The God has created a man in order that he creates that the God fails to do

Tuesday, 26 August 2014

Foundations of modern physics 6: Lagrangian formalism

Lagrangian formalism on fibre bundles is formulated in a strict mathematical way. Therefore, it can be applied, e. g. to classical field theory (#) and non-autonomous classical mechanics (#) where dynamic variables are sections of fibre bundles.

Let Y->X be a fibre bundle over an n-dimensional smooth manifold X. A Lagrangian density Ld^{n}x (or, simply, a Lagrangian) of order r is defined as an exterior n-form on the r-order jet manifold J^{r}Y of Y->X. A Lagrangian can be introduced as an element of the variational bicomplex of a differential graded algebra of exterior forms on jet manifolds of Y->X of all order. The coboundary operator of this bicomplex contains the variational operator which, acting on a Lagrangian, defines the associated Euler – Lagrange operator and the corresponding Euler – Lagrange equations.

First and second Noether theorems also are formulated. To study symmetries of a Lagrangian, one considers vector fields on a fibre bundle Y which are treated as infinitesimal generators of one-parameter groups of automorphisms of Y. Such a vector field u is called a symmetry of a Lagrangian L if the Lie derivative of L along u vanishes. In this case, the first Noether theorem leads to a conservation law of the corresponding symmetry current.


WikipediA: Lagrangian system

G. Sardanashvily, Five lectures on the jet manifolds in field theory, arXiv: hep-th/9411089

G.Sardanashvily, Fibre bundles, jet manifolds and Lagrangian theory. Lectures for theoreticians, arXiv: 0908.1886v1

Friday, 15 August 2014

What academic social networks are most popular?

What academic social networks are most popular? See the brilliant article: Richard van Norden, Online collaboration: Scientists and the social network, Nature 512 N7513 (2014) (#)

The results are summarized in the following diagram:

Saturday, 9 August 2014

Obituary Prof. Giovanni Giachetta, my colleague and co-author

I am sorry to inform that Prof. Giovanni Giachetta, my colleague and co-author of over 80 our common works and 4 monographs, passed away on the 6th August 2014.

Giovanni Giachetta  was born on the 12th May 1961 in Camerino (MC), Italy and passed away on the 6th August 2014 in San Severino Marche (MC).  He was an Associate Professor in mathematical physics at the University of Camerino, Italy. He has held this position since 2002.   His scientific interests covered a wide range of topics, including the application of Differential Geometry in Mathematical Physics, Classical Mechanics, Field Theory, Calculus of Variations, Symmetries and Conservation Laws. Author of over 100 papers and 4 monographs. Co-founder, Associate Editor (2003-2012) and a member of the Editorial Board of International Journal of Geometric Methods in Modern Physics.

Sunday, 3 August 2014

Impact Factor 2013 of Journals in Mathematical Physics

Impact Factor 2013 of the most authoritative Journals in Mathematical Physics

Journal Title