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

Friday, 25 October 2013

Geometry of the composite bundles (from my Scientific Biography)

"The jet formalism, when I first met it, was quite developed in application to theory of differential operators and differential equations, differential geometry, and also, as I have already mentioned, in main aspects to Lagrangian formalism. It seemed that I as a theoretician should only apply it to the particular field models: gauge theory, gravitation theory, etc. However, I had to do develop a number of its basic issues: geometry of composite bundles, Lagrangian theory in formalism of a variational bicomplex, Noether identities and the second Noether theorem.

A composition of fibre bundles Y->S->X is called the composite bundle. They arise in a number of models of field theory and mechanics. In mechanics, these are models with parameters described by sections of a fibre bundle S->X. In field theory, they are systems with a background field and models with spontaneous symmetry breaking, e.g., gravitation theory, when sections of  a fibre bundle S->X are Higgs fields. A key point is that, if h is a section of a fibre bundle S->X, then the restriction of Y->S to a submanifold h(X) of S is a subbundle h*Y->X of a fibre bundle Y->X, describing a system in the presence of a background field (or a parametric function) h(X).

Using a relation between jet manifolds of fibre bundles Y->X, Y->S and S->X, I obtained that between connections on these bundles and, most importantly, the new differential operator on sections of a fibre bundle Y->S, called the vertical covariant differential determined by a connection A on Y->S. The fact is that, being restricted to h(X), this operator coincides with the familiar covariant differential yielded by the restriction of a connection A onto h*Y->X. Thus, this vertical covariant differential should appear in description of the dynamics of field systems on a composite bundle. This result was published in 1991 in the article [64] and was already used in the book [9] for description of spinors in a gravitational field. Subsequently, I have used it in different models of field theory and mechanics. One of them, the key to construct the gauge gravitation theory, is classical field theory with spontaneous symmetry breaking."


Monday, 14 October 2013

What is Nobel Prize in Physics 2013 for?

Nobel Prize in Physics 2013 is awarded to Fran├žois Englert and Peter Higgs "for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental  particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider".

A curios is that, in accordance with the Higgs mechanism of mass generation, quantum particles get a mass due to their interaction with a constant background Higgs field  responsible for spontaneous symmetry breaking, but not a quantum Higgs boson. This constant background Higgs field  is treated as a Higgs vacuum, whose physical origin however remains unclear. For instance, one thinks of it as being sue generis a condensate by analogy with a condensate of Cooper pairs in superconductivity.  

Thursday, 3 October 2013

Who is who among universities in 2013 by THE World University Rankings

New world ranking of universities "Times Higher Education World University Rankings 2013-2014" # has been published. It contains 400 universities.

The top ten positions are occupied by 7 universities of USA and the 3 ones of United Kingdom.

In the top twenty: 15 - USA, 3 - United Kingdom, 1 – Switzerland and Canada.

In the first 50 Universities: 29 – USA; 7 - United Kingdom; 3 – Canada; 2 – Switzerland, Australia and China; 1 - Hong-Kong, Japan, Sweden and Korea.