These notes are to accompany my talk on gauge xing in quantum eld theories (QFTs), and the mathematical tricks associated with this procedure. In Section 1 I will look at gauge xing for Abelian elds, considering the speci c case of the Maxwell theory describing photons. In Section 2 I consider a non-Abelian generalization of the Maxwell theory called Yang Mills theory, which describes vector bo...

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable rational systems with time-varying memoryless nonlinearities subject to sector conditions. The proposed suucient conditions are expressed in terms of easy-to-check Linear Matrix Inequalities , or under a frequency-domain form well-suited for robustness issues, and lead to simple graphical interp...

We consider robustness analysis of heterogeneous and homogeneous networked systems based on integral quadratic constraints (IQCs). First, we show how the analysis decomposes into lower dimensional problems if the interconnection structure is exploited. This generally leads to a significant reduction of the computational complexity. Secondly, by considering a set of IQCs that characterizes the e...

In a companion paper ('Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous-time theory'), Lyapunov functions were constructed in a unified framework to prove sufficiency in the small gain, positivity, circle, and Popov theorems. In this Part II, analogous results are develo...

This paper shows the existence of Lur’e-Postkinov Lyapunov functions for the generalized multivariable discrete-time Popov criterion. The nonlinearities in the Lur’e system considered here are monotonic, sectorand slope-restricted. We discuss the cases where the nonlinearities are diagonal and non-diagonal. Our derivation is based on the discrete-time Kalman-Yakubovich-Popov (KYP) lemma and the...

Some problems related to Gribov copies in lattice gauge-fixing and their possible solution are discussed. 1 Gribov and Gauge-Fixing Problem The Faddeev-Popov[1] quantization gives a meaning to the formal (euclidean) expectation value of a gauge invariant observable operator: 〈O〉 = ∫ δA exp[−S(A)] O(A) ∫ δA exp[−S(A)] (1) The Faddeev-Popov method requires the choice of a gauge fixing condition: ...

Université Paris Diderot (Paris 7), UFR de Mathématiques, case 7012 (Site Chevaleret), F–75205 Paris Cedex 13, France e-mail: [email protected], url: http://www.proba.jussieu.fr/∼comets Instituto de Matemática e Estat́ıstica, Universidade de São Paulo, rua do Matão 1010, CEP 05508–090, São Paulo SP, Brasil e-mail: [email protected], url: http://www.ime.usp.br/∼popov Forschungszentrum Jülich ...