Search results for "Invariant"
showing 10 items of 783 documents
Bridges, channels and Arnold's invariants for generic plane curves
2002
Abstract We define sums of plane curves that generalize the idea of connected sum and show how Arnol'd's invariants behave with respect to them. We also consider the inverse process of decomposition of a curve and as an application, obtain a new method that reduces considerably the amounts of computation involved in the calculation of Arnold's invariants.
Quantum moment maps and invariants for G-invariant star products
2002
We study a quantum moment map and propose an invariant for $G$-invariant star products on a $G$-transitive symplectic manifold. We start by describing a new method to construct a quantum moment map for $G$-invariant star products of Fedosov type. We use it to obtain an invariant that is invariant under $G$-equivalence. In the last section we give two simple examples of such invariants, which involve non-classical terms and provide new insights into the classification of $G$-invariant star products.
A closed formula for the evaluation of foams
2020
International audience; We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov-Rozansky link homology categorifying the sl(N) link polynomial. We also provide connections to the equivariant cohomology rings of partial flag varieties.
Lévy flights and Lévy-Schrödinger semigroups
2010
We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.
NUMERICAL IMPLEMENTATION OF A K.A.M. ALGORITHM
1993
We discuss a numerical implementation of a K.A.M. algorithm to determine invariant tori, for systems that are quadratic in the action variables. The method has the advantage that the iteration procedure does not produce higher order terms in the actions, allowing thus a systematic control of the convergence.
On a possible origin of quantum groups
1991
A Poisson bracket structure having the commutation relations of the quantum group SLq(2) is quantized by means of the Moyal star-product on C∞(ℝ2), showing that quantum groups are not exactly quantizations, but require a quantization (with another parameter) in the background. The resulting associative algebra is a strongly invariant nonlinear star-product realization of the q-algebra Uq(sl(2)). The principle of strong invariance (the requirement that the star-commutator is star-expressed, up to a phase, by the same function as its classical limit) implies essentially the uniqueness of the commutation relations of Uq(sl(2)).
Observation of an Anomalous Line Shape of theη′π+π−Mass Spectrum near thepp¯Mass Threshold inJ/ψ→γη′π+π−
2016
Using 1.09 x 10(9) J/psi events collected by the BESIII experiment in 2012, we study the J / psi -> gamma eta'pi(+)pi(-) process and observe a significant abrupt change in the slope of the eta'pi(+)pi(-) invariant mass distribution at the proton-antiproton (p (p) over bar) mass threshold. We use two models to characterize the eta'pi(+)pi(-) line shape around 1.85 GeV/c(2): one that explicitly incorporates the opening of a decay threshold in the mass spectrum (Flatte formula), and another that is the coherent sum of two resonant amplitudes. Both fits show almost equally good agreement with data, and suggest the existence of either a broad state around 1.85 GeV/c(2) with strong couplings to t…
Definition of theΔmass and width
2007
In the framework of effective field theory we show that, at two-loop order, the mass and width of the $\ensuremath{\Delta}$ resonance defined via the (relativistic) Breit-Wigner parametrization both depend on the choice of field variables. In contrast, the complex-valued position of the pole of the propagator is independent of this choice.
QCD sum rule analysis of the pentaquark
2005
We perform a QCD sum rule calculation to determine the mass and the parity of the lowest lying pentaquark state. We include operators up to dimension $d=13$ in the OPE and the direct instanton contributions. We find evidence for a positive parity state. The contribution from operators of dimension $d>5$ is instrumental in determining the parity of the state and achieving the convergence of the sum rule.
Search forB0→ϕ(K+π−)decays with largeK+π−invariant mass
2007
Motivated by the polarization anomaly in the B→ (1020)K*(892) decay, we extend our search for other K* final states in the decay B0→ (1020)K*0 with the K*0→K+π- invariant mass above 1.6 GeV. The final states considered include the K*(1680)0, K3*(1780)0, K4*(2045)0, and a Kπ spin-zero nonresonant component. We also search for B0→ D0 decay with the same final state. The analysis is based on a sample of about 384×106 BB pairs recorded with the BABAR detector. We place upper limits on the branching fractions B(B0→ K*(1680)0)<3.5×10-6, B(B0→ K3*(1780)0) <2.7×10-6, B(B0→ K4*(2045)0)<15.3×10-6, and B(B0→ D0)<11.7×10-6 at 90% C.L. The nonresonant contribution is consistent with the measurements in …