26 research outputs found
Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems
We derive the sampling probability density function (pdf) of an ideal
localized random electromagnetic field, its amplitude and intensity in an
electromagnetic environment that is quasi-statically time-varying statistically
homogeneous or static statistically inhomogeneous. The results allow for the
estimation of field statistics and confidence intervals when a single spatial
or temporal stochastic process produces randomization of the field. Results for
both coherent and incoherent detection techniques are derived, for Cartesian,
planar and full-vectorial fields. We show that the functional form of the
sampling pdf depends on whether the random variable is dimensioned (e.g., the
sampled electric field proper) or is expressed in dimensionless standardized or
normalized form (e.g., the sampled electric field divided by its sampled
standard deviation). For dimensioned quantities, the electric field, its
amplitude and intensity exhibit different types of
Bessel sampling pdfs, which differ significantly from the asymptotic
Gauss normal and ensemble pdfs when is relatively
small. By contrast, for the corresponding standardized quantities, Student ,
Fisher-Snedecor and root- sampling pdfs are obtained that exhibit
heavier tails than comparable Bessel pdfs. Statistical uncertainties
obtained from classical small-sample theory for dimensionless quantities are
shown to be overestimated compared to dimensioned quantities. Differences in
the sampling pdfs arising from de-normalization versus de-standardization are
obtained.Comment: 12 pages, 15 figures, accepted for publication in Phys. Rev. E, minor
typos correcte
Index theorem for topological excitations on R^3 * S^1 and Chern-Simons theory
We derive an index theorem for the Dirac operator in the background of
various topological excitations on an R^3 \times S^1 geometry. The index
theorem provides more refined data than the APS index for an instanton on R^4
and reproduces it in decompactification limit. In the R^3 limit, it reduces to
the Callias index theorem. The index is expressed in terms of topological
charge and the eta-invariant associated with the boundary Dirac operator.
Neither topological charge nor eta-invariant is typically an integer, however,
the non-integer parts cancel to give an integer-valued index. Our derivation is
based on axial current non-conservation--an exact operator identity valid on
any four-manifold--and on the existence of a center symmetric, or approximately
center symmetric, boundary holonomy (Wilson line). We expect the index theorem
to usefully apply to many physical systems of interest, such as low temperature
(large S^1, confined) phases of gauge theories, center stabilized Yang-Mills
theories with vector-like or chiral matter (at S^1 of any size), and
supersymmetric gauge theories with supersymmetry-preserving boundary conditions
(also at any S^1). In QCD-like and chiral gauge theories, the index theorem
should shed light into the nature of topological excitations responsible for
chiral symmetry breaking and the generation of mass gap in the gauge sector. We
also show that imposing chirally-twisted boundary condition in gauge theories
with fermions induces a Chern-Simons term in the infrared. This suggests that
some QCD-like gauge theories should possess components with a topological
Chern-Simons phase in the small S^1 regime.Comment: 29 pages, refs added, published versio
Geometric Aspects of Confining Strings
Confining strings in 4D are effective, thick strings describing the
confinement phase of compact U(1) and, possibly, also non-Abelian gauge fields.
We show that these strings are dual to the gauge fields, inasmuch as their
perturbative regime corresponds to the strong coupling (large e) regime of the
gauge theory. In this regime they describe smooth surfaces with long-range
correlations and Hausdorff dimension two. For lower couplings e and monopole
fugacities z, a phase transition takes place, beyond which the smooth string
picture is lost. On the critical line intrinsic distances on the surface
diverge and correlators vanish, indicating that world-sheets become fractal.Comment: 19 pages, 4 figures, harvma
Monopole Condensation and Antisymmetric Tensor Fields: Compact QED and the Wilsonian RG Flow in Yang-Mills Theories
A field theoretic description of monopole condensation in strongly coupled
gauge theories is given by actions involving antisymmetric tensors B_{\mu\nu}
of rank 2. We rederive the corresponding action for 4d compact QED, summing
explicitly over all possible monopole configurations. Its gauge symmetries and
Ward identities are discussed. Then we consider the Wilsonian RGs for
Yang-Mills theories in the presence of collective fields (again tensors
B_{\mu\nu}) for the field strengths F_{\mu \nu} associated to the U(1)
subgroups. We show that a ``vector-like'' Ward identity for the Wilsonian
action involving B_{\mu\nu}, whose validity corresponds to monopole
condensation, constitutes a fixed point of the Wilsonian RG flow.Comment: 18 pages (LaTeX2e), 1 fi
Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field
The spin coherent state path integral describing the dynamics of a
spin-1/2-system in a magnetic field of arbitrary time-dependence is considered.
Defining the path integral as the limit of a Wiener regularized expression, the
semiclassical approximation leads to a continuous minimal action path with
jumps at the endpoints. The resulting semiclassical propagator is shown to
coincide with the exact quantum mechanical propagator. A non-linear
transformation of the angle variables allows for a determination of the
semiclassical path and the jumps without solving a boundary-value problem. The
semiclassical spin dynamics is thus readily amenable to numerical methods.Comment: 16 pages, submitted to Journal of Physics
Strings with Negative Stiffness and Hyperfine Structure
We propose a new string model by adding a higher-order gradient term to the
rigid string, so that the stiffness can be positive or negative without loosing
stability. In the large-D approximation, the model has three phases, one of
which with a new type of generalized "antiferromagnetic" orientational
correlations. We find an infrared-stable fixed point describing world-sheets
with vanishing tension and Hausdorff dimension D_H=2. Crumpling is prevented by
the new term which suppresses configurations with rapidly changing extrinsic
curvature.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re27
The superstring Hagedorn temperature in a pp-wave background
The thermodynamics of type IIB superstring theory in the maximally
supersymmetric plane wave background is studied. We compute the thermodynamic
partition function for non-interacting strings exactly and the result differs
slightly from previous computations. We clarify some of the issues related to
the Hagedorn temperature in the limits of small and large constant RR 5-form.
We study the thermodynamic behavior of strings in the case of geometries in the presence of NS-NS and RR 3-form backgrounds. We
also comment on the relationship of string thermodynamics and the thermodynamic
behavior of the sector of Yang-Mills theory which is the holographic dual of
the string theory.Comment: 22 pages, JHEP style, minor misprints corrected, some comments adde
Photon mixing in universes with large extra-dimensions
In presence of a magnetic field, photons can mix with any particle having a
two-photon vertex. In theories with large compact extra-dimensions, there
exists a hierachy of massive Kaluza-Klein gravitons that couple to any photon
entering a magnetic field. We study this mixing and show that, in comparison
with the four dimensional situation where the photon couples only to the
massless graviton, the oscillation effect may be enhanced due to the existence
of a large number of Kaluza-Klein modes. We give the conditions for such an
enhancement and then investigate the cosmological and astrophysical
consequences of this phenomenon; we also discuss some laboratory experiments.
Axions also couple to photons in the same way; we discuss the effect of the
existence of bulk axions in universes with large extra-dimensions. The results
can also be applied to neutrino physics with extra-dimensions.Comment: 41 pages, LaTex, 6 figure
Infrared and ultraviolet asymptotic solutions to gluon and ghost propagators in Yang-Mills theory
We examine the possibility that there may exist a logarithmic correction to
the infrared asymptotic solution with power behavior which has recently been
found for the gluon and Faddeev-Popov ghost propagators in the Landau gauge. We
propose a new Ansatz to find a pair of solutions for the gluon and ghost form
factors by solving the coupled Schwinger-Dyson equation under a simple
truncation. This Ansatz enables us to derive the infrared and ultraviolet
asymptotic solutions simultaneously and to understand why the power solution
and the logarithmic solution is possible only in the infrared and ultraviolet
limit respectively. Even in the presence of the logarithmic correction, the
gluon propagator vanishes and the ghost propagator is enhanced in the infrared
limit, and the gluon-ghost-antighost coupling constant has an infrared fixed
point (but with a different function). This situation is consistent
with Gribov-Zwanziger confinement scenario and color confinement criterion of
Kugo and Ojima.Comment: 15 pages, 2 figures, version to appear in Phys. Lett.