2,211 research outputs found
Generating functional for the gravitational field: implementation of an evolutionary quantum dynamics
We provide a generating functional for the gravitational field, associated to
the relaxation of the primary constraints as extended to the quantum sector.
This requirement of the theory, relies on the assumption that a suitable time
variable exist, when taking the T-products of the dynamical variables. More
precisely, we start from the gravitational field equations written in the
Hamiltonian formalism and expressed via Misner-like variables; hence we
construct the equation to which the T-products of the dynamical variables obey
and transform this paradigm in terms of the generating functional, as taken on
the theory phase-space. We show how the relaxation of the primary constraints
(which correspond to break down the invariance of the quantum theory under the
4-diffeomorphisms) is summarized by a free functional taken on the Lagrangian
multipliers, accounting for such constraints in the classical theory. The issue
of our analysis is equivalent to a Gupta-Bleuler approach on the quantum
implementation of all the gravitational constraints; in fact, in the limit of
small , the quantum dynamics is described by a Schr\"odinger equation,
as soon as the mean values of the momenta, associated to the lapse function and
the shift vector, are not vanishing. Finally we show how, in the classical
limit, the evolutionary quantum gravity reduces to General Relativity in the
presence of an Eckart fluid, which corresponds to the classical counterpart of
the physical clock, introduced in the quantum theory.Comment: 23 pages, no figures, to appear on International Journal of Modern
Physics
Entanglement of Dirac fields in non-inertial frames
We analyze the entanglement between two modes of a free Dirac field as seen
by two relatively accelerated parties. The entanglement is degraded by the
Unruh effect and asymptotically reaches a non-vanishing minimum value in the
infinite acceleration limit. This means that the state always remains entangled
to a degree and can be used in quantum information tasks, such as
teleportation, between parties in relative uniform acceleration. We analyze our
results from the point of view afforded by the phenomenon of entanglement
sharing and in terms of recent results in the area of multi-qubit
complementarity.Comment: 15 pages, with 8 figures (Mar 2006); accepted to Physical Review A,
July 2006 - slightly revise
Probability in Orthodox Quantum Mechanics: Probability as a Postulate Versus Probability as an Emergent Phenomenon
The role of probability in quantum mechanics is reviewed, with a discussion
of the ``orthodox'' versus the statistical interpretive frameworks, and of a
number of related issues. After a brief summary of sources of unease with
quantum mechanics, a survey is given of attempts either to give a new
interpretive framework assuming quantum mechanics is exact, or to modify
quantum mechanics assuming it is a very accurate approximation to a more
fundamental theory. This survey focuses particularly on the issues of whether
probabilities in quantum mechanics are postulated or emergent.Comment: Latex; Submitted to the Proceedings of the Ischia Conference on
``Chance in Physics: Foundations and Perspectives'
Nonthermal nature of incipient extremal black holes
We examine particle production from spherical bodies collapsing into extremal
Reissner-Nordstr\"om black holes. Kruskal coordinates become ill-defined in the
extremal case, but we are able to find a simple generalization of them that is
good in this limit. The extension allows us to calculate the late-time
worldline of the center of the collapsing star, thus establishing a
correspondence with a uniformly accelerated mirror in Minkowski spacetime. The
spectrum of created particles associated with such uniform acceleration is
nonthermal, indicating that a temperature is not defined. Moreover, the
spectrum contains a constant that depends on the history of the collapsing
object. At first sight this points to a violation of the no-hair theorems;
however, the expectation value of the stress-energy-momentum tensor is zero and
its variance vanishes as a power law at late times. Hence, both the no-hair
theorems and the cosmic censorship conjecture are preserved. The power-law
decay of the variance is in distinction to the exponential fall-off of a
nonextremal black hole. Therefore, although the vanishing of the stress
tensor's expectation value is consistent with a thermal state at zero
temperature, the incipient black hole does not behave as a thermal object at
any time and cannot be regarded as the thermodynamic limit of a nonextremal
black hole, regardless of the fact that the final product of collapse is
quiescent.Comment: 13 pages, 2 epsf figures, RevTeX 3. Minor changes, version published
in PR
Laser photon merging in proton-laser collisions
The quantum electrodynamical vacuum polarization effects arising in the
collision of a high-energy proton beam and a strong, linearly polarized laser
field are investigated. The probability that laser photons merge into one
photon by interacting with the proton`s electromagnetic field is calculated
taking into account the laser field exactly. Asymptotics of the probability are
then derived according to different experimental setups suitable for detecting
perturbative and nonperturbative vacuum polarization effects. The
experimentally most feasible setup involves the use of a strong optical laser
field. It is shown that in this case measurements of the polarization of the
outgoing photon and and of its angular distribution provide promising tools to
detect these effects for the first time.Comment: 38 pages, 9 figure
The phase of a quantum mechanical particle in curved spacetime
We investigate the quantum mechanical wave equations for free particles of
spin 0,1/2,1 in the background of an arbitrary static gravitational field in
order to explicitly determine if the phase of the wavefunction is , as is often quoted in the literature. We work
in isotropic coordinates where the wave equations have a simple managable form
and do not make a weak gravitational field approximation. We interpret these
wave equations in terms of a quantum mechanical particle moving in medium with
a spatially varying effective index of refraction. Due to the first order
spatial derivative structure of the Dirac equation in curved spacetime, only
the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as
indicated above. The second order spatial derivative structure of the spin 0
and spin 1 wave equations yield the above phase only to lowest order in
. We develop a WKB approximation for the solution of the spin 0 and spin
1 wave equations and explore amplitude and phase corrections beyond the lowest
order in . For the spin 1/2 particle we calculate the phase appropriate
for neutrino flavor oscillations.Comment: 30 pages, no figures. Submitted to Gen.Rel.Grav 17 Oct 0
Finite temperature amplitudes and reaction rates in Thermofield dynamics
We propose a method for calculating the reaction rates and transition
amplitudes of generic process taking place in a many body system in
equilibrium. The relationship of the scattering and decay amplitudes as
calculated in Thermo Field Dynamics the conventional techniques is established.
It is shown that in many cases the calculations are relatively easy in TFD.Comment: 32 pages, RevTex, 2 PS figures, to appear in Phys. Rev.
A statistical mechanics approach to autopoietic immune networks
The aim of this work is to try to bridge over theoretical immunology and
disordered statistical mechanics. Our long term hope is to contribute to the
development of a quantitative theoretical immunology from which practical
applications may stem. In order to make theoretical immunology appealing to the
statistical physicist audience we are going to work out a research article
which, from one side, may hopefully act as a benchmark for future improvements
and developments, from the other side, it is written in a very pedagogical way
both from a theoretical physics viewpoint as well as from the theoretical
immunology one.
Furthermore, we have chosen to test our model describing a wide range of
features of the adaptive immune response in only a paper: this has been
necessary in order to emphasize the benefit available when using disordered
statistical mechanics as a tool for the investigation. However, as a
consequence, each section is not at all exhaustive and would deserve deep
investigation: for the sake of completeness, we restricted details in the
analysis of each feature with the aim of introducing a self-consistent model.Comment: 22 pages, 14 figur
Understanding entangled spins in QED
The stability of two entangled spins dressed by electrons is studied by
calculating the scattering phase shifts. The interaction between electrons is
interpreted by fully relativistic QED and the screening effect is described
phenomenologically in the Debye exponential form . Our results
show that if the (Einstein-Podolsky-Rosen-) EPR-type states are kept stable
under the interaction of QED, the spatial wave function must be
parity-dependent. The spin-singlet state and the polarized state along the z-axis\QTR{bf}{\}give rise to two
different kinds of phase shifts\QTR{bf}{.} Interestingly, the interaction
between electrons in the spin-singlet pair is found to be attractive. Such an
attraction could be very useful when we extract the entangled spins from
superconductors. A mechanism to filter the entangled spins is also discussed.Comment: 6 pages, 3 figures. changes adde
Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length
The (D+1)-dimensional -two-parameter Lorentz-covariant
deformed algebra introduced by Quesne and Tkachuk [C. Quesne and V. M. Tkachuk,
J. Phys. A: Math. Gen. \textbf {39}, 10909 (2006).], leads to a nonzero minimal
uncertainty in position (minimal length). The Klein-Gordon equation in a
(3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant
deformed algebra is studied in the case where up to first order
over deformation parameter . It is shown that the modified Klein-Gordon
equation which contains fourth-order derivative of the wave function describes
two massive particles with different masses. We have shown that physically
acceptable mass states can only exist for which
leads to an isotropic minimal length in the interval . Finally, we have shown that the above estimation of
minimal length is in good agreement with the results obtained in previous
investigations.Comment: 10 pages, no figur
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