70 research outputs found
Toward loop quantization of plane gravitational waves
The polarized Gowdy model in terms of Ashtekar–Barbero variables is reduced with an additional constraint derived from the Killing equations for plane gravitational waves with parallel rays. The new constraint is formulated in a diffeomorphism invariant manner and, when it is included in the model, the resulting constraint algebra is first class, in contrast to the prior work done in special coordinates. Using an earlier work by Banerjee and Date, the constraints are expressed in terms of classical quantities that have an operator equivalent in loop quantum gravity, making these plane gravitational wave spacetimes accessible to loop quantization techniques
Plane gravitational waves and loop quantization
Starting from the polarized Gowdy model in Ashtekar variables, the Killing equations characteristic for plane-fronted parallel gravitational waves are introduced in part as a set of first-class constraints, in addition to the standard ones of General Relativity. These constraints are expressed in terms of quantities that have an operator equivalent in Loop Quantum Gravity, making plane wave space-times accessible to loop quantization techniques
Lax Tensors, Killing Tensors and Geometric Duality
The solution of the Lax tensor equations in the case
was analyzed. The Lax tensors on
the dual metrics were investigated. We classified all two dimensional metrics
having the symmetric Lax tensor . The Lax tensors of the
flat space, Rindler system and its dual were found.Comment: 9 pages LATE
Towards Loop Quantization of Plane Gravitational Waves
The polarized Gowdy model in terms of Ashtekar-Barbero variables is further
reduced by including the Killing equations for plane-fronted parallel
gravitational waves with parallel rays. The resulting constraint algebra,
including one constraint derived from the Killing equations in addition to the
standard ones of General Relativity, are shown to form a set of first-class
constraints. Using earlier work by Banerjee and Date the constraints are
expressed in terms of classical quantities that have an operator equivalent in
Loop Quantum Gravity, making space-times with pp-waves accessible to loop
quantization techniques.Comment: 14 page
Isotropic Loop Quantum Cosmology with Matter
A free massless scalar field is coupled to homogeneous and isotropic loop
quantum cosmology. The coupled model is investigated in the vicinity of the
classical singularity, where discreteness is essential and where the quantum
model is non-singular, as well as in the regime of large volumes, where it
displays the expected semiclassical features. The particular matter content
(massless, free scalar) is chosen to illustrate how the discrete structure
regulates pathological behavior caused by kinetic terms of matter Hamiltonians
(which in standard quantum cosmology lead to wave functions with an infinite
number of oscillations near the classical singularity). Due to this
modification of the small volume behavior the dynamical initial conditions of
loop quantum cosmology are seen to provide a meaningful generalization of
DeWitt's initial condition.Comment: 18 pages, 4 figure
Quantum field and uniformly accelerated oscillator
We present an exact treatment of the influences on a quantum scalar field in
its Minkowski vacuum state induced by coupling of the field to a uniformly
accelerated harmonic oscillator. We show that there are no radiation from the
oscillator in the point of view of a uniformly accelerating observer. On the
other hand, there are radiations in the point of view of an inertial observer.
It is shown that Einstein-Podolsky-Rosen (EPR) like correlations of Rindler
particles in Minkowski vacuum states are modified by a phase factor in front of
the momentum-symmetric Rindler operators. The exact quantization of a
time-dependent oscillator coupled to a massless scalar field was given.Comment: 28 pages, LaTe
Paired accelerated arames: The perfect interferometer with everywhere smooth wave amplitudes
Rindler's acceleration-induced partitioning of spacetime leads to a
nature-given interferometer. It accomodates quantum mechanical and wave
mechanical processes in spacetime which in (Euclidean) optics correspond to
wave processes in a ``Mach-Zehnder'' interferometer: amplitude splitting,
reflection, and interference. These processes are described in terms of
amplitudes which behave smoothly across the event horizons of all four Rindler
sectors. In this context there arises quite naturally a complete set of
orthonormal wave packet histories, one of whose key properties is their
"explosivity index". In the limit of low index values the wave packets trace
out fuzzy world lines. By contrast, in the asymptotic limit of high index
values, there are no world lines, not even fuzzy ones. Instead, the wave packet
histories are those of entities with non-trivial internal collapse and
explosion dynamics. Their details are described by the wave processes in the
above-mentioned Mach-Zehnder interferometer. Each one of them is a double slit
interference process. These wave processes are applied to elucidate the
amplification of waves in an accelerated inhomogeneous dielectric. Also
discussed are the properties and relationships among the transition amplitudes
of an accelerated finite-time detector.Comment: 38 pages, RevTex, 10 figures, 4 mathematical tutorials. Html version
of the figures and of related papers available at
http://www.math.ohio-state.edu/~gerlac
Radiation from a uniformly accelerating harmonic oscillator
We consider a radiation from a uniformly accelerating harmonic oscillator
whose minimal coupling to the scalar field changes suddenly. The exact time
evolutions of the quantum operators are given in terms of a classical solution
of a forced harmonic oscillator. After the jumping of the coupling constant
there occurs a fast absorption of energy into the oscillator, and then a slow
emission follows. Here the absorbed energy is independent of the acceleration
and proportional to the log of a high momentum cutoff of the field. The emitted
energy depends on the acceleration and also proportional to the log of the
cutoff. Especially, if the coupling is comparable to the natural frequency of
the detector () enormous energies are radiated away
from the oscillator.Comment: 26 pages, 1 eps figure, RevTeX, minor correction in grammar, add a
discussio
Stochastic Theory of Accelerated Detectors in a Quantum Field
We analyze the statistical mechanical properties of n-detectors in arbitrary
states of motion interacting with each other via a quantum field. We use the
open system concept and the influence functional method to calculate the
influence of quantum fields on detectors in motion, and the mutual influence of
detectors via fields. We discuss the difference between self and mutual
impedance and advanced and retarded noise. The mutual effects of detectors on
each other can be studied from the Langevin equations derived from the
influence functional, as it contains the backreaction of the field on the
system self-consistently. We show the existence of general fluctuation-
dissipation relations, and for trajectories without event horizons,
correlation-propagation relations, which succinctly encapsulate these quantum
statistical phenomena. These findings serve to clarify some existing confusions
in the accelerated detector problem. The general methodology presented here
could also serve as a platform to explore the quantum statistical properties of
particles and fields, with practical applications in atomic and optical physics
problems.Comment: 32 pages, Late
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