Greetings,
This week there was some progress on the research front. Arjan, a post-doc at my lab was kind enough to show me a little trick to figure out what all the Lorentz-invariant contractions of the Riemann-tensor are for a given order. I basically reduces the problem to solving a kind of Sudoko puzzle, not unlike the Cartan root system for Lie algebra's.
Remember my search for good differential geometry tests? The Cambridge lecture notes were very helpful, but there's always more isn't there. A math professor at my university suggested the following book (no, I haven't taken over Lubos' obsession with Amazon adds, it's just the only place I could find it).
http://www.amazon.com/Geometry-Physics-Introduction-Second/dp/0521539277
The aforementioned math professor is studying it himself. It's good to see people from the math department taking an interest in the link between mathematics and physics, something that's rather close to my heart. I think I'll ask my dad to bring it with him when he gets back to Belgium, since it appears to be alot cheaper and more easily available in the States.
-Dimi
Showing posts with label Research. Show all posts
Showing posts with label Research. Show all posts
Sunday, November 26, 2006
Sunday, October 29, 2006
Needed : math
Hi all,
I was faced with a problem this week. Well, several problems. The start of it all (the meta-problem if you will) was te realisation that dawns on you constantly when you try to do anything in string theory, and any branch of theoretical physics for that matter; I don't know enough mathematics.
Fair enough, this is where we get some studying done. The plan for the coming weeks is to get a good grasp of differential geometry. It's pretty hard to find a good text that describes it at the level that I need. I don't need it to be too rigorous (my apologies to the mathematicians), but it needs to be rigorous enough. I think that my long search is over. Prof. Gary Gibbons from Cambridge was kind enough to post the following lecture notes on his website
Applications of Differential Geometry to Physics
The notes are from a Part III course in Cambridge, which seems to be exaclty what I need.
The main reason why I need this is that I want to understand more about vector bundles. Remember that I'm working on gravity in the string theory context? Well, gravity is described by General Relativity, who'se mathematical language is that of tensor calculus on manifolds. I'm trying to use methods found by my advisor to construct exact solutions that hopefully will shed some light on the high energy behaviour. These methods arised in the context of gauge theories, which are described mathematically by symmetry groups called Lie groups. Fibre bundles (at least to me) seem to be the natural bridge between the two. Apparently, gauge fields can be seen as connections on vector bundles. This is what I want to understand better.
-Dimi
I was faced with a problem this week. Well, several problems. The start of it all (the meta-problem if you will) was te realisation that dawns on you constantly when you try to do anything in string theory, and any branch of theoretical physics for that matter; I don't know enough mathematics.
Fair enough, this is where we get some studying done. The plan for the coming weeks is to get a good grasp of differential geometry. It's pretty hard to find a good text that describes it at the level that I need. I don't need it to be too rigorous (my apologies to the mathematicians), but it needs to be rigorous enough. I think that my long search is over. Prof. Gary Gibbons from Cambridge was kind enough to post the following lecture notes on his website
Applications of Differential Geometry to Physics
The notes are from a Part III course in Cambridge, which seems to be exaclty what I need.
The main reason why I need this is that I want to understand more about vector bundles. Remember that I'm working on gravity in the string theory context? Well, gravity is described by General Relativity, who'se mathematical language is that of tensor calculus on manifolds. I'm trying to use methods found by my advisor to construct exact solutions that hopefully will shed some light on the high energy behaviour. These methods arised in the context of gauge theories, which are described mathematically by symmetry groups called Lie groups. Fibre bundles (at least to me) seem to be the natural bridge between the two. Apparently, gauge fields can be seen as connections on vector bundles. This is what I want to understand better.
-Dimi
Thursday, October 12, 2006
Colloquia en Lectures
Some news about that new aspect of my new life, qolloquia, symposia and the likes.
Next week I'm invited to the following :
Solvay Colloquium by Professor C.N. Yang
THEMATIC MELODIES OF TWENTIETH CENTURY PHYSICS: QUANTIZATION, SYMMETRY AND PHASE FACTOR
The Inaugural Lecture of the 2006 International Solvay Chair in Physics by Professor Ludwig Fadeev
THE MASS PROBLEM IN YANG-MILLS GAUGE THEORY
Sounds fun doesn't it? I'm going to attend, but I'll mentally prepare myself that I will be feeling rather stupid afterwards.
As for other news... all I can say is : curse Blackadder DVD's! I really ougth to have gotten more work done yesterday. No matter, I'll make up for it today.
Party tonight as well. I'll post op pictures if I don't forget my camera.
Next week I'm invited to the following :
Solvay Colloquium by Professor C.N. Yang
THEMATIC MELODIES OF TWENTIETH CENTURY PHYSICS: QUANTIZATION, SYMMETRY AND PHASE FACTOR
The Inaugural Lecture of the 2006 International Solvay Chair in Physics by Professor Ludwig Fadeev
THE MASS PROBLEM IN YANG-MILLS GAUGE THEORY
Sounds fun doesn't it? I'm going to attend, but I'll mentally prepare myself that I will be feeling rather stupid afterwards.
As for other news... all I can say is : curse Blackadder DVD's! I really ougth to have gotten more work done yesterday. No matter, I'll make up for it today.
Party tonight as well. I'll post op pictures if I don't forget my camera.
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