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

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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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1-Cobordism Part 3

I was going to say that there’s not much more to say about 1-cobordisms 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

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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

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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

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