Wednesday, October 7, 2009

Video Lecture Part 2 and 3

Today we had the video screening of Prof Shiraz Minwalla's String Theory Lecture Part 3 in the Physics Department. Naturally the number of people coming for the lectures has decreased a lot compared to the lecture part 1. In part 2 he talked about Weyl transformations $$ {g}_{\alpha \beta} \rightarrow e^{\phi} g_{\alpha \beta} $$ as well as reparameterization invariance and how we can use them to remove one degree of freedom from the world-sheet metric and write it as $ g_{\alpha \beta} = \eta_{\alpha \beta} $ where $ \eta $ is the Minkowski metric. Then he showed how to write the action in light-cone world sheet coordinates. Then he used the constraints as well as reparameterization invariance in the light-cone world sheet coordinates to remove two degrees of freedom which results in D-2 modes of oscillations.

Today's lecture (part 3) was a bit more technical : how to quantize the action. He started with the action
$ -\frac{1}{4 \pi \alpha} \int \surd{-g} g^{\alpha \beta} \partial_{\alpha} X^{\mu} \partial_{\beta} X_{\mu} $
and went ahead to quantize it. He did not follow the conventional approach which most of the string theory books follow: find the classical canonical momenta and quantize it by giving operator meaning to the various involved quantities. He used symplectic structure approach in which he wrote the action in terms of two-forms. That part was really confusing since he was writing and erasing so many things on the black board. He mentioned that this symplectic structure approach will be very useful while doing compactifications. He is basically strictly following the string theory book by Luest and Theisen, may be looking at that book will help to understand the things he did today in a better way.

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