Recent content by asub

One approach to get a relativistic QM might be to take hamiltonian as sqrt(p2c2 +m2c4). But apparently this does not work because expanding H in inverse powers of c2 will lead to higher order derivative in space. Apparently, one reason this is bad is because higher derivatives mean that the...

Hi all, I am wondering why the "creeping along" proof of Heine-Borel theorem doesn't work for open subsets. I have adapted Spivak's proof in "Calculus on Manifolds" here, but I can't seem to find where I am wrong: The theorem for open sets would be: The open interval (a, b) is compact...

I came across a formula that gives radiant energy density as 4 * sigma * T^4 / c. I am trying to figure out how this formula follows from Stefan-Boltzmann law. Shouldn't it be 4*pi instead of just 4? I am also wondering why one can just stick in c. TIA

Hi pmb_phy, sorry for being pedantic, but I guess this thread is about being pedantic :) When I was pointing out Boothby's book, I was not pointing out his definition of Euclidean space--after all it was defined by Euclid. And Euclid's definition of E^2 has nothing to do with numbers or...

I think the motivation for differential geometry becomes clear when one stops indentifying R^n with E^n (incorrectly). Euclidean space is defined by a set of axioms and is actually not even a vector space (it's affine space). Some time between high school and college most people identify R^n...

Hi all, What is a good introductory book on tensor products and tensor algebras? For motivation, I have found Tom Coates's http://www.math.harvard.edu/~tomc/math25/tensor.pdf" to be quite helpful, but I would like to do see some examples and do problems to understand it more thoroughly...