Browse & Filter

As the name  itself suggests, pages  in this heirarchy are Bits and Pieces of resources. Most of these are targets of links in other pages on this site and  also in pdf files distributed by email. Links may be  provided to students, and friends alike for quickly checking some points.

The contant of most of  resources will be obvious to the experts and also an experienced students

Some Bits and Pieces are collected to fill gaps left in text books and may serve useful purpose for a beginner. Many of these might be moved or removed completely in future.

The following (from notes for a lecture I was preparing) might help explain the context: The first gauge theory was Hermann Weyl's extension of Einstein's general theory of relativity with a parallel transport that can change the scale or 'gauge' of lengths of the transported vector. About this one can read in P. G. Bergman's book on Relativity. The Hamiltonian formulation of electrodynamics, and in particular, the replacement of \(\vec{p}\) by \(\vec{p}-e\vec{A}/c \) was given by Larmor in his book "Aether and Matter", Cambridge (1900). [quoted by Pauli in ''General Principles of Quantum Mechanics" , Section 4. (Tr. by P. Achuthan and K. Venkatesan of 1958 German edition) Allied, New Delhi 1980.] In quantum mechanics the 'canonical momentum' \(\vec{p}-e\vec{A}/c\) becomes \(-i\hbar[\nabla-ie\vec{A}/(\hbar c)]\). The gauge invariance of the Schrodinger theory under \(\vec{A}\to \vec{A}+\nabla f\) and \(\phi\to \phi-(e/c)\frac{\partial f}{\partial t} \) when \(\Psi\) is changed by a phase was first given by V. Fock (1927). The analogy of this group of transformations to the Weyl theory on gravitation and electricity was pointed out by F. London (1927). The connection of this group to charge conservation was pointed out by Weyl while writing variational principle for the wave equation. [See Pauli as above.]

Jacobi Action Principle
A Second Variational Principle for Conservative Systems

Hamilton.'s action principle in classical mechanics is widely taught. There is a lesser known, but important Jacobi principle which is like Fermat's principle for waves. This form of action principle  was used by Schrodinger to arrive at his hafous equation for qunatum mechanics of a point particles.