This section of Warehouse contains a wide variety of resources such as:Short Examples;Short Questions:Recall and Understanding Questions;Comprehension Check UpsWebQuestand many more, which do not fit into any other repository.These resources are meant to be mostly used as building blocks of other resources in Proofs. Each resource belongs to a definite topic of a definite area.This part of the tree hierarchy is the same as that used for all other repositories.
Miscelleaneous pages of quick reminder, need as prerequisite as some where else, will appear here
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.]
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