Recent content by espen180

Hi. I am currently in a situation where I have a function handle giving as putput an array of doubles. I would like to convert this to a cell array of function handles, each giving a component of the previous array. The original function handle is produced by a built-in MATLAB function, so...

But isn't Nakahara basically a math book but without the proofs? I think it is a stretch to call is a physics book, even if it is standard in the physics curriculum. And I agree, insofar as "pure math" refers to the business to proving theorems.

Although I'm not aquainted with the full content of Spivak, the following popped up after a quick search. You can tell me whether the material is contained within standard textbooks or not. http://arxiv.org/abs/0809.3596 http://arxiv.org/abs/gr-qc/0402105 http://arxiv.org/abs/hep-th/9706092...

Of course, but does that include theoretical general relativity?

@WannabeNewton: I hope you're not arguing that learning the proper mathematics is useless because it isn't necessary in the end-of-chapter problems in your textbooks! When the time comes to actually do some research, I'm sure you'll be glad you studied it.

From my experience, a first grad-level GR course will only deal with local phenomena, so you can pretend to be working on a topologically trivial manifold. I suppose if you want to work in more exotic contexts, like on a non-orientable manifold, or in general any case where the problem of...

I second Lee's topological manifolds as a good book for topology. Follow up with his smooth manifolds book and you have a solig grounding in differential topology and you can dive head-first into differential geometry. For linear algebra, Steven Roman's book "Advanced linear algebra" is the...

Differential geometry is locally (multivariable) real analysis, so it is absolutely necessary. For example, many basic results use the inverse and implicit function theorems, and the very definition of a manifold assumes you know basic multivariable real analysis. In addition, the whole point of...

Thanks for the tip. :smile: I haven't gotten around to Wald yet, but it's definitely on my reading list.

Sorry. It is "Higher Dimensional Algebra and Topological Quantum Field Theory", on page 2. Arxiv: http://arxiv.org/abs/q-alg/9503002 He doesn't give a reference though.

Group theory really shines only when you go to higher physics. -In QM, the symmetry group of space-time is what gives rise to observable quantities. More precisely, the generators of the associated Lie algebra generate the observables. Take for example p_x=e^{i\hbar \frac{d}{dx}}, where...

Lorentz symmetry is actually related to the center of mass. http://physics.stackexchange.com/questions/12559/what-conservation-law-corresponds-to-lorentz-boosts

I mordern classical mechanics, dynamical systems are described by so-called Lagrangian and Hamiltonian functions. A Lagranigan or Hamiltonian function is a mathematical expression in certain variables, which gives rise to the equations of motion of the system in a canonical way. Purely...

I think it is a postulate. It also gives the correct equations for joint probability distributions and is, in a sense, the natural way to represent a joint wavefunction. This might not be the best explanation (it is certainly not he most well put together), but here is another argument for it...

For the sake of claification, do you mean taking linear combinations of finite products of raising and lowering operators?