1,436 research outputs found
Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II
In the first part, we have constructed several families of interacting
wedge-local nets of von Neumann algebras. In particular, there has been
discovered a family of models based on the endomorphisms of the U(1)-current
algebra of Longo-Witten.
In this second part, we further investigate endomorphisms and interacting
models. The key ingredient is the free massless fermionic net, which contains
the U(1)-current net as the fixed point subnet with respect to the U(1) gauge
action. Through the restriction to the subnet, we construct a new family of
Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting
wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the
structure of particle numbers and the S-matrices of the models constructed here
do mix the spaces with different particle numbers of the bosonic Fock space.Comment: 33 pages, 1 tikz figure. The final version is available under Open
Access. CC-B
On the equivalence of two deformation schemes in quantum field theory
Two recent deformation schemes for quantum field theories on the
two-dimensional Minkowski space, making use of deformed field operators and
Longo-Witten endomorphisms, respectively, are shown to be equivalent.Comment: 14 pages, no figure. The final version is available under Open
Access. CC-B
Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations
Using appropriate harmonics, we study the future asymptotic behavior of
massless scalar fields on a class of cosmological vacuum spacetimes. The
spatial manifold is assumed to be a circle bundle over a higher genus surface
with a locally homogeneous metric. Such a manifold corresponds to the
SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III
type). After a technical preparation including an introduction of suitable
harmonics for the circle-fibered Bianchi VIII to separate variables, we derive
systems of ordinary differential equations for the scalar field. We present
future asymptotic solutions for these equations in a special case, and find
that there is a close similarity with those on the circle-fibered Bianchi III
spacetime. We discuss implications of this similarity, especially to
(gravitational) linear perturbations. We also point out that this similarity
can be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi
Ground state representations of loop algebras
Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in
S^1 and identifying the real line with the punctured circle, we consider the
subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the
translation-invariant 2-cocycles on Sg. We show that the ground state
representation of Sg is unique for each cocycle. These ground states correspond
precisely to the vacuum representations of Lg.Comment: 22 pages, no figur
A model independent and rephase invariant parametrization of CP violation
The phenomenological description of the neutral B meson system is proposed in
terms of the fundamental CP-violating observables and within a rephasing
invariant formalism. This generic formalism can select the time-dependent and
time-integrated asymmetries which provide the basic tools to discriminate the
different kinds of possible CP-violating effects in dedicated experimental
B-meson facilities.Comment: 19 pages, Plain Te
A Universal Intrinsic Scale of Hole Concentration for High-Tc Cuprates
We have measured thermoelectric power (TEP) as a function of hole
concentration per CuO2 layer, Ppl, in Y1-xCaxBa2Cu3O6 (Ppl = x/2) with no
oxygen in the Cu-O chain layer. The room-temperature TEP as a function of Ppl,
S290(Ppl), of Y1-xCaxBa2Cu3O6 behaves identically to that of La2-zSrzCuO4 (Ppl
= z). We argue that S290(Ppl) represents a measure of the intrinsic equilibrium
electronic states of doped holes and, therefore, can be used as a common scale
for the carrier concentrations of layered cuprates. We shows that the Ppl
determined by this new universal scale is consistent with both hole
concentration microscopically determined by NQR and the hole concentration
macroscopically determined by the Cu valency. We find two characteristic
scaling temperatures, TS* and TS2*, in the TEP vs. temperature curves that
change systematically with doping. Based on the universal scale, we uncover a
universal phase diagram in which almost all the experimentally determined
pseudogap temperatures as a function of Ppl fall on two common curves; upper
pseudogap temperature defined by the TS* versus Ppl curve and lower pseudogap
temperature defined by the TS2* versus Ppl curve. We find that while pseudogaps
are intrinsic properties of doped holes of a single CuO2 layer for all high-Tc
cuprates, Tc depends on the number of layers, therefore the inter-layer
coupling, in each individual system.Comment: 11 pages, 9 figures, accepted for publication in Physical Review
Democratic Neutrino Mixing and Radiative Corrections
The renormalization effect on a specific ansatz of lepton mass matrices,
arising naturally from the breaking of flavor democracy for charged leptons and
that of mass degeneracy for light neutrinos, is studied from a superhigh energy
scale M_0 \sim 10^{13} GeV to the electroweak scale in the framework of the
minimal supersymmetric standard model. We find that the democratic neutrino
mixing pattern obtained from this ansatz may in general be instable against
radiative corrections. With the help of similar flavor symmetries we prescribe
a slightly different scheme of lepton mass matrices at the scale M_0, from
which the democratic mixing pattern of lepton flavors can be achieved, after
radiative corrections, at the experimentally accessible scales.Comment: RevTex 8 pages. Phys. Rev. D (in printing
Asymptotic completeness in a class of massless relativistic quantum field theories
This paper presents the first examples of massless relativistic quantum field
theories which are interacting and asymptotically complete. These
two-dimensional theories are obtained by an application of a deformation
procedure, introduced recently by Grosse and Lechner, to chiral conformal
quantum field theories. The resulting models may not be strictly local, but
they contain observables localized in spacelike wedges. It is shown that the
scattering theory for waves in two dimensions, due to Buchholz, is still valid
under these weaker assumptions. The concepts of interaction and asymptotic
completeness, provided by this theory, are adopted in the present
investigation.Comment: 15 pages, LaTeX. As appeared in Communications in Mathematical
Physic
Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics
We show examples which reveal influences of spatial topologies to dynamics,
using a class of spatially {\it closed} inhomogeneous cosmological models. The
models, called the {\it locally U(1)U(1) symmetric models} (or the {\it
generalized Gowdy models}), are characterized by the existence of two commuting
spatial {\it local} Killing vectors. For systematic investigations we first
present a classification of possible spatial topologies in this class. We
stress the significance of the locally homogeneous limits (i.e., the Bianchi
types or the `geometric structures') of the models. In particular, we show a
method of reduction to the natural reduced manifold, and analyze the
equivalences at the reduced level of the models as dynamical models. Based on
these fundamentals, we examine the influence of spatial topologies on dynamics
by obtaining translation and reflection operators which commute with the
dynamical flow in the phase space.Comment: 32 pages, 1 figure, LaTeX2e, revised Introduction slightly. To appear
in CQ
Mathematics Indicates That an HIV-Style Strategy Could Be Applied to Manage the Coronavirus
We have learned to live with many potentially deadly viruses for which there
is no vaccine, no immunity, and no cure. We do not live in constant fear of
these viruses, instead, we have learned how to outsmart them and reduce the
harm they cause. A new mathematical model that combines the spread of diseases
that do not confer immunity together with the evolution of human behaviors
indicates that we may be able to fight new diseases with the same type of
strategy we use to fight viruses like HIV.Comment: This article is available open access online here:
https://link.springer.com/chapter/10.1007%2F16618_2020_2
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