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Monthly Archives: January 2014
String Theory, Part III: Boundary Conditions
Because we are starting with an open string, we must define constraints on the string at the boundary points. We will start by varying the action , where dotted denotes the derivative with respect to time, and primed denotes the derivative with … Continue reading
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Maximal Tori – Math Colloquia 1/29/2014
On Wednesday of this past week (1/29/2014) I went to the weekly colloquium in my department. The title was Involutions and “Fixing” the World: Symmetric Spaces and it was given by Catherine Buell of Bates College. The talk was interesting and … Continue reading
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GL examples/properties
I’m aiming to include some Lie theory into current study. Before worrying about those details I’m going to work some examples/problems from Brickell and Clark’s Differential Manifolds text on the general linear group which is the group of invertible matrices. … Continue reading
Tangent Space – 1
The idea of this first post is to construct the idea of a tangent space. The intuitive idea comes from surfaces in euclidean space. At each point on a smooth surface you can approximate the surface by a tangent plane … Continue reading
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1Cobordism Part 3
I was going to say that there’s not much more to say about 1cobordisms but then I realized I’ll probably return to these periodically to add some details. I’ll add a few now. First there’s the notion of cobordism classes, … Continue reading
Gauge Invariance
You can see the original post here. I’m learning about the Dirac field, and I’ve been working my way through Ch. 3 of Peskin & Schroeder, which starts off by considering what kind of Lorentz invariant theory of spin 1/2 particles … Continue reading
Knot cobordisms – a brief aside
As I mentioned in Spheres – 1 I was momentarily sniped by the idea of knot cobordisms. I’ve downloaded a few papers and will stow those away for later but I want to post just a bit more before I leave … Continue reading