908 research outputs found
When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?
In this work we investigate the question, under what conditions Hilbert
spaces that are induced by measures on the space of generalized connections
carry a representation of certain non-Abelian analogues of the electric flux.
We give the problem a precise mathematical formulation and start its
investigation. For the technically simple case of U(1) as gauge group, we
establish a number of "no-go theorems" asserting that for certain classes of
measures, the flux operators can not be represented on the corresponding
Hilbert spaces.
The flux-observables we consider play an important role in loop quantum
gravity since they can be defined without recourse to a background geometry,
and they might also be of interest in the general context of quantization of
non-Abelian gauge theories.Comment: LaTeX, 21 pages, 5 figures; v3: some typos and formulations
corrected, some clarifications added, bibliography updated; article is now
identical to published versio
Pairwise wave interactions in ideal polytropic gases
We consider the problem of resolving all pairwise interactions of shock
waves, contact waves, and rarefaction waves in 1-dimensional flow of an ideal
polytropic gas. Resolving an interaction means here to determine the types of
the three outgoing (backward, contact, and forward) waves in the Riemann
problem defined by the extreme left and right states of the two incoming waves,
together with possible vacuum formation. This problem has been considered by
several authors and turns out to be surprisingly involved. For each type of
interaction (head-on, involving a contact, or overtaking) the outcome depends
on the strengths of the incoming waves. In the case of overtaking waves the
type of the reflected wave also depends on the value of the adiabatic constant.
Our analysis provides a complete breakdown and gives the exact outcome of each
interaction.Comment: 39 page
Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model
Generalized universality, as recently proposed, postulates a universal
non-Gaussian form of the probability density function (PDF) of certain global
observables for a wide class of highly correlated systems of finite volume N.
Studying the 2D XY -model, we link its validity to renormalization group
properties. It would be valid if there were a single dimension 0 operator, but
the actual existence of several such operators leads to T-dependent
corrections. The PDF is the Fourier transform of the partition function Z(q) of
an auxiliary theory which differs by a dimension 0 perturbation with a very
small imaginary coefficient iq/N from a theory which is asymptotically free in
the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).Comment: To be published in Phys. Rev.
A transition in the spectrum of the topological sector of theory at strong coupling
We investigate the strong coupling region of the topological sector of the
two-dimensional theory. Using discrete light cone quantization (DLCQ),
we extract the masses of the lowest few excitations and observe level
crossings. To understand this phenomena, we evaluate the expectation value of
the integral of the normal ordered operator and we extract the number
density of constituents in these states. A coherent state variational
calculation confirms that the number density for low-lying states above the
transition coupling is dominantly that of a kink-antikink-kink state. The
Fourier transform of the form factor of the lowest excitation is extracted
which reveals a structure close to a kink-antikink-kink profile. Thus, we
demonstrate that the structure of the lowest excitations becomes that of a
kink-antikink-kink configuration at moderately strong coupling. We extract the
critical coupling for the transition of the lowest state from that of a kink to
a kink-antikink-kink. We interpret the transition as evidence for the onset of
kink condensation which is believed to be the physical mechanism for the
symmetry restoring phase transition in two-dimensional theory.Comment: revtex4, 14 figure
Markov quantum fields on a manifold
We study scalar quantum field theory on a compact manifold. The free theory
is defined in terms of functional integrals. For positive mass it is shown to
have the Markov property in the sense of Nelson. This property is used to
establish a reflection positivity result when the manifold has a reflection
symmetry. In dimension d=2 we use the Markov property to establish a sewing
operation for manifolds with boundary circles. Also in d=2 the Markov property
is proved for interacting fields.Comment: 14 pages, 1 figure, Late
The numerical study of the solution of the model
We present a numerical study of the nonlinear system of equations
of motion. The solution is obtained iteratively, starting from a precise
point-sequence of the appropriate Banach space, for small values of the
coupling constant. The numerical results are in perfect agreement with the main
theoretical results established in a series of previous publications.Comment: arxiv version is already officia
Trees, forests and jungles: a botanical garden for cluster expansions
Combinatoric formulas for cluster expansions have been improved many times
over the years. Here we develop some new combinatoric proofs and extensions of
the tree formulas of Brydges and Kennedy, and test them on a series of
pedagogical examples.Comment: 37 pages, Ecole Polytechnique A-325.099
- …