16,846 research outputs found
-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions
Nonlocal quantum theory of one-component scalar field in -dimensional
Euclidean spacetime is studied in representations of -matrix
theory for both polynomial and nonpolynomial interaction Lagrangians. The
theory is formulated on coupling constant in the form of an infrared smooth
function of argument for space without boundary. Nonlocality is given by
evolution of Gaussian propagator for the local free theory with ultraviolet
form factors depending on ultraviolet length parameter . By representation
of the -matrix in terms of abstract functional integral over
primary scalar field, the form of a grand canonical partition
function is found. And, by expression of -matrix in terms of the
partition function, the representation for in terms of basis
functions is obtained. Derivations are given for discrete case where basis
functions are Hermite functions, and for continuous case where basis functions
are trigonometric functions. The obtained expressions for the
-matrix are investigated within the framework of variational
principle based on Jensen inequality. Equations with separable kernels
satisfied by variational function are found and solved, yielding results
for both the polynomial theory and the nonpolynomial sine-Gordon
theory. A new definition of the -matrix is proposed to solve
additional divergences which arise in application of Jensen inequality for the
continuous case. Analytical results are illustrated numerically. For simplicity
of numerical calculation: the case is considered, and propagator for the
free theory is in the form of Gaussian function typically in the
Virton-Quark model. The formulation for nonlocal QFT in momentum space of
extra dimensions with subsequent compactification into physical spacetime is
discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and
plots edited, references and acknowledgments added; prepared for the special
issue of the journal Particles in memory of G.V. Efimo
Pion-Nucleon Phase Shifts in Heavy Baryon Chiral Perturbation Theory
We calculate the phase shifts in the pion-nucleon scattering using the heavy
baryon formalism. We consider phase shifts for the pion energy range of 140 to
MeV. We employ two different methods for calculating the phase shifts -
the first using the full third order calculation of the pion-nucleon scattering
amplitude and the second by including the resonances and as
explicit degrees of freedom in the Lagrangian. We compare the results of the
two methods with phase shifts extracted from fits to the pion-nucleon
scattering data. We find good to fair agreement between the calculations and
the phase shifts from scattering data.Comment: 14 pages, Latex, 6figures. Revised version to appear in Phys.Rev.
Topics in Chiral Perturbation Theory
I consider some selected topics in chiral perturbation theory (CHPT). For the
meson sector, emphasis is put on processes involving pions in the isospin zero
S-wave which require multi-loop calculations. The advantages and shortcomings
of heavy baryon CHPT are discussed. Some recent results on the structure of the
baryons are also presented.Comment: 30 pp, TeX, Review talk, Third Workshop on High Energy Particle
Physics (WHEPP III), Madras, India, January 1994. 7 figures available upon
request. CRN--94/0
Predictions for Polarized-Beam/Vector-Polarized-Target Observables in Elastic Compton Scattering on the Deuteron
Motivated by developments at HIGS at TUNL that include increased photon flux
and the ability to circularly polarize photons, we calculate several
beam-polarization/target-spin dependent observables for elastic Compton
scattering on the deuteron. This is done at energies of the order of the pion
mass within the framework of Heavy Baryon Chiral Perturbation Theory. Our
calculation is complete to O(Q^3) and at this order there are no free
parameters. Consequently, the results reported here are predictions of the
theory. We discuss paths that may lead to the extraction of neutron
polarizabilities. We find that the photon/beam polarization asymmetry is not a
good observable for the purpose of extracting \alpha_n and \beta_n. However,
one of the double polarization asymmetries, \Sigma_x, shows appreciable
sensitivity to \gamma_{1n} and could be instrumental in pinning down the
neutron spin polarizabilities.Comment: 26 pages, 13 figures, revised version to be published in PR
Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion
Nonlocal QFT of one-component scalar field in -dimensional
Euclidean spacetime is considered. The generating functional (GF) of complete
Green functions as a functional of external source , coupling
constant , and spatial measure is studied. An expression for GF
in terms of the abstract integral over the primary field
is given. An expression for GF in terms of integrals
over the primary field and separable Hilbert space (HS) is obtained by means of
a separable expansion of the free theory inverse propagator over the
separable HS basis. The classification of functional integration measures
is formulated, according to which trivial and
two nontrivial versions of GF are obtained. Nontrivial versions
of GF are expressed in terms of -norm and -norm,
respectively. The definition of the -norm generator is suggested.
Simple cases of sharp and smooth generators are considered. Expressions for GF
in terms of integrals over the separable HS with new integrands
are obtained. For polynomial theories and for
the nonpolynomial theory , integrals over the separable HS in
terms of a power series over the inverse coupling constant for
both norms (-norm and -norm) are calculated. Critical values of model
parameters when a phase transition occurs are found numerically. A
generalization of the theory to the case of the uncountable integral over HS is
formulated. A comparison of two GFs , one in the case of
uncountable HS integral and one obtained using the Parseval-Plancherel
identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared
for the special issue "QCD and Hadron Structure" of the journal Particles;
v3: minimal corrections; v4: paragraphs added related to Reviewer comment
Chiral phase transition in lattice QCD as a metal-insulator transition
We investigate the lattice QCD Dirac operator with staggered fermions at
temperatures around the chiral phase transition. We present evidence of a
metal-insulator transition in the low lying modes of the Dirac operator around
the same temperature as the chiral phase transition. This strongly suggests the
phenomenon of Anderson localization drives the QCD vacuum to the chirally
symmetric phase in a way similar to a metal-insulator transition in a
disordered conductor. We also discuss how Anderson localization affects the
usual phenomenological treatment of phase transitions a la Ginzburg-Landau.Comment: 7 pages, 6 figures, references added, typos corrected, journal
versio
Towards an understanding of isospin violation in pion-nucleon scattering
We investigate isospin breaking in low-energy pion-nucleon scattering in the
framework of chiral perturbation theory. This work extends the systematic
analysis of [1] to the energy range above threshold. Various relations, which
identically vanish in the limit of isospin symmetry, are used to quantify
isospin breaking effects. We study the energy dependence of the S- and P-wave
projections of these ratios and find dramatic effects in the S-waves of those
two relations which are given in terms of isoscalar quantities only. This
effect drops rather quickly with growing center-of-mass energy.Comment: 12 pp, REVTeX, 8 figs, FZJ-IKP(TH)-2000-2
On the number of Mather measures of Lagrangian systems
In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact
the minimizers of a "universal" infinite dimensional linear programming
problem. This fundamental result has many applications, one of the most
important is to the estimates of the generic number of Mather measures.
Ma\~n\'e obtained the first estimation of that sort by using finite dimensional
approximations. Recently, we were able with Gonzalo Contreras to use this
method of finite dimensional approximation in order to solve a conjecture of
John Mather concerning the generic number of Mather measures for families of
Lagrangian systems. In the present paper we obtain finer results in that
direction by applying directly some classical tools of convex analysis to the
infinite dimensional problem. We use a notion of countably rectifiable sets of
finite codimension in Banach (and Frechet) spaces which may deserve independent
interest
Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory
By means of the Inverse Amplitude Method we unitarize the elastic
pion-nucleon scattering amplitudes obtained from Heavy Baryon Chiral
Perturbation Theory to O(q^3). Within this approach we can enlarge their
applicability range and generate the Delta(1232) resonance. We can find a
reasonable description of the pion nucleon phase shifts with (q^2) parameters
in agreement with the resonance saturation hypothesis. However, the
uncertainties in the analysis of the low energy data as well as the large
number of chiral parameters, which can have strong correlations, allow us to
obtain very good fits with rather different sets of chiral constants.Comment: Shortened version to appear in Phys. Rev. D. Brief Report
The Space Station Photovoltaic Panels Plasma Interaction Test Program: Test plan and results
The Plasma Interaction Test performed on two space station solar array panels is addressed. This includes a discussion of the test requirements, test plan, experimental set-up, and test results. It was found that parasitic current collection was insignificant (0.3 percent of the solar array delivered power). The measured arcing threshold ranged from -210 to -457 V with respect to the plasma potential. Furthermore, the dynamic response of the panels showed the panel time constant to range between 1 and 5 microsec, and the panel capacitance to be between .01 and .02 microF
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