426 research outputs found
On the Observables Describing a Quantum Reference Frame
A reference frame F is described by the element g of the Poincare' group P
which connects F with a given fixed frame F_0. If F is a quantum frame, defined
by a physical object following the laws of quantum physics, the parameters of g
have to be considered as quantum observables. However, these observables are
not compatible and some of them, namely the coordinates of the origin of F,
cannot be represented by self-adjoint operators. Both these difficulties can be
overcome by considering a positive-operator-valued measure (POVM) on P,
covariant with respect to the left translations of the group, namely a
covariance system. We develop a construction procedure for this kind of
mathematical structure. The formalism is also used to discuss the quantum
observables measured with respect to a quantum reference frame.Comment: 23 pages, no figure
Time-of-arrival formalism for the relativistic particle
A suitable operator for the time-of-arrival at a detector is defined for the
free relativistic particle in 3+1 dimensions. For each detector position, there
exists a subspace of detected states in the Hilbert space of solutions to the
Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of
the time-of-arrival operator apply inside this subspace, opening up a standard
probabilistic interpretation.Comment: 16 pages, no figures, uses LaTeX. The section "Interpretation" has
been completely rewritten and some errors correcte
Non locality and causal evolution in QFT
Non locality appearing in QFT during the free evolution of localized field
states and in the Feynman propagator function is analyzed. It is shown to be
connected to the initial non local properties present at the level of quantum
states and then it does not imply a violation of Einstein's causality. Then it
is investigated a simple QFT system with interaction, consisting of a classical
source coupled linearly to a quantum scalar field, that is exactly solved. The
expression for the time evolution of the state describing the system is given.
The expectation value of any arbitrary ``good'' local observable, expressed as
a function of the field operator and its space and time derivatives, is
obtained explicitly at all order in the field-matter coupling constant. These
expectation values have a source dependent part that is shown to be always
causally retarded, while the non local contributions are source independent and
related to the non local properties of zero point vacuum fluctuations.Comment: Submitted to Journal of Physics B: 16 pages: 1 figur
Non-Linear Relativity in Position Space
We propose two methods for obtaining the dual of non-linear relativity as
previously formulated in momentum space. In the first we allow for the (dual)
position space to acquire a non-linear representation of the Lorentz group
independently of the chosen representation in momentum space. This requires a
non-linear definition for the invariant contraction between momentum and
position spaces. The second approach, instead, respects the linearity of the
invariant contraction. This fully fixes the dual of momentum space and dictates
a set of energy-dependent space-time Lorentz transformations. We discuss a
variety of physical implications that would distinguish these two strategies.
We also show how they point to two rather distinct formulations of theories of
gravity with an invariant energy and/or length scale.Comment: 7 pages, revised versio
Observers and Measurements in Noncommutative Spacetimes
We propose a "Copenhagen interpretation" for spacetime noncommutativity. The
goal is to be able to predict results of simple experiments involving signal
propagation directly from commutation relations. A model predicting an energy
dependence of the speed of photons of the order E/E_Planck is discussed in
detail. Such effects can be detectable by the GLAST telescope, to be launched
in 2006.Comment: 10 pp; v2: equivalence of observers explicitely stated; v3: minor
changes, references and remarks added, burst spreading with energy emphasized
as a signature rather than nois
The Impact of Olfactory Disorders in the United Kingdom
Olfactory disorders are believed to affect 5% of the general population and have been shown to bear significant psychosocial consequences to sufferers. Although more common than blindness and profound deafness in the United Kingdom, the impact of these disorders has not been assessed to date and the plight of British patients has yet to be quantified. In 2012, a patient support organization, Fifth Sense, was founded to provide information and support to sufferers of chemosensory disorders. Following a recent members conference, a survey of the membership was conducted anonymously using a series of questions based on an existing olfactory disorders questionnaire. From 496 respondents, this has demonstrated high rates of depression (43%) and anxiety (45%), impairment of eating experience (92%), isolation (57%), and relationship difficulties (54%). Women appear to have significantly more issues than men in terms of social and domestic dysfunction relating to olfactory loss (P = 0.01). Qualitative disorders also affected more than 1 in 5 members with parosmia reported in 19% and phantosmia in 24%. This paper discusses the details of the British story of anosmia and other related disorders as depicted by those most affected
The norm-1-property of a quantum observable
A normalized positive operator measure has the
norm-1-property if \no{E(X)}=1 whenever . This property reflects
the fact that the measurement outcome probabilities for the values of such
observables can be made arbitrary close to one with suitable state
preparations. Some general implications of the norm-1-property are
investigated. As case studies, localization observables, phase observables, and
phase space observables are considered.Comment: 14 page
Lower Neutrino Mass Bound from SN1987A Data and Quantum Geometry
A lower bound on the light neutrino mass is derived in the framework
of a geometrical interpretation of quantum mechanics. Using this model and the
time of flight delay data for neutrinos coming from SN1987A, we find that the
neutrino masses are bounded from below by eV, in
agreement with the upper bound
eV currently available. When the model is applied to photons with effective
mass, we obtain a lower limit on the electron density in intergalactic space
that is compatible with recent baryon density measurements.Comment: 22 pages, 3 figure
Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique
We present a Master equation for description of fermions and bosons for
special relativities with two invariant scales, SR2, (c and lambda_P). We
introduce canonically-conjugate variables (chi^0, chi) to (epsilon, pi) of
Judes-Visser. Together, they bring in a formal element of linearity and
locality in an otherwise non-linear and non-local theory. Special relativities
with two invariant scales provide all corrections, say, to the standard model
of the high energy physics, in terms of one fundamental constant, lambda_P. It
is emphasized that spacetime of special relativities with two invariant scales
carries an intrinsic quantum-gravitational character. In an addenda, we also
comment on the physical importance of a phase factor that the whole literature
on the subject has missed and present a brief critique of SR2. In addition, we
remark that the most natural and physically viable SR2 shall require
momentum-space and spacetime to be non-commutative with the non-commutativity
determined by the spin content and C, P, and T properties of the examined
representation space. Therefore, in a physically successful SR2, the notion of
spacetime is expected to be deeply intertwined with specific properties of the
test particle.Comment: Int. J. Mod. Phys. D (in press). Extended version of a set of two
informal lectures given in "La Sapienza" (Rome, May 2001
Field on Poincare group and quantum description of orientable objects
We propose an approach to the quantum-mechanical description of relativistic
orientable objects. It generalizes Wigner's ideas concerning the treatment of
nonrelativistic orientable objects (in particular, a nonrelativistic rotator)
with the help of two reference frames (space-fixed and body-fixed). A technical
realization of this generalization (for instance, in 3+1 dimensions) amounts to
introducing wave functions that depend on elements of the Poincare group . A
complete set of transformations that test the symmetries of an orientable
object and of the embedding space belongs to the group . All
such transformations can be studied by considering a generalized regular
representation of in the space of scalar functions on the group, ,
that depend on the Minkowski space points as well as on the
orientation variables given by the elements of a matrix .
In particular, the field is a generating function of usual spin-tensor
multicomponent fields. In the theory under consideration, there are four
different types of spinors, and an orientable object is characterized by ten
quantum numbers. We study the corresponding relativistic wave equations and
their symmetry properties.Comment: 46 page
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