7 research outputs found
Quantum Particle on a Quantum Circle
We describe a -deformed dynamical system corresponding to the quantum free
particle moving along the circle. The algebra of observables is constructed and
discussed. We construct and classify irreducible representations of the system.Comment: 11 pages, LaTe
Entanglement and Tensor Product Decomposition for Two Fermions
The problem of the choice of tensor product decomposition in a system of two
fermions with the help of Bogoliubov transformations of creation and
annihilation operators is discussed. The set of physical states of the
composite system is restricted by the superselection rule forbidding the
superposition of fermions and bosons. It is shown that the Wootters concurrence
is not proper entanglement measure in this case. The explicit formula for the
entanglement of formation is found and its dependence on tensor product
decompositions of the Hilbert space is discussed. It is shown that the set of
separable states is narrower than in two-qubit case. Moreover, there exist
states which are separable with respect to all tensor product decompositions of
the Hilbert space.Comment: 8pp, published versio
New varying speed of light theories
We review recent work on the possibility of a varying speed of light (VSL).
We start by discussing the physical meaning of a varying , dispelling the
myth that the constancy of is a matter of logical consistency. We then
summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz
invariance; bimetric theories (where the speeds of gravity and light are not
the same); locally Lorentz invariant VSL theories; theories exhibiting a color
dependent speed of light; varying induced by extra dimensions (e.g. in the
brane-world scenario); and field theories where VSL results from vacuum
polarization or CPT violation. We show how VSL scenarios may solve the
cosmological problems usually tackled by inflation, and also how they may
produce a scale-invariant spectrum of Gaussian fluctuations, capable of
explaining the WMAP data. We then review the connection between VSL and
theories of quantum gravity, showing how ``doubly special'' relativity has
emerged as a VSL effective model of quantum space-time, with observational
implications for ultra high energy cosmic rays and gamma ray bursts. Some
recent work on the physics of ``black'' holes and other compact objects in VSL
theories is also described, highlighting phenomena associated with spatial (as
opposed to temporal) variations in . Finally we describe the observational
status of the theory. The evidence is currently slim -- redshift dependence in
the atomic fine structure, anomalies with ultra high energy cosmic rays, and
(to a much lesser extent) the acceleration of the universe and the WMAP data.
The constraints (e.g. those arising from nucleosynthesis or geological bounds)
are tight, but not insurmountable. We conclude with the observational
predictions of the theory, and the prospects for its refutation or vindication.Comment: Final versio