58 research outputs found
Quantum algebraic representation of localization and motion of a Dirac electron
Quantum algebraic observables representing localization in space-time of a
Dirac electron are defined. Inertial motion of the electron is represented in
the quantum algebra with electron mass acting as the generator of motion. Since
transformations to uniformly accelerated frames are naturally included in this
conformally invariant description, the quantum algebra is also able to deal
with uniformly accelerated motion.Comment: 10 pages, Frontier Tests of QED and Physics of the Vacuum, Trieste,
5-11/10/200
Quantum Langevin Equations and Stability
Different quantum Langevin equations obtained by coupling a particle to a
field are examined. Instabilities or violations of causality affect the motion
of a point charge linearly coupled to the electromagnetic field. In contrast,
coupling a scatterer with a reflection cut-off to radiation pressure leads to
stable and causal motions. The radiative reaction force exerted on a scatterer,
and hence its quasistatic mass, depend on the field state. Explicit expressions
for a particle scattering a thermal field in a two dimensional space-time are
given.Comment: 12 page
Inertia of Casimir energy
Moving mirrors are submitted to reaction forces by vacuum fields. The
motional force is known to vanish for a single mirror uniformly accelerating in
vacuum. We show that inertial forces (proportional to accelerations) arise in
the presence of a second scatterer, exhibiting properties expected for a
relative inertia: the mass corrections depend upon the distance between the
mirrors, and each mirror experiences a force proportional to the acceleration
of the other one. When the two mirrors move with the same acceleration, the
mass correction obtained for the cavity represents the contribution to inertia
of Casimir energy. Accounting for the fact that the cavity moves as a stressed
rigid body, it turns out that this contribution fits Einstein's law of inertia
of energy.Comment: 10 page
Motional Casimir force
We study the situation where two point like mirrors are placed in the vacuum
state of a scalar field in a two-dimensional spacetime. Describing the
scattering upon the mirrors by transmittivity and reflectivity functions
obeying unitarity, causality and high frequency transparency conditions, we
compute the fluctuations of the Casimir forces exerted upon the two motionless
mirrors. We use the linear response theory to derive the motional forces
exerted upon one mirror when it moves or when the other one moves. We show that
these forces may be resonantly enhanced at the frequencies corresponding to the
cavity modes. We interpret them as the mechanical consequence of generation of
squeezed fields.Comment: 14 page
Casimir force between partially transmitting mirrors
The Casimir force can be understood as resulting from the radiation pressure
exerted by the vacuum fluctuations reflected by boundaries. We extend this
local formulation to the case of partially transmitting boundaries by
introducing reflectivity and transmittivity coefficients obeying conditions of
unitarity, causality and high frequency transparency. We show that the
divergences associated with the infiniteness of the vacuum energy do not appear
in this approach. We give explicit expressions for the Casimir force which hold
for any frequency dependent scattering and any temperature. The corresponding
expressions for the Casimir energy are interpreted in terms of phase shifts.
The known results are recovered at the limit of a perfect reflection.Comment: 12 page
Quantum fluctuations of position of a mirror in vacuum
A mirror scattering vacuum fields is submitted to a quantum fluctuating
radiation pressure. It also experiences a motional force, related to force
fluctuations through fluctuation-dissipation relations. The resulting position
fluctuations of the coupled mirror are related to the dissipative part of the
mechanical admittance. We compute the time dependent position commutator, which
makes apparent the difference between the low-frequency and high-frequency
masses, and the anticommutator noise spectrum, which describes the ultimate
sensitivity in a length measurement using mirrors.Comment: 12 page
Quantum Localisation Observables and Accelerated Frames
We define quantum observables associated with Einstein localisation in
space-time. These observables are built on Poincare' and dilatation generators.
Their commutators are given by spin observables defined from the same symmetry
generators. Their shifts under transformations to uniformly accelerated frames
are evaluated through algebraic computations in conformal algebra. Spin number
is found to vary under such transformations with a variation involving further
observables introduced as irreducible quadrupole momenta. Quadrupole
observables may be dealt with as non commutative polarisations which allow one
to define step operators increasing or decreasing the spin number by unity.Comment: 14 page
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