74 research outputs found
Quantum Electrodynamics at Large Distances II: Nature of the Dominant Singularities
Accurate calculations of macroscopic and mesoscopic properties in quantum
electrodynamics require careful treatment of infrared divergences: standard
treatments introduce spurious large-distances effects. A method for computing
these properties was developed in a companion paper. That method depends upon a
result obtained here about the nature of the singularities that produce the
dominant large-distance behaviour. If all particles in a quantum field theory
have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on
the singularities of the scattering functions. These conditions are severely
weakened in quantum electrodynamics by effects of points where photon momenta
vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared
specifically to the pole-decomposition functions that dominate the macroscopic
behaviour in quantum electrodynamics, and leads to strong results for these
functions at points where photon momenta vanish.Comment: 40 pages, 11 encapsulated postscript figures, latexed,
math_macros.tex can be found on Archive. full postscript available from
http://theorl.lbl.gov/www/theorgroup/papers/35972.p
On the Singularities of the Magnon S-matrix
We investigate the analytic structure of the magnon S-matrix in the
spin-chain description of planar SUSY Yang-Mills/ strings. Semiclassical analysis suggests that the exact S-matrix must
have a large family of poles near the real axis in momentum space. In this
article we show that these are double poles corresponding to the exchange of
pairs of BPS magnons. Their locations in the complex plane are uniquely fixed
by the known dispersion relation for the BPS particles. The locations precisely
agree with the recent conjecture for the matrix by Beisert, Hernandez,
Lopez, Eden and Staudacher (hep-th/0609044 and hep-th/0610251). These poles do
not signal the presence of new bound states. In fact, a certain non-BPS
localized classical solution, which was thought to give rise to new bound
states, can actually decay into a pair of BPS magnons.Comment: 40 pages, 14 figures; typos corrected, references adde
Wedge-Local Quantum Fields and Noncommutative Minkowski Space
Within the setting of a recently proposed model of quantum fields on
noncommutative Minkowski spacetime, the consequences of the consistent
application of the proper, untwisted Poincare group as the symmetry group are
investigated. The emergent model contains an infinite family of fields which
are labelled by different noncommutativity parameters, and related to each
other by Lorentz transformations. The relative localization properties of these
fields are investigated, and it is shown that to each field one can assign a
wedge-shaped localization region of Minkowski space. This assignment is
consistent with the principles of covariance and locality, i.e. fields
localized in spacelike separated wedges commute.
Regarding the model as a non-local, but wedge-local, quantum field theory on
ordinary (commutative) Minkowski spacetime, it is possible to determine
two-particle S-matrix elements, which turn out to be non-trivial. Some partial
negative results concerning the existence of observables with sharper
localization properties are also obtained.Comment: Version to appear in JHEP, 27 page
Deformations of Fermionic Quantum Field Theories and Integrable Models
Considering the model of a scalar massive Fermion, it is shown that by means
of deformation techniques it is possible to obtain all integrable quantum field
theoretic models on two-dimensional Minkowski space which have factorizing
S-matrices corresponding to two-particle scattering functions S_2 satisfying
S_2(0) = -1. Among these models there is for example the Sinh-Gordon model. Our
analysis provides a complement to recent developments regarding deformations of
quantum field theories. The deformed model is investigated also in higher
dimensions. In particular, locality and covariance properties are analyzed.Comment: 20 page
Proposal to improve the behaviour of self-energy contributions to the S-matrix
A simple modification of the definition of the S-matrix is proposed. It is
expected that the divergences related to nonzero self-energies are considerably
milder with the modified definition than with the usual one. This conjecture is
verified in a few examples using perturbation theory. The proposed formula is
written in terms of the total Hamiltonian operator and a free Hamiltonian
operator and is therefore applicable in any case when these Hamiltonian
operators are known.Comment: 24 pages, 1 figure; v2: revised version; v3: section 3 improved.
Accepted for publication in Central European Journal of Physics; v4: minor
text misprints correcte
Four electrons in a two-leg Hubbard ladder: exact ground states
In the case of a two-leg Hubbard ladder we present a procedure which allows
the exact deduction of the ground state for the four particle problem in
arbitrary large lattice system, in a tractable manner, which involves only a
reduced Hilbert space region containing the ground state. In the presented
case, the method leads to nine analytic, linear, and coupled equations
providing the ground state. The procedure which is applicable to few particle
problems and other systems as well is based on an r-space representation of the
wave functions and construction of symmetry adapted orthogonal basis wave
vectors describing the Hilbert space region containing the ground state. Once
the ground state is deduced, a complete quantum mechanical characterization of
the studied state can be given. Since the analytic structure of the ground
state becomes visible during the use of the method, its importance is not
reduced only to the understanding of theoretical aspects connected to exact
descriptions or potential numerical approximation scheme developments, but is
relevant as well for a large number of potential technological application
possibilities placed between nano-devices and quantum calculations, where the
few particle behavior and deep understanding are important key aspects to know.Comment: 19 pages, 5 figure
Area distribution of the planar random loop boundary
We numerically investigate the area statistics of the outer boundary of
planar random loops, on the square and triangular lattices. Our Monte Carlo
simulations suggest that the underlying limit distribution is the Airy
distribution, which was recently found to appear also as area distribution in
the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
Integrable models: from dynamical solutions to string theory
We review the status of integrable models from the point of view of their
dynamics and integrability conditions. Some integrable models are discussed in
detail. We comment on the use it is made of them in string theory. We also
discuss the Bethe Ansatz solution of the SO(6) symmetric Hamiltonian with SO(6)
boundary.
This work is especially prepared for the seventieth anniversaries of
Andr\'{e} Swieca (in memoriam) and Roland K\"{o}berle.Comment: 24 pages, to appear in Brazilian Journal of Physic
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