [E.A. Galapon, R. Caballar, R. Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)] where it is shown that formulating the free quantum time of arrival problem in a segment of the real line…
A number of approaches to the problem of defining arrival and dwell time probabilities in quantum theory make use of idealised models of clocks. An interesting question is the extent to which the probabilities obtained in this way are…
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 Newton-Wigner states and operator are widely accepted to provide an adequate notion of spatial localization of a particle in quantum field theory on a spacelike hypersurface. Replacing the spacelike with a timelike hypersurface, we…
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
A relation expressing the covariant transformation properties of a relativistic position operator is derived. This relation differs from the one existing in the literature expressing manifest covariance by some factor ordering. The relation…
There are enough reasons for us to consider time as a dynamical variable or operator; but according to Pauli's argument the existence of a self-adjoint time operator is incompatible with the semi-boundedness of Hamiltonian spectrum. In this…
The self adjoint operator of time in non-relativistic quantum mechanics is found within the approach where the ordinary Hamiltonian is not taken to be conjugate to time. The operator version of the reexpressed Liouville equation with the…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For…
New families of time-dependent potentials related to the parametric oscillator are introduced. This is achieved by introducing some general time-dependent operators that factorize the appropriate constant of motion (quantum invariant) of…