1,160 reputation
1511
bio website code.google.com/p/notebk
location Los Angeles, CA
age
visits member for 1 year, 11 months
seen 26 mins ago

A mathematician, a programmer, etc. etc.

My interests are limited to classical general relativity, quantum gravity, mathematical aspects of quantum field theory, and related fields.


9h
comment Link between a topological space and a manifold
The topology is the collection of open sets of the space (by definition, a member of the topology is called an "open set"). But when a manifold "locally looks Euclidean", you're talking about charts...the image of a chart is itself an open set in the manifold, which requires a topology to talk about...
20h
comment Dimensional analysis
I don't normally recommend it, but this is one of the rare circumstances when wikipedia has a great article on the subject...
1d
comment Why so much geometry in principia and others
I think it was an attempt more to mimic "the glory of geometry that from those few principles, brought from without, it is able to produce so many thing" (as Newton said in the Principia) rather than for actual calculus reasons...since Leibniz had no problem inventing calculus from Cartesian geometry...
1d
comment Rigorous mathematical formalism of particle physics
Actually, the book The Structure and Interpretation of the Standard Model addresses this very question!
Apr
12
comment Lagrangian for relativistic massless particle
...and then we get precisely the solution @Qmechanic posted.
Apr
12
comment Lagrangian for relativistic massless particle
@Flint72, the problem with such reasoning is that it requires QFT to underpin it. The OP was asking about a null geodesic. You produced a section of a bundle. Clearly these are inequivalent, both mathematically and physically (since null geodesics are spin 0 whereas your field is spin 1). If one were to try to write a particle as a field, it'd have its action $I=\int\delta(x-z(\lambda))\sqrt{g_{\mu\nu}\dot{z}^{\mu}\dot{z}^{\nu}}\,\mathrm{‌​d}^{4}x\,\mathrm{d}\lambda$ where dots denote $\lambda$ derivatives, and we "fix" $z$ when considering variations.
Apr
11
comment Lagrangian for relativistic massless particle
"All known massless relativistic particles are represented as fields in their respective Lagrangians." Which makes sense only in the quantum setting. The OP is asking in the classical setting...
Apr
3
comment Paths in the path integral
@yess, that's correct.
Apr
2
comment Why do we use functional integration in QFT?
@user10001 ...but when you say "$x^0$ is the $t$-coordinate" when doing computations in the path integral approach, you just performed the same space+time splitting as in the canonical approach. The remark that this destroys Lorentz invariance would be true if it depends on a particular choice of splitting. Since neither the canonical nor path-integral approaches explicitly depends on this choice, both are equally as Lorentz-invariant. This is particular important in quantum gravity, see, e.g., arXiv:0809.0097 for a review.
Apr
2
comment Why do we use functional integration in QFT?
@user10001, (iii) is a myth FWIW, since Lorentz invariance is handled representation theoretically. Further, when you make a choice of which component is the time component, you make a similar choice in the path integral approach which supposedly "breaks the manifest Lorentz invariance".
Apr
2
comment Paths in the path integral
For gauge theories, you need to be careful and mod out the gauge transformations. That is, integrate over physically distinct states. See, e.g., Sergey V. Shabanov's "Phase space structure and the path integral for gauge theories on a cylinder" arXiv:hep-th/9308002 for a study of 2d examples.
Apr
1
comment Entropy in biological systems
Wouldn't that presuppose that a human is a closed system? Is that really a valid assumption to make?
Mar
30
comment Why do we require manifolds to be a topological space?
...because it's meaningless to discuss continuous functions without topology, and calculus requires at least having continuity...
Mar
30
revised Local Lorentz invariance or local Poincaré invariance?
Don't use TeX when markdown will do...
Mar
30
suggested suggested edit on Local Lorentz invariance or local Poincaré invariance?
Mar
29
answered What are the restrictions on the Hamiltonian in QM?
Mar
29
comment What are the restrictions on the Hamiltonian in QM?
You end up with ambiguities from the expression $(T+V)^2$ for, e.g., the simple harmonic oscillator. This is because we cannot consistently quantize terms involving higher than quadratic powers, and the cross terms would be a nightmare to deal with adequately...
Mar
25
revised Three integrals in Peskin's Textbook
Added another solution...
Mar
25
answered Three integrals in Peskin's Textbook
Mar
25
revised Three integrals in Peskin's Textbook
Improved the TeX formatting