I've recently started my second course in Quantum Theory and am now often required to prove more complex commutation relations. I'm aware that the Levi-Civita symbol often makes this sort of thing a lot slicker, but I'm finding it really hard to crack. There are some great answers to individual queries relating to it online, but I was wondering if anyone knew of somewhere (book, site etc.) I could learn how to use it from the ground up? Maybe with exercises/solutions?

  • $\begingroup$ Are you aware of the techniques of tensor calculus? A quick google search on this topic may help you along quite a bit, although you're at risk of spending a lot of time learning all the details of this formalism :D $\endgroup$ – Danu Oct 25 '14 at 14:05
  • $\begingroup$ See en.wikipedia.org/wiki/Levi-Civita_symbol $\endgroup$ – Urgje Oct 25 '14 at 14:12
  • $\begingroup$ I'm afraid I'm not. My degree is in Mathematics and I've mainly done pure but chose Quantum for a bit of variety. Would that be the best place to start? $\endgroup$ – user37154 Oct 25 '14 at 14:13
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    $\begingroup$ Maybe you need to look at an intro GR book - there is a lot more tensor calculus in such courses, so it will give you a better introduction. Check out the first couple chapters of Sean Carroll's review article: arxiv.org/abs/gr-qc/9712019, or the text that grew out of it. $\endgroup$ – levitopher Oct 25 '14 at 14:40
  • $\begingroup$ Oh also the first chapter of Landau's EM book has a footnote which contains some Levi-Civita stuff. I know that sounds obscure, but it's actually the first place I always go to when I need to know something about it! $\endgroup$ – levitopher Oct 25 '14 at 14:41

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