8,709 research outputs found
Existence results for mean field equations
Let be an annulus. We prove that the mean field equation
-\Delta\psi=\frac{e\sp{-\beta\psi}}{\int\sb{\Omega}e\sp{-\beta\psi}} admits
a solution with zero boundary for . This is a
supercritical case for the Moser-Trudinger inequality.Comment: Filling a gap in the argument and adding 2 referrence
Analytical results for O(\alpha_s) radiative corrections to e+ e- -> tbar t(pol.) up to a given gluon energy cut
We determine the O(\alpha_s) radiative corrections to polarized top quark
pair production in e+ e- -annihilations with a specified gluon energy cut. We
write down fully analytical results for the unpolarized and polarized
O(\alpha_s) cross sections e+ e- -> tbar t (G) and e+ e- -> tbar t(pol.) (G)
including their polar orientation dependence relative to the beam direction. In
the soft gluon limit we recover the usual factorizing form known from the soft
gluon approximation. In the limit when the gluon energy cut takes its maximum
value we recover the totally inclusive unpolarized and polarized cross sections
calculated previously. We provide some numerical results on the cut-off
dependence of the various polarized and unpolarized cross sections and discuss
how the exact results numerically differ from the approximate soft-gluon
results.Comment: 49 pages in LaTeX, including 17 encapsulated PostScript figure
CPT Violation Implies Violation of Lorentz Invariance
An interacting theory that violates CPT invariance necessarily violates
Lorentz invariance. On the other hand, CPT invariance is not sufficient for
out-of-cone Lorentz invariance. Theories that violate CPT by having different
particle and antiparticle masses must be nonlocal.Comment: Minor changes in the published versio
Extrapolation of K to \pi\pi decay amplitude
We examine the uncertainties involved in the off-mass-shell extrapolation of
the decay amplitude with emphasis on those aspects that
have so far been overlooked or ignored. Among them are initial-state
interactions, choice of the extrapolated kaon field, and the relation between
the asymptotic behavior and the zeros of the decay amplitude. In the inelastic
region the phase of the decay amplitude cannot be determined by strong
interaction alone and even its asymptotic value cannot be deduced from
experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell
values of hadronic matrix elements in general. Though we are hampered with
complexity of intermediate-energy meson interactions, we attempt to obtain a
quantitative idea of the uncertainties due to the inelastic region and find
that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE
Optimal Topological Test for Degeneracies of Real Hamiltonians
We consider adiabatic transport of eigenstates of real Hamiltonians around
loops in parameter space. It is demonstrated that loops that map to nontrivial
loops in the space of eigenbases must encircle degeneracies. Examples from
Jahn-Teller theory are presented to illustrate the test. We show furthermore
that the proposed test is optimal.Comment: Minor corrections, accepted in Phys. Rev. Let
KMS, etc
A general form of the ``Wick rotation'', starting from imaginary-time Green
functions of quantum-mechanical systems in thermal equilibrium at positive
temperature, is established. Extending work of H. Araki, the role of the KMS
condition and of an associated anti-unitary symmetry operation, the ``modular
conjugation'', in constructing analytic continuations of Green functions from
real- to imaginary times, and back, is clarified.
The relationship between the KMS condition for the vacuum with respect to
Lorentz boosts, on one hand, and the spin-statistics connection and the PCT
theorem, on the other hand, in local, relativistic quantum field theory is
recalled.
General results on the reconstruction of local quantum theories in various
non-trivial gravitational backgrounds from ``Euclidian amplitudes'' are
presented. In particular, a general form of the KMS condition is proposed and
applied, e.g., to the Unruh- and the Hawking effects.
This paper is dedicated to Huzihiro Araki on the occasion of his seventieth
birthday, with admiration, affection and best wishes.Comment: 56 pages, submitted to J. Math. Phy
Modelling the mid-Pliocene Warm Period climate with the IPSL coupled model and its atmospheric component LMDZ5A
This paper describes the experimental design and model results of the climate simulations of the mid-Pliocene Warm Period (mPWP, ca. 3.3–3 Ma) using the Institut Pierre Simon Laplace model (IPSLCM5A), in the framework of the Pliocene Model Intercomparison Project (PlioMIP). We use the IPSL atmosphere ocean general circulation model (AOGCM), and its atmospheric component alone (AGCM), to simulate the climate of the mPWP. Boundary conditions such as sea surface temperatures (SSTs), topography, ice-sheet extent and vegetation are derived from the ones imposed by the Pliocene Model Intercomparison Project (PlioMIP), described in Haywood et al. (2010, 2011). We first describe the IPSL model main features, and then give a full description of the boundary conditions used for atmospheric model and coupled model experiments. The climatic outputs of the mPWP simulations are detailed and compared to the corresponding control simulations. The simulated warming relative to the control simulation is 1.94 °C in the atmospheric and 2.07 °C in the coupled model experiments. In both experiments, warming is larger at high latitudes. Mechanisms governing the simulated precipitation patterns are different in the coupled model than in the atmospheric model alone, because of the reduced gradients in imposed SSTs, which impacts the Hadley and Walker circulations. In addition, a sensitivity test to the change of land-sea mask in the atmospheric model, representing a sea-level change from present-day to 25 m higher during the mid-Pliocene, is described. We find that surface temperature differences can be large (several degrees Celsius) but are restricted to the areas that were changed from ocean to land or vice versa. In terms of precipitation, impact on polar regions is minor although the change in land-sea mask is significant in these areas
Representation of Markov chains by random maps: existence and regularity conditions
We systematically investigate the problem of representing Markov chains by
families of random maps, and which regularity of these maps can be achieved
depending on the properties of the probability measures. Our key idea is to use
techniques from optimal transport to select optimal such maps. Optimal
transport theory also tells us how convexity properties of the supports of the
measures translate into regularity properties of the maps via Legendre
transforms. Thus, from this scheme, we cannot only deduce the representation by
measurable random maps, but we can also obtain conditions for the
representation by continuous random maps. Finally, we present conditions for
the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including
extended discussion of many detail
Why is CPT fundamental?
G. L\"uders and W. Pauli proved the theorem based on
Lagrangian quantum field theory almost half a century ago. R. Jost gave a more
general proof based on ``axiomatic'' field theory nearly as long ago. The
axiomatic point of view has two advantages over the Lagrangian one. First, the
axiomatic point of view makes clear why is fundamental--because
it is intimately related to Lorentz invariance. Secondly, the axiomatic proof
gives a simple way to calculate the transform of any
relativistic field without calculating , and
separately and then multiplying them. The purpose of this
pedagogical paper is to ``deaxiomatize'' the theorem by
explaining it in a few simple steps. We use theorems of distribution theory and
of several complex variables without proof to make the exposition elementary.Comment: 17 pages, no figure
String-- and Brane--Localized Causal Fields in a Strongly Nonlocal Model
We study a weakly local, but nonlocal model in spacetime dimension
and prove that it is maximally nonlocal in a certain specific quantitative
sense. Nevertheless, depending on the number of dimensions , it has
string--localized or brane--localized operators which commute at spatial
distances. In two spacetime dimensions, the model even comprises a covariant
and local subnet of operators localized in bounded subsets of Minkowski space
which has a nontrivial scattering matrix. The model thus exemplifies the
algebraic construction of local observables from algebras associated with
nonlocal fields.Comment: paper re-written with a change of emphasis and new result
- …