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    Volume of a sphere in Schwarzschild metric

    Update : e-mailed my teacher and there's something we haven't time to see in class (Kruskal coordinates) that was required for this problem. -_-
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    Volume of a sphere in Schwarzschild metric

    Homework Statement Calculate the volume of a sphere of radius ##r## in the Schwarzschild metric. Homework Equations I know that \begin{align} dV&=\sqrt{g_\text{11}g_\text{22}g_\text{33}}dx^1dx^2dx^3 \nonumber \\ &= \sqrt{(1-r_s/r)^{-1}(r^2)(r^2\sin^2\theta)} \nonumber \end{align} in the...
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    Proof of trace theorems for gamma matrices

    Right! Thanks king vitamin for the additional info, I do realize that it's even clearer written that way indeed! Oh by the way, I'm new to PF, I think they tell you to "rate" or "like" the people that take the time to answer your questions, how do I do that? I do see a Like button, is there...
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    Proof of trace theorems for gamma matrices

    Oh okay, thanks for the precision. I might have been mixed up by Griffith's scalar/matrix notation, and by my teacher telling me that ##\gamma^\mu## can be both vectors in the Minkowski space or matrices in spinors space.
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    Proof of trace theorems for gamma matrices

    Right I get it now : you can't repeat indices on both sides of the equality, thus the contradiction. Thanks vela. About the ##g^{\mu\nu}## metric though, is my comprehension at least correct? The anticommutation relation is a scalar equality, i.e. the product ##\gamma^\mu \gamma^\nu## gives...
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    Proof of trace theorems for gamma matrices

    vela, I'm not sure I follow when you say to take the trace on both side of the anticommutation relation because the way Griffith presented it, the relation ##\gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2g^{\mu\nu}## says that when specifying ##\mu## and ##\nu##, you have ##\gamma^\mu...
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    Proof of trace theorems for gamma matrices

    Hi, I'm currently going through Griffith's Particle Physics gamma matrices proofs. There's one that puzzles me, it's very simple but I'm obviously missing something (I'm fairly new to tensor algebra). 1. Homework Statement Prove that ##\text{Tr}(\gamma^\mu \gamma^\nu) = 4g^{\mu\nu}##...
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    I Metric tensor : raising/lowering indices

    Hi everyone, I'm currently studying Griffith's Intro to Elementary Particles and in chapter 7 about QED, there's one part of an operation on tensors I don't follow in applying Feynman's rules to electron-muon scattering : ## \gamma^\mu g_{\mu\nu} \gamma^\nu = \gamma^\mu \gamma_\mu## My...
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