3,243 research outputs found
Very Special Relativity
By Very Special Relativity (VSR) we mean descriptions of nature whose
space-time symmetries are certain proper subgroups of the Poincar\'e group.
These subgroups contain space-time translations together with at least a
2-parameter subgroup of the Lorentz group isomorphic to that generated by
and . We find that VSR implies special relativity
(SR) in the context of local quantum field theory or of CP conservation. Absent
both of these added hypotheses, VSR provides a simulacrum of SR for which most
of the consequences of Lorentz invariance remain wholly or essentially intact,
and for which many sensitive searches for departures from Lorentz invariance
must fail. Several feasible experiments are discussed for which
Lorentz-violating effects in VSR may be detectable.Comment: 3 pages, revte
Disentangling Neutrino Oscillations
The theory underlying neutrino oscillations has been described at length in
the literature. The neutrino state produced by a weak decay is usually
portrayed as a linear superposition of mass eigenstates with, variously, equal
energies or equal momenta. We point out that such a description is incomplete,
that in fact, the neutrino is entangled with the other particle or particles
emerging from the decay. We offer an analysis of oscillation phenomena
involving neutrinos (applying equally well to neutral mesons) that takes
entanglement into account. Thereby we present a theoretically sound proof of
the universal validity of the oscillation formulae ordinarily used. In so
doing, we show that the departures from exponential decay reported by the GSI
experiment cannot be attributed to neutrino mixing. Furthermore, we demonstrate
that the `Mossbauer' neutrino oscillation experiment proposed by Raghavan,
while technically challenging, is correctly and unambiguously describable by
means of the usual oscillation formalae.Comment: 16 page
Parameter Uncertainty in the Kalman--Bucy Filter
In standard treatments of stochastic filtering one first has to estimate the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional source of statistical uncertainty. We propose an approach to address this problem when working with the continuous time Kalman--Bucy filter, by making evaluations via a nonlinear expectation. We show how our approach may be reformulated as an optimal control problem, and proceed to analyze the corresponding value function. In particular we present a novel uniqueness result for the associated Hamilton--Jacobi--Bellman equation
Ergodic backward stochastic difference equations
We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain this result, we use a Nummelin splitting argument to obtain ergodicity estimates for a discrete time Markov chain which hold uniformly under suitable perturbations of its transition matrix. We conclude with an application of this theory to a treatment of an ergodic control problem
Pathwise stochastic control with applications to robust filtering
We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming. As an application, we use pathwise stochastic control in the context of stochastic filtering to construct filters which are robust to parameter uncertainty, demonstrating an original application of rough path theory to statistics
- …