399 research outputs found
Planck Fluctuations, Measurement Uncertainties and the Holographic Principle
Starting from a critical analysis of recently reported surprisingly large
uncertainties in length and position measurements deduced within the framework
of quantum gravity, we embark on an investigation both of the correlation
structure of Planck scale fluctuations and the role the holographic hypothesis
is possibly playing in this context. While we prove the logical independence of
the fluctuation results and the holographic hypothesis (in contrast to some
recent statements in that direction) we show that by combining these two topics
one can draw quite strong and interesting conclusions about the fluctuation
structure and the microscopic dynamics on the Planck scale. We further argue
that these findings point to a possibly new and generalized form of quantum
statistical mechanics of strongly (anti)correlated systems of degrees of
freedom in this fundamental regime.Comment: 19 pages, Latex, no figures, some new references, to appear
ModPhysLett
Topological features of massive bosons on two dimensional Einstein space-time
In this paper we tackle the problem of constructing explicit examples of
topological cocycles of Roberts' net cohomology, as defined abstractly by
Brunetti and Ruzzi. We consider the simple case of massive bosonic quantum
field theory on the two dimensional Einstein cylinder. After deriving some
crucial results of the algebraic framework of quantization, we address the
problem of the construction of the topological cocycles. All constructed
cocycles lead to unitarily equivalent representations of the fundamental group
of the circle (seen as a diffeomorphic image of all possible Cauchy surfaces).
The construction is carried out using only Cauchy data and related net of local
algebras on the circle.Comment: 41 pages, title changed, minor changes, typos corrected, references
added. Accepted for publication in Ann. Henri Poincare
Unitary Positive-Energy Representations of Scalar Bilocal Quantum Fields
The superselection sectors of two classes of scalar bilocal quantum fields in
D>=4 dimensions are explicitly determined by working out the constraints
imposed by unitarity. The resulting classification in terms of the dual of the
respective gauge groups U(N) and O(N) confirms the expectations based on
general results obtained in the framework of local nets in algebraic quantum
field theory, but the approach using standard Lie algebra methods rather than
abstract duality theory is complementary. The result indicates that one does
not lose interesting models if one postulates the absence of scalar fields of
dimension D-2 in models with global conformal invariance. Another remarkable
outcome is the observation that, with an appropriate choice of the Hamiltonian,
a Lie algebra embedded into the associative algebra of observables completely
fixes the representation theory.Comment: 27 pages, v3: result improved by eliminating redundant assumptio
A geometrical origin for the covariant entropy bound
Causal diamond-shaped subsets of space-time are naturally associated with
operator algebras in quantum field theory, and they are also related to the
Bousso covariant entropy bound. In this work we argue that the net of these
causal sets to which are assigned the local operator algebras of quantum
theories should be taken to be non orthomodular if there is some lowest scale
for the description of space-time as a manifold. This geometry can be related
to a reduction in the degrees of freedom of the holographic type under certain
natural conditions for the local algebras. A non orthomodular net of causal
sets that implements the cutoff in a covariant manner is constructed. It gives
an explanation, in a simple example, of the non positive expansion condition
for light-sheet selection in the covariant entropy bound. It also suggests a
different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio
Massive Vector Mesons and Gauge Theory
We show that the requirements of renormalizability and physical consistency
imposed on perturbative interactions of massive vector mesons fix the theory
essentially uniquely. In particular physical consistency demands the presence
of at least one additional physical degree of freedom which was not part of the
originally required physical particle content. In its simplest realization
(probably the only one) these are scalar fields as envisaged by Higgs but in
the present formulation without the ``symmetry-breaking Higgs condensate''. The
final result agrees precisely with the usual quantization of a classical gauge
theory by means of the Higgs mechanism. Our method proves an old conjecture of
Cornwall, Levin and Tiktopoulos stating that the renormalization and
consistency requirements of spin=1 particles lead to the gauge theory structure
(i.e. a kind of inverse of 't Hooft's famous renormalizability proof in
quantized gauge theories) which was based on the on-shell unitarity of the
-matrix. We also speculate on a possible future ghostfree formulation which
avoids ''field coordinates'' altogether and is expected to reconcile the
on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.
Developed turbulence: From full simulations to full mode reductions
Developed Navier-Stokes turbulence is simulated with varying wavevector mode
reductions. The flatness and the skewness of the velocity derivative depend on
the degree of mode reduction. They show a crossover towards the value of the
full numerical simulation when the viscous subrange starts to be resolved. The
intermittency corrections of the scaling exponents of the pth order velocity
structure functions seem to depend mainly on the proper resolution of the
inertial subrange. Universal scaling properties (i.e., independent of the
degree of mode reduction) are found for the relative scaling exponents rho
which were recently defined by Benzi et al.Comment: 4 pages, 5 eps-figures, replaces version from August 5th, 199
Tidal controls on the flow of ice streams
The flow of many Antarctic ice streams is known to be significantly influenced by tides. In the past, modeling studies have implemented the tidal forces acting on a coupled ice stream/ice shelf system in a number of different ways, but the consequences that this has on the modeled response of ice streams to tides have, until now, not been considered. Here we investigate for the first time differences in model response that are only due to differences in the way tidal forcings are implemented. We find that attempts to simplify the problem by neglecting flexural stresses are generally not valid and forcing models with only changes in ocean back pressure will not capture either the correct amplitudes or length scale
Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory
A summary of some lines of ideas leading to model-independent frameworks of
relativistic quantum field theory is given. It is followed by a discussion of
the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki
modular objects associated with the quantum field vacuum state and certain
algebras of observables. The distillability concept, which is significant in
specifying useful entanglement in quantum information theory, is discussed
within the setting of general relativistic quantum field theory.Comment: 26 pages. Contribution for the Proceedings of a Conference on Special
Relativity held at Potsdam, 200
Hyperentangled States
We investigate a new class of entangled states, which we call
'hyperentangled',that have EPR correlations identical to those in the vacuum
state of a relativistic quantum field. We show that whenever hyperentangled
states exist in any quantum theory, they are dense in its state space. We also
give prescriptions for constructing hyperentangled states that involve an
arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review
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