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Apr
7
accepted Would Special Relativity Predict Time Dilation of a Geostationary Satellite Compared to an Observer on Earth?
Apr
7
comment Would Special Relativity Predict Time Dilation of a Geostationary Satellite Compared to an Observer on Earth?
Amazing, thank you.
Apr
7
asked Would Special Relativity Predict Time Dilation of a Geostationary Satellite Compared to an Observer on Earth?
Mar
4
accepted Is my Summary of a Spinor Bundle Associated with a String Worldsheet Correct?
Mar
4
comment Is my Summary of a Spinor Bundle Associated with a String Worldsheet Correct?
Awesome, thanks again!
Mar
4
comment Is my Summary of a Spinor Bundle Associated with a String Worldsheet Correct?
Thanks for the reply Tobias. Wouldn't $F_{x}$ be the space of oriented and pseudo-orthonormal frames of $T_{x}M$, just to be a little more precise? (Since $T_{x}M$ has Lorentzian metric signature). And I understand the $Spin(1,1)$-bundle now, thank you.
Mar
3
revised Is my Summary of a Spinor Bundle Associated with a String Worldsheet Correct?
grammar
Mar
3
asked Is my Summary of a Spinor Bundle Associated with a String Worldsheet Correct?
Feb
19
revised The Covariant Spinor Derivative in the Locally Supersymmetric Generalisation of the Polyakov Action and Potential Mistakes in the Literature
Explained how the Thesis and Wikipedia covariant derivatives don't match!
Feb
19
asked The Covariant Spinor Derivative in the Locally Supersymmetric Generalisation of the Polyakov Action and Potential Mistakes in the Literature
Feb
18
comment How to understand worldsheet fermion as a section?
Sorry for resurrecting this discussion. Just to make sure I understand the upshot of all this: Do the spinors $\psi_{+}$ and $\psi_{-}$ correspond to the sections of the spinor bundles $S=K^{1/2}$ and $S=\bar{K}^{1/2}$ respectively? Whilst $\psi^{i}_{+} \dfrac{\partial}{\partial \phi^{i}}$ and $\psi^{i}_{-} \dfrac{\partial}{\partial \phi^{i}}$ are sections of $K^{1/2} \times \phi*(TX)$ and $\bar{K}^{1/2} \times \phi*(TX)$ respectiveley?
Jan
10
comment Why can you re-write the functional measure of a real-valued field $\phi(x)$ as $\mathcal{D}\phi=\prod_{k_n^0>0}dRe \phi(k_n) d Im \phi(k_n)$?
Just to add to this discussion: I think the importance of the transformation being unitary might be the fact that unitary transformations don't alter the integration measure. So before the Fourier transformation we had $\mathcal{D} \phi(x)$ and after the transformation we still have $\mathcal{D} \phi(x)$, it just so happens that this can be expressed in terms of real and imaginary $\phi(k)$. Non-unitary transformations may have altered the integration measure so that $\mathcal{D} \phi(x)$ can't be used. It would be helpful if somebody could either confirm or reject this reasoning however.
Jan
8
awarded  Benefactor
Jan
7
comment Calculation of the Abelian Induced Chern-Simons Term
Awesome, thanks once again!
Jan
7
accepted Calculation of the Abelian Induced Chern-Simons Term
Jan
7
comment Calculation of the Abelian Induced Chern-Simons Term
Ok, I think I get it now! In the first diagram I drew assume both the incoming and outgoing p's are from left to right. It would be perfectly consistent to change the arrow of the outgoing such that it points from right to left so long as it's also relabelled -p. Thus both arrows are incoming but momentum is still conserved. Is this right?
Jan
7
comment Calculation of the Abelian Induced Chern-Simons Term
Also thanks for clarifying.
Jan
7
comment Calculation of the Abelian Induced Chern-Simons Term
I see what you're saying, but would you not have to stick to the same choice of direction for both the incoming and outgoing momenta (such that both would be p or both would be -p). It seems odd (cheating?) to change the direction arbitrarily from one part of the diagram to another.
Jan
7
comment Calculation of the Abelian Induced Chern-Simons Term
Ah I see, so is it correct that the first diagram I drew isn't complete, it's just the internal part of another (arbitrary) larger diagram? Would this be true also for the diagram that gives equation (9.80) on page 305 of Peskin and Schroeder? Also I don't completely understand how both momenta can point inwards without violating momentum conservation. I would have thought the momentum 'going in' has to equal the momentum 'going out'. That is to say, I would have though both gauge fields would need the same momentum (p for both).
Jan
7
awarded  Promoter