4,295 research outputs found
Path-Integral for Quantum Tunneling
Path-integral for theories with degenerate vacua is investigated. The origin
of the non Borel-summability of the perturbation theory is studied. A new
prescription to deal with small coupling is proposed. It leads to a series,
which at low orders and small coupling differs from the ordinary perturbative
series by nonperturbative amount, but is Borel-summable.Comment: 25 pages + 12 figures (not included, but available upon request) [No
changed in content in this version. Problem with line length fixed.
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
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
Dynamical Generation of Non-Abelian Gauge Group via the Improved Perturbation Theory
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has
three phases and that in one of them a non-Abelian gauge symmetry is
dynamically generated. The analysis was at the one-loop level around a
classical solution of fuzzy sphere type. We obtain evidences that three phases
are indeed realized as nonperturbative vacua by using the improved perturbation
theory. It also gives a good example that even if we start from a trivial
vacuum, the improved perturbation theory around it enables us to observe
nontrivial vacua.Comment: 31 pages, published versio
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
Vortex core transitions in superfluid 3He in globally anisotropic aerogels
Core structures of a single vortex in A-like and B-like phases of superfluid
3He in uniaxially compressed and stretched aerogels are studied by numerically
solving Ginzburg-Landau equations derived microscopically. It is found that,
although any uniaxial deformation leads to a wider A-like phase with the axial
pairing in the pressure-temperature phase diagram, the vortex core states in
the two phases in aerogel depend highly on the type of deformation. In a
compressed aerogel, the first-order vortex core transition (VCT) previously
seen in the bulk B phase appears at any pressure in the B-like phase while no
strange vortex core is expected in the corresponding A-like phase. By contrast,
in a stretched aerogel, the VCT in the B-like phase is lost while another VCT
is expected to occur between a nonunitary core and a polar one in the A-like
phase. Experimental search for these results is hoped to understand correlation
between superfluid 3He and aerogel structure.Comment: 7 pages, 6 figures Text was changed. Resubmitted versio
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
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