14,205 research outputs found
Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms
Hyperfine intervals in light hydrogenic atoms and ions are among the most
accurately measured quantities in physics. The theory of QED corrections has
recently advanced to the point that uncalculated terms for hydrogenic atoms and
ions are probably smaller than 0.1 parts per million (ppm), and the experiments
are even more accurate. The difference of the experiments and QED theory is
interpreted as the effect on the hyperfine interaction of the (finite) nuclear
charge and magnetization distributions, and this difference varies from tens to
hundreds of ppm. We have calculated the dominant component of the 1s hyperfine
interval for deuterium, tritium and singly ionized helium, using modern
second-generation potentials to compute the nuclear component of the hyperfine
splitting for the deuteron and the trinucleon systems. The calculated nuclear
corrections are within 3% of the experimental values for deuterium and tritium,
but are about 20% discrepant for singly ionized helium. The nuclear corrections
for the trinucleon systems can be qualitatively understood by invoking SU(4)
symmetry.Comment: 26 pages, 1 figure, latex - submitted to Physical Review
Calculating the Rest Tension for a Polymer of String Bits
We explore the application of approximation schemes from many body physics,
including the Hartree-Fock method and random phase approximation (RPA), to the
problem of analyzing the low energy excitations of a polymer chain made up of
bosonic string bits. We accordingly obtain an expression for the rest tension
of the bosonic relativistic string in terms of the parameters
characterizing the microscopic string bit dynamics. We first derive an exact
connection between the string tension and a certain correlation function of the
many-body string bit system. This connection is made for an arbitrary
interaction potential between string bits and relies on an exact dipole sum
rule. We then review an earlier calculation by Goldstone of the low energy
excitations of a polymer chain using RPA. We assess the accuracy of the RPA by
calculating the first order corrections. For this purpose we specialize to the
unique scale invariant potential, namely an attractive delta function potential
in two (transverse) dimensions. We find that the corrections are large, and
discuss a method for summing the large terms. The corrections to this improved
RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint,
UFIFT-HEP-94
Internet data packet transport: from global topology to local queueing dynamics
We study structural feature and evolution of the Internet at the autonomous
systems level. Extracting relevant parameters for the growth dynamics of the
Internet topology, we construct a toy model for the Internet evolution, which
includes the ingredients of multiplicative stochastic evolution of nodes and
edges and adaptive rewiring of edges. The model reproduces successfully
structural features of the Internet at a fundamental level. We also introduce a
quantity called the load as the capacity of node needed for handling the
communication traffic and study its time-dependent behavior at the hubs across
years. The load at hub increases with network size as .
Finally, we study data packet traffic in the microscopic scale. The average
delay time of data packets in a queueing system is calculated, in particular,
when the number of arrival channels is scale-free. We show that when the number
of arriving data packets follows a power law distribution, ,
the queue length distribution decays as and the average delay
time at the hub diverges as in the limit when , being the network degree
exponent.Comment: 5 pages, 4 figures, submitted to International Journal of Bifurcation
and Chao
The Algebras of Large N Matrix Mechanics
Extending early work, we formulate the large N matrix mechanics of general
bosonic, fermionic and supersymmetric matrix models, including Matrix theory:
The Hamiltonian framework of large N matrix mechanics provides a natural
setting in which to study the algebras of the large N limit, including
(reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We
find in particular a broad array of new free algebras which we call symmetric
Cuntz algebras, interacting symmetric Cuntz algebras, symmetric
Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the
role of these algebras in solving the large N theory. Most important, the
interacting Cuntz algebras are associated to a set of new (hidden) local
quantities which are generically conserved only at large N. A number of other
new large N phenomena are also observed, including the intrinsic nonlocality of
the (reduced) trace class operators of the theory and a closely related large N
field identification phenomenon which is associated to another set (this time
nonlocal) of new conserved quantities at large N.Comment: 70 pages, expanded historical remark
Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
We study the minimal unitary representation (minrep) of SO(4,2) over an
Hilbert space of functions of three variables, obtained by quantizing its
quasiconformal action on a five dimensional space. The minrep of SO(4,2), which
coincides with the minrep of SU(2,2) similarly constructed, corresponds to a
massless conformal scalar in four spacetime dimensions. There exists a
one-parameter family of deformations of the minrep of SU(2,2). For positive
(negative) integer values of the deformation parameter \zeta one obtains
positive energy unitary irreducible representations corresponding to massless
conformal fields transforming in (0,\zeta/2) ((-\zeta/2,0)) representation of
the SL(2,C) subgroup. We construct the supersymmetric extensions of the minrep
of SU(2,2) and its deformations to those of SU(2,2|N). The minimal unitary
supermultiplet of SU(2,2|4), in the undeformed case, simply corresponds to the
massless N=4 Yang-Mills supermultiplet in four dimensions. For each given
non-zero integer value of \zeta, one obtains a unique supermultiplet of
massless conformal fields of higher spin. For SU(2,2|4) these supermultiplets
are simply the doubleton supermultiplets studied in arXiv:hep-th/9806042.Comment: Revised with an extended introduction and additional references.
Typos corrected. 49 pages; Latex fil
Exact averages of central values of triple product L-functions
We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product L-function proved by Gross and Kudla
Perturbation Theory in Two Dimensional Open String Field Theory
In this paper we develop the covariant string field theory approach to open
2d strings. Upon constructing the vertices, we apply the formalism to calculate
the lowest order contributions to the 4- and 5- point tachyon--tachyon tree
amplitudes. Our results are shown to match the `bulk' amplitude calculations of
Bershadsky and Kutasov. In the present approach the pole structure of the
amplitudes becomes manifest and their origin as coming from the higher string
modes transparent.Comment: 26 page
High Spin Gauge Fields and Two-Time Physics
All possible interactions of a point particle with background
electromagnetic, gravitational and higher-spin fields is considered in the
two-time physics worldline formalism in (d,2) dimensions. This system has a
counterpart in a recent formulation of two-time physics in non-commutative
field theory with local Sp(2) symmetry. In either the worldline or field theory
formulation, a general Sp(2) algebraic constraint governs the interactions, and
determines equations that the background fields of any spin must obey. The
constraints are solved in the classical worldline formalism (h-bar=0 limit) as
well as in the field theory formalism (all powers of h-bar). The solution in
both cases coincide for a certain 2T to 1T holographic image which describes a
relativistic particle interacting with background fields of any spin in (d-1,1)
dimensions. Two disconnected branches of solutions exist, which seem to have a
correspondence as massless states in string theory, one containing low spins in
the zero Regge slope limit, and the other containing high spins in the infinite
Regge slope limit.Comment: LaTeX 22 pages. Typos corrected in version
Ratio of Tensions from Vacuum String Field Theory
We show analytically that the ratio of the norm of sliver states agrees with
the ratio of D-brane tensions. We find that the correct ratio appears as a
twist anomaly.Comment: 13 pages, lanlmac; version to appear in JHE
Difficulties in Inducing a Gauge Theory at Large N
It is argued that the recently proposed Kazakov-Migdal model of induced gauge
theory, at large , involves only the zero area Wilson loops that are
effectively trees in the gauge action induced by the scalars. This retains only
a constant part of the gauge action excluding plaquettes or anything like them
and the gauge variables drop out.Comment: 6 pages, Latex, AZPH-TH/93-01, COLO-HEP/30
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