Recent content by hawkdron496

Yep, I follow. In retrospect that should have been clear given that we're subtracting a number from its conjugate and then multiplying by ##i##.

Right, okay. So I need to be more careful about the use of the word "scalar". Thank you for clarifying. I think I may still be missing something, though. Rubakov defines a current: #\varphi# transforms under the fundamental representation of ##SU(n)##, which, if I'm understanding things...

I'm sorry, I think I'm confused again. I was under the impression that by definition if we have a rank 2 antisymmetric tensor ##F##, and local coordinates ##(x^1, ... x^n)## in an open set ##U##, that ##F_{\mu \nu} = F(\partial_\mu, \partial_\nu)## and is a locally defined function ##U...

Right, okay. So how do I want to think about these things? Usually when I see something with, say, two lower indicies, I read "this is a thing that eats two tangent vectors at a point and gives me a number". In the case of something with an internal index and two spacetime indicies like...

So, a "scalar field" per Rubakov would be a vector (for instance) field on spacetime that at every point is unchanged by the action of a matrix in the Lorentz group? Most things that I'd consider to be Lorentz scalars (proper time, rest mass, etc...) are all still indexless objects that you get...

So, recently I've been working through "Classical Theory of Gauge Fields" by Rubakov. I've more-or-less been able to do the exercises as they've come up, but every once in a while I feel like I'm symbol pushing to get the correct answer, or ignoring certain confusions I have in favour of doing...

Yep, I suppose I will. Thank you for the help.

So, that strange notation occurs again, later in the paper: which makes it feel less likely that it's a typo.

From what I've been able to find online, the symbol ##\tilde{D}(S)## is the same as the usual symbol for domain of dependence, but only for timelike curves rather than any causal curve, according to this stack overflow post...

Will do: the relevant paragraph is here: The questionable notation is in the Proof section of the proposition.

I'm not clear on what it means when he takes ##\mathfrak{I}^+(q)##. Is it just the set of null rays going off to infinity that pass through q?

I'm reading Tipler's 1976 paper, "Causality Violation in Asymptotically Flat Spacetimes" and he keeps using a symbol which seems to resemble the symbol for Future Null Infinity in a strange font, but it's usage doesn't make sense with what I would expect if that's what the symbol meant. He...

I believe this clarifies things a lot, thank you for the help, I appreciate it.

Surely though if in one frame the endpoint of the worldline is ##(\tau, 0,0,0)##, in the frame transformed according to ##t' = 2t## the worldlike would end at ##(2\tau, 0,0,0)##, meaning someone using the second set of coordinates wouldn't measure proper time along the path? I think the root of...

Is what you're saying that the proper time quantity won't be equal to the coordinate time quantity in the ##t'## frame, because in the ##t'## frame you're essentially measuring time in half-units, and once you do the unit conversion it will stop being an issue? Surely though you could construct...