1,438 research outputs found
Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
Fractional generalization of an exterior derivative for calculus of
variations is defined. The Hamilton and Lagrange approaches are considered.
Fractional Hamilton and Euler-Lagrange equations are derived. Fractional
equations of motion are obtained by fractional variation of Lagrangian and
Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
Quark loop contribution to \pi^0 \to 4\gamma
We find the contribution of constituent quark loop mechanism to the branching
ratio B_{4\gamma} = \Gamma_{4\gamma}/\Gamma_{4\gamma} \sim 5.45 \cdot 10^{-16}
for the reasonable choice of constituent quark mass m \sim 280 MeV. This result
is in agreement with vector-dominance approach result obtained years ago. Thus
the main contribution arises from QED mechanism \pi^0 \to \gamma (\gamma^*) \to
\gamma (3\gamma) including light-light scattering block with electron loop.
This contribution was investigated in paper of one of us and gave B_{4\gamma}
\sim 2.6 \cdot 10^{-11}.Comment: 7 pages, 2 figure
Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly
We present the results of analytical calculations of the 3-loop contributions
to the asymptotic photon vacuum polarization function, in the on shell scheme,
and of the 4-loop contributions to the on shell QED beta-function. These are
used to evaluate various 4-loop and 5-loop contributions to the muon anomaly.
Our analytical contributions to (g-2)_\mu differ significantly from previous
numerical results. A very recent numerical re-evaluation of 4-loop muon-anomaly
contributions has yielded results much closer to ours.Comment: LaTex, 11 pages, figures available from O.V.T. CERN--TH. 6602/92,
OUT--4102--39, BI--TP--92/3
Fractional Derivative as Fractional Power of Derivative
Definitions of fractional derivatives as fractional powers of derivative
operators are suggested. The Taylor series and Fourier series are used to
define fractional power of self-adjoint derivative operator. The Fourier
integrals and Weyl quantization procedure are applied to derive the definition
of fractional derivative operator. Fractional generalization of concept of
stability is considered.Comment: 20 pages, LaTe
Nonholonomic Constraints with Fractional Derivatives
We consider the fractional generalization of nonholonomic constraints defined
by equations with fractional derivatives and provide some examples. The
corresponding equations of motion are derived using variational principle.Comment: 18 page
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