Supersymmetry series at TowardsTengen Friday, Jul 7 2006

Background: Nothing more than basic Quantum Mechanics, actually. Knowing a bit of QFT would be useful, but not essential.

I’m trying to write up a bit about what I’ve been doing, the first (badly written) installment is up here.  In case you check it out, let me know if there are any errors or mistakes.

Enjoy Physics …

Link Dump Friday, Jul 7 2006

This post is mainly a collection of a lot of nice links to Physics related resources. Enjoy! :

• Predrag Cvitanović:
• A nice couple of what the authour calls “webboks” are available here.

• African Summer Theory Institute:
• 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 …

• John Baez:
• 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!

• Mark Sredniki:
• 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.

Introduction to the Quantum theory of computation Friday, Apr 28 2006

Background : According to David Deutsch who gave these video lectures

This is a series of lectures designed to be used either

* as an introduction to the quantum theory of computation, by people intending to do research in the field; or
* as an introduction to quantum physics itself.

Very little knowledge of physics is assumed. Anyone who knows what a vector space is and what the eigenvalues of a matrix are will probably know enough mathematics to be able to follow the course.

I will just quote the site.

These lectures have a dual-use philosophy. They are designed to be an introduction to the quantum theory of computation for (say) graduate students intending to do research in the field.

Simultaneously, they are an introduction to quantum theory itself for (say) undergraduate physics students.

The links to the individual lectures are as follows.

Lecture 1: The Qubit
Introducing quantum theory, the quantum theory of computation, physical systems, observations, and the simplest quantum physical system,
the qubit.

Lecture 2: Interference Performing and analysing a single-photon interference experiment.

Lecture 3 : Measurement How to analyse pairs of interacting quantum systems.

Lecture 4 : The Schroedinger Picture Introducing the Schroedinger Picture, density matrices, state vectors, pure states and the Schroedinger equation.

Lecture 5 : A Quantum Algorithm The Deutsch Algorithm and how it works.

Lecture 6 : Grover’s Search Algorithm How to use quantum computation to search through N possibilities in a time proportional to the square root of N.

Deutsch has a very interesting perspective on Quantum mechanics ! So, even if you know quantum mechanics, you might just like to hear a different perspective.

Posted by : Loganayagam.R.(Tom)

Symmetry breaking Saturday, Apr 1 2006

Necessary Background: Not much as the article starts out at a sort of popular science level, but those of us doing Particle Physics now, may appreciate this a bit more.

Comment: This blog is quite interesting by the way, with a lot of interesting discussions by a few High energy and Astrophysics people, so check it out when you have the time at http://www.cosmicvariance.com/ or http://cosmicvariance.com/category/science/

Posted by: Shanth

Identical Particles Saturday, Apr 1 2006

This came up during a Particle Physics discussion :

Here is a proof that the wavefunction of n identical particles has to be either completely symmetric or anti-symmetric.

Wavefunction ψ=ψ(a1,a2,……..,an)

Let Pij be the operator which flips particles i and j

Now indistinguishability requires

Pijψ=c ψ

Since flipping twice results in the same wavefunction

Pij Pij ψ = ψ

Implies c=1 or -1

Now consider this relation

Pij=Pik Pkj Pki

One can easily veryify that this true by looking at the action of Pij on the ordrerd set (i,j,k).

Since Pik Pik=1

Pij=Pkj

Extending this simlarly one gets

Pij = Pik = Pkl for any k,l

Thus Pfg = c for all f,g

Thus the wavefunction has to be completely symmetric or antisymmetric.

Venkateshan

PS: I took the liberty of tidying up the notation, hope I didn't make any mistake/ change your argument. –Shanth

Does Position operator generate momentum Saturday, Apr 1 2006

$\langle x|p \rangle =e^{i\mathbf{p.x}}$

Consider

$U = e^{i\mathbf{X.p}}$ (Capitals for Operators)

$\langle x|e^{i\mathbf{X.p'}}|p\rangle= \int dx' \langle x|e^{i\mathbf{X.p'}}|x'\rangle \langle x'|p\rangle$

$= e^{i\mathbf{(p+p').x}}$ (skipped the delta function integ. step)

does this imply that position operator generates momentum?

Posted By : Venkateshan

Half-integral spins and Pauli exclusion Saturday, Apr 1 2006

Necessary Background : Basics of quantum statistics(bosons fermions and all that) , a bit of topology(basically knowing what the word homotopy means)and some geometric imagination.

half-integral spins and Pauli exclusion

Comment :
It is a kind of popular science explanation on why fermions obey Pauli’s principle

Posted By : Loganayagam.R.(Tom)

Do We Really Understand Quantum Mechanics ? Saturday, Apr 1 2006

Necessary Background : Basic ideas in quantum mechanics, Bra-Ket Notation and yeah interest in Interpretation of quantum mechanics,EPR, Wave-function collapse and stuff like that . 🙂

Do we really understand quantum mechanics?
Authors:
Franck Laloe (LKB – Lhomond)
Journal-ref:
American Journal of Physics 69 (2001) 655 – 701

Comment :
This is an article which appeared on AJP quite sometime ago. I think it does a good job of talking about various weird things which crop up in quantum theory. It’s quite loooong, but I guess depending on what your background and interests are, you can safely skip a lot of it.

So, tell me what do you think of this article. You can post any interesting link related to this subject in the comments below. By the way, for those who are not familiar to blogs, you can click the link below with “comments” written on it and leave your comments there.

And well, if you worry so much about your privacy that you don’t want to leave your name here (Horrors !) , then comment with name as anonymous , but do leave a valid e-mail(Say the iitk email) so that we among ourselves can figure out who is commenting. The email ID will not appear here – to see the email ids of the commenters one has to login using username+Passwd. We will soon try to come up with an About page How to post in this blog page with all such info.