3,835 research outputs found
N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -
We investigate particular models which can be N-fold supersymmetric at
specific values of a parameter in the Hamiltonians. The models to be
investigated are a periodic potential and a parity-symmetric sextic triple-well
potential. Through the quantitative analyses on the non-perturbative
contributions to the spectra by the use of the valley method, we show how the
characteristic features of N-fold supersymmetry which have been previously
reported by the authors can be observed. We also clarify the difference between
quasi-exactly solvable and quasi-perturbatively solvable case in view of the
dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX
Eighth-Order Vacuum-Polarization Function Formed by Two Light-by-Light-Scattering Diagrams and its Contribution to the Tenth-Order Electron g-2
We have evaluated the contribution to the anomalous magnetic moment of the
electron from six tenth-order Feynman diagrams which contain eighth-order
vacuum-polarization function formed by two light-by-light scattering diagrams
connected by three photons. The integrals are constructed by two different
methods. In the first method the subtractive counter terms are used to deal
with ultraviolet (UV) singularities together with the requirement of
gauge-invariance. In the second method, the Ward-Takahashi identity is applied
to the light-by-light scattering amplitudes to eliminate UV singularities.
Numerical evaluation confirms that the two methods are consistent with each
other within their numerical uncertainties. Combining the two results
statistically and adding small contribution from the muons and/or tau leptons,
we obtain . We also evaluated the
contribution to the muon from the same set of diagrams and found .Comment: 27 page
Fuzzy Algebrae of the General Kaehler Coset Space G/H\otimesU(1)^k
We study the fuzzy structure of the general Kaehler coset space
G/S\otimes{U(1)}^k deformed by the Fedosov formalism. It is shown that the
Killing potentials satisfy the fuzzy algebrae working in the Darboux
coordinates.Comment: 8 pages, LaTex, no figur
Proper Eighth-Order Vacuum-Polarization Function and its Contribution to the Tenth-Order Lepton g-2
This paper reports the Feynman-parametric representation of the
vacuum-polarization function consisting of 105 Feynman diagrams of the eighth
order, and its contribution to the gauge-invariant set called Set I(i) of the
tenth-order lepton anomalous magnetic moment. Numerical evaluation of this set
is carried out using FORTRAN codes generated by an automatic code generation
system gencodevpN developed specifically for this purpose. The contribution of
diagrams containing electron loop to the electron g-2 is 0.017 47 (11)
(alpha/pi)^5. The contribution of diagrams containing muon loop is 0.000 001 67
(3) (alpha/pi)^5. The contribution of tau-lepton loop is negligible at present.
The sum of all these terms is 0.017 47 (11) (alpha/pi)^5. The contribution of
diagrams containing electron loop to the muon g-2 is 0.087 1 (59) (alpha/pi)^5.
That of tau-lepton loop is 0.000 237 (1) (alpha/pi)^5. The total contribution
to a_mu, the sum of these terms and the mass-independent term, is 0.104 8 (59)
(alpha/pi)^5.Comment: 48 pages, 6 figures. References are correcte
Loop Variables and Gauge Invariant Interactions - I
We describe a method of writing down interacting equations for all the modes
of the bosonic open string. It is a generalization of the loop variable
approach that was used earlier for the free, and lowest order interacting
cases. The generalization involves, as before, the introduction of a parameter
to label the different strings involved in an interaction. The interacting
string has thus becomes a ``band'' of finite width. The interaction equations
expressed in terms of loop variables, has a simple invariance that is exact
even off shell. A consistent definition of space-time fields requires the
fields to be functions of all the infinite number of gauge coordinates (in
addition to space time coordinates). The theory is formulated in one higher
dimension, where the modes appear massless. The dimensional reduction that is
needed to make contact with string theory (which has been discussed earlier for
the free case) is not discussed here.Comment: 40 pages, Latex. Revised version: some typos corrected. Final version
to appear in Int. J. of Mod. Phys.
Equal-Spin Pairing State of Superfluid He in Aerogel
The equal-spin pairing (ESP) state, the so-called A-like phase, of superfluid
He in aerogels is studied theoretically in the Ginzburg-Landau (GL) region
by examining thermodynamics, and the resulting equilibrium phase diagram is
mapped out. We find that, among the ABM, planar, and robust pairing states, the
ABM state with presumably quasi long-ranged superfluid order is the best
candidate of the A-like phase with a strange lowering of the polycritical point
(PCP) observed experimentally.Comment: 4 pages, 1 figure, one reference added, accepted for publication in
Phys. Rev.
Generalized exclusion statistics and degenerate signature of strongly interacting anyons
We show that below the degenerate temperature the distribution profiles of
strongly interacting anyons in one dimension coincide with the most probable
distributions of ideal particles obeying generalized exclusion statistics
(GES). In the strongly interacting regime the thermodynamics and the local
two-particle correlation function derived from the GES are seen to agree for
low temperatures with the results derived for the anyon model using the
thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a
continuous range of GES, providing a signature of strongly interacting anyons,
including the strongly interacting one-dimensional Bose gas.Comment: 7 pages, 3 figures, expanded versio
Thermodynamic Geometry of Fractional Statistics
We extend our earlier study about the fractional exclusion statistics to
higher dimensions in full physical range and in the non-relativistic and
ultra-relativistic limits. Also, two other fractional statistics, namely
Gentile and Polychronakos fractional statistics, will be considered and
similarities and differences between these statistics will be explored.
Thermodynamic geometry suggests that a two dimensional Haldane fractional
exclusion gas is more stable than higher dimensional gases. Also, a complete
picture of attractive and repulsive statistical interaction of fractional
statistics is given. For a special kind of fractional statistics, by
considering the singular points of thermodynamic curvature, we find a
condensation for a non-pure bosonic system which is similar to the
Bose-Einstein condensation and the phase transition temperature will be worked
out.Comment: 29 pages, 12 figure
Revised value of the eighth-order electron g-2
The contribution to the eighth-order anomalous magnetic moment (g-2) of the
electron from a set of diagrams without closed lepton loops is recalculated
using a new FORTRAN code generated by an automatic code generator. Comparing
the contributions of individual diagrams of old and new calculations, we found
an inconsistency in the old treatment of infrared subtraction terms in two
diagrams. Correcting this error leads to the revised value -1.9144 (35)
(alpha/pi)^4 for the eighth-order term. This theoretical change induces the
shift of the inverse of the fine structure constant by -6.41180(73)x10^{-7}.Comment: 4 pages, 1 figure, typo is correcte
- …