I found a School website containing lecture notes on various topics in condensed matter, so thought of posting here:
Most of it look quite well organized for independent reading.
Previous post reminded me of one link I wanted to post earlier but somehow forgot:
Geometry and Topology for Physicists
I think these are quite a gem.
As the webpage says: “No particular mathematics background is required beyond that usually expected of graduate students in physics (linear algebra, complex analysis, etc), but it will help if you have some familiarity with mathematical notation and ways of thinking”.
Prereq. : Varies. But, I guess some amount of “math-maturity” and interest can take one far. 😉
Some good mathematical books written by sternberg. The books available are
* Theory of Functions of real variable (2 Meg PDF)
* Advanced Calculus (58 Meg PDF)
* Dynamical systems (1 Meg PDF)
* Lie Algebras (900 K PDF)
* Geometric Asymptotics (AMS Books online)
* Semiriemannian Geometry (1 Meg PDF)
And over here, you can see a list with names of many math books.
This post is mainly a collection of a lot of nice links to Physics related resources. Enjoy! :
A nice couple of what the authour calls “webboks” are available here.
Online, available video lectures, on QFT, Quantum mechanics, Supersymmetry etc. It really is a wonder, why these aren’t more popular. They are available here
And the best for the last …
Baez is a mathematical physicist at the university of California. He writes a weekly column on This Week’s Finds in mathematical Physics. Wonderfully written, and a really nice source of information of all sorts. This may require a little bit of maths, but he writes in a lucid and interesting way that even if you’re in your first year, UG, you will definitely learn something from each article, and the good news is there are archives going back to around 200 weeks!
This is a nice QFT book, it’s available online now, soon, it’s going to be taken off after it is published in print, so hurry and get your copy now! [Thanks to Tarun, for pointing this on out]. I’ve seen this once earlier, and it seemed really nice, especially has a nice section on spinors, and dotted & undotted indices, unless I’m confusing it with something else.
Martinus Veltman, Recipient of 1999 Nobel Prize in Physics
Via Amar, I came to know of a treasure-trove of web lectures named 2001- A Spacetime odyssey. As far as the required background is concerned , I guess it is one of those things where nothing is reallly sufficient 😉
These web lectures are a part of a web-lecture archive. To quote
The Web Lecture Archive Project is a joint venture between the UM-ATLAS Collaboratory Project, the University of Michigan Media Union, and CERN, the European Laboratory for Particle Physics. Its goal is to implement this electronic archival system for slide-based presentations on the Internet.
Actually, there are much more material in that site than you might realise at first glance. Try for example , The CERN Academic Training lectures(2000) which is a kind of overview of particle physics. Especially, have a look at the lecture titled An Introduction to Field theory by Kleiss. You can find the lecture notes for these lectures here. I guess the required background is some amount of quantum mechanics, though I might be wrong…..
Then, there is the lecture by Veltman at CERN just after his Nobel prize. And there are some presentations by undergraduates at University of Michigan as a part of undergraduate research programme there.
The last but not the least is of course a series of popular science lectures called saturday morning physics at U.Mich. I especially loved the lecture titled
Quantum Tornadoes Near Absolute Zero by Paul Haljan. If you haven’ t seen it already, you should definitely see it. After all, it’s a popular science lecture so it should be accessible to everyone.
And this is Paul Haljan for you
And by the way, in case you didn’t notice, this is the first post at blogphysica by an IITK alumni 😉 Happy Summer Holidays , everybody !
(The above figure shows the three fundamental moves that one can use in Knot theory to see whether two knots are equivalent.)
Background : Well, Knot theory is an interesting part of mathematical physics with a lot of applications in diverse fields. It does not fit directly into the standard curriculum for the five basic themes of undergrad-theoretical-physics ( Classical, Quantum, Statistical, Field theoretic and Mathematical methods) .
So, this is just for fun – and like many other things in life done for fun , you should be open-minded enough to learn new things as you go along. I can’t guarantee that you would understand everything here ( partly because I don’t understand everything and mainly because nobody understands everything 😉 ), but it is fun if you like it.
Note that Knot theory to start with does not require much background in physics ( It is afterall a branch of topology and so much of the required background is from the math side ). But, if you really want to see some beautiful ways Knot theory enters physics, you should have a background in Quantum field theory( in particular some familiarity with Feynman’s diagrammatic way of doing perturbation theory and path integrals at the level of say Quantum Field Theory in a Nutshell by A. Zee) .
As always, if you have no idea what Knot theory is about, you can do no better than start off with the article on Knot theory from Wikipedia and then proceed to different sites which talk about knot theory Then there is a site which has enough links to keep you busy throughout the summers 🙂 This should give you an idea of what is this all about.
If you are not in mood for all this stuff, then you might like to read some stories ! Here is an interesting article titled Scottish Physics and Knot Theory’s Odd Origins which talks about the history of knot theory and how Kelvin invented it for modelling vortices in ether 🙂 It talks about the role played by Maxwell, Kelvin and Tait(He is a mathematician who is supposed to have invented dimples in the golf ball ;)) in Knot theory. A bit more serious article is A brief history of knot theory which I got from here.
Now, for some serious stuff. This is A Knot Theory Primer. See also Knot Knotes by J.D.Roberts which I found at this site having lots of good books on physics and math( I am thinking of a separate post for that site, so that people don’t miss it ). You can also see a short course by Kauffman.
Ok, I’ve come so far and I’ve not even come to the QFT applications of Knot theory many of which go under the name of Witten. Since, this post has already become so long, I will just point you to an AJP article before I finish.
Knots and physics: Old wine in new bottles
(Should be accessible inside IITK)
Allen C. Hirshfeld
Physics Department, The University of Dortmund, D-44221 Dortmund, Germany
(Received 3 July 1997; accepted 15 May 1998)
The history of the interplay between physics and mathematics in the theory of knots is briefly reviewed. In particular, Gauss’ original definition of the linking number in the context of electromagnetism is presented, along with analytical, algebraical, and geometrical derivations. In a modern context, the linking number appears in the first-order term in the perturbation expansion of a Wilson loop in Chern–Simons quantum field theory. New knot invariants, the Vassiliev numbers, arise in higher-order terms of the expansion, and can be written in a form which shows them to be generalizations of the linking number. ©1998 American Association of Physics Teachers.
Update(10/5) : Ok, I give in to temptation. I can’t just leave a post on Knot theory without talking more about its relations with Topological Quantum Field theories. One of the landmark papers in this field is of course Witten’s Quantum field theory and the Jones polynomial. But, since it is a bit high-brow stuff, it is better to start with an article on that paper. ( you can also see a talk by Witten where he talks about the period when this paper was written.) By the way, If I remember correctly, it is this paper which led to Witten’s Field’s medal…
Try your hands at “Quantum Topology and Quantum Computing”, by Kauffman and “Quantum Topology and the Jones Polynomial”, by Kauffman . Lots of pages in the first paper are devoted to introducing quantum mechanics so you can just skip it if you feel like it.
Background: These are some immensely useful notes on many things that are not quantum. It should be useful to everyone.
These are the lecture notes for a course offered by Kip.S.Thorne at Caltech. They cover a wide range of topics in a beautiful way. I am just giving here the chapter names so that you can get an idea.
Chapter 1: Physics in Euclidean Space and Flat Spacetime: Geometric Viewpoint
Chapter 2: Kinetic Theory
Chapter 3: Statistical Mechanics
Chapter 4: Statistical Thermodynamics
Chapter5: Random Processes
Chapter6: Geometric Optics
Chapter 7: Diffraction
Chapter 8: Interference
Chapter 9: Nonlinear Optics
Chapter 10: Elastostatics
Chapter 11: Elastodynamics
Chapter 12: Foundations of Fluid Dynamics
Chapter 13: Vorticity
Chapter 14: Turbulence
Chapter 15: Waves and Rotating Flows
Chapter 15: Waves and Rotating Flows [
Chapter 16: Compressible and Supersonic Flow
Chapter 17: Convection
Chapter 18: Magnetohydrodynamics
Chapter 19: Particle Kinetics of Plasma
Chapter 20: Waves in Cold Plasmas: Two-Fluid Formalism
Chapter 21: Kinetic Theory of Warm Plasmas
Chapter 22: Nonlinear Dynamics of Plasmas
Chapter 23: From Special to General Relativity
Chapter 24: Fundamental Concepts of General Relativity
Chapter 25: Stars and Black Holes
Chapter 26: Gravitational Waves and Experimental Tests of General Relativity
Chapter 27: Cosmology
Appendix A: Concept-Based Outline of Book
Appendix B: Some Unifying Concepts
Posted by : Loganayagam.R,
Background : Some amount of Quantum Field theory would help. Though the article doesnot go very much deep into quantum field theory as such, it is a bit difficult to understand the context of renormalisation, if you’ ve not seen it either in field theory or statistical mechanics.
A hint of renormalization
Authors: B. Delamotte
Comments: 17 pages, pedagogical article
Subj-class: High Energy Physics – Theory; Statistical Mechanics
Journal-ref: Am.J.Phys. 72 (2004) 170-184
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what is specific to field theory and what is intrinsic to renormalization. We link the general arguments and results to real phenomena encountered in particle physics and statistical mechanics.
The abstract says it all. And yeah, all the best for endsems everyone 🙂
Update : See also
Per Kraus and David J. Griffiths
Physics Department, Reed College, Portland, Oregon 97202
(Received 9 December 1991; accepted 30 April 1992)
Renormalization is the technique used to eliminate infinities that arise in quantum field theory. This paper shows how to renormalize a particularly simple model, in which a single mass counterterm of second order in the coupling constant suffices to cancel all divergences. The model serves as an accessible introduction to Feynman diagrams, covariant perturbation theory, and dimensional regularization, as well as the renormalization procedure itself. ©1992 American Association of Physics Teachers
Posted by : Loganayagam.R.(Tom)
Background : I guess this should be useful for all. Bookmark this links – even if you think it is above your level now, at some point of time you might find it very useful.
Link : THE NET ADVANCE OF PHYSICS
Review Articles and Tutorials in an Encyclopædic Format
Well, the name says it all. it is an MIT site.(Well, I am thinking of sitting down and creating a collection like that over here in this blog. Any help would be welcome…). These are some review articles and tutorials in physics arranged alphabetically – often very useful especially when you are doing termpapers 😉
Do have a look at the special review on condensed matter physics. It is quite a comprehensive collection of review articles in condensed matter physics.
Posted by : Loganayagam.R.(Tom)