IN LOW DIMENSIONS
To the Reader
These Lectures are arranged in
the form of a Hypertext. This means that, in parallel
to the plane text with usual formulae, tables and figures, it contais LINKS to different
material which plays the role of either a prerequisite, the Reader must know, or an extension.
The reader, therefore, has an opportunity to refresh his/her knowledge of the material, which
has no real relation to these lectures, or to develope the knowledge some further.
Before beginning to study the
subject, check whether you are in full command of the
Prerequisites, which include Quantum Mechanics in the Feynman's Path Integral formulation,
Quantum Statistical Mechanics (or the Matsubara Technology), and Quantum Kinetics ( or the
Keldysh's Technology ) . You will also need to master the Coherent States Path Integral
for Bosons and Fermions. Don't get discouraged if any (or all) these words sound not
familiar to you. Go to the Prerequisites section, read it, don't forget to visit the Problems
section to obtain a practice. Do this and come back to the main material. If, in the course
of your study, you meet a difficulty with any other subject: ordinary crystallography,
group theory, topology, renormalisation group or anything else - look at a useful link, go
to the relevant section, don't forget to practice with the problems, return back and enjoy
Studying Many Body Physcs at
Low Dimensions, it is very useful, some times, to recall the
lessons of the Many Body Theory in 3 Dimensional Space. You can find a brief reminder of
these lessons in the Prerequisites section.
Beninning a jorney through the
country of Reduced dimensions, the traveller, quite
naturally, would like to learn what are the key differences from conventional 3D World
one could expect en route. We are going to discuss these general differences in the
Introduction. Another aim of the Introduction is to give a brief description of Geography
of the World of Reduced dimensions, i.e. to tell about typical physical systems which
provide the playground for the physics of reduced dimensions.
The lectures suppose to cover
a lot of material. Nevertheless, the lecturer, quite often,
cannot afford many digressions from the straight path. As the result, quite pitifully, some
real gems slip away. The reader can find them presented in Appendices tho the Lectures.
These seems to be all the words
of preparation, and we may now begin the journeys.