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Monthly Archives: February 2011
EM Lagrangian
Here’s something I’ve been working on and I found a derivation in a book called Quantum Field Theory Demystified by McMahon. Hardly a canonical text, however it has a lot of worked out examples and yes its a bit dumbed … Continue reading
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Hamilton’s equations…sort of
Suppose you’ve got a Lagrangian on the Tangent bundle of your configuration space. Fiber derivatives of L give you momenta, Which transform like the components of a covector. There is the remaining question (this is probably obvious but I’m missing … Continue reading
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Chasing lambda
I’ve read that the cotangent bundle (phase space) to the configuration space (base manifold) is a more special space than the tangent bundle. This is rather interesting. The cotangent bundle is where we do Lagrangian mechanics while the cotangent bundle … Continue reading
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Why the position of the indices matter
A question was asked today about what the difference was between and I’ve got to admit I wondered the same, let’s do it out and see. Let be the components of the Minkowski metric tensor (just so we have something … Continue reading
Poisson Bracket
When I first learned about the Poisson bracket in classical mechanics I was very excited. I had learned about the commutator in quantum first and this looked a lot alike. For any dynamical quantity that we’re interested in, Where H … Continue reading
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