No Arabic abstract
The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a single parameter algebra $SU_q(2)$. This fact gives some relations between $SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra. In this paper are mentioned the relations concerning: Casimir operators, eigenvectors, matrix elements, Clebsch Gordan coefficients and irreducible tensors.
We consider integrals $tau_{rho}=int_0^1rhoxi^2,dx$, where $xi$ is Wiener process and $rho$ is generalized function from some class of multipliers. In the case when multiplier $rho$ belongs to the trace-class, it is shown that $tau_{rho}$ has $chi^2$-distribution (or analogous). An example of multiplier $rho$ not belonging to the trace-class is constructed.
We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model.
The analysis of the LHCb data on $X(6900)$ found in the di-$jpsi$ system is performed using a momentum-dependent Flatt{e}-like parameterization. The use of the pole counting rule and spectral density function sum rule give consistent conclusions that both confining states and molecular states are possible, or it is unable to distinguish the nature of $X(6900)$, if only the di-$jpsi$ experimental data with current statistics are available. Nevertheless, we found that the lowest state in the di-$J/psi$ system has very likely the same quantum numbers as $X(6900)$, and $X(6900)$ is probably not interpreted as a $J/psi-psi(2S)$ molecular state.
Using techniques from motivic homotopy theory, we prove a conjecture of Anthony Blanc about semi-topological K-theory of dg categories with finite coefficients. Along the way, we show that the connective semi-topological K-theories defined by Friedlander-Walker and by Blanc agree for quasi-projective complex varieties and we study etale descent of topological K-theory of dg categories.
We propose a slight correction and a slight improvement on the main result contained in A lecture on Classical KAM Theorem by J. P{o}schel.