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Homework Help: Quick question, index notation, alternating tensor.

  1. Dec 26, 2013 #1
    Q) I am using index notation to show that ε[itex]^{0123}[/itex]=-1 given that ε[itex]_{0123}[/itex]=1.

    The soluton is:

    ε[itex]^{0123}[/itex]=g[itex]^{00}[/itex]g[itex]^{11}[/itex]g[itex]^{22}[/itex]g[itex]^{33}[/itex]ε[itex]_{0123}[/itex]=-ε[itex]_{0123}[/itex]

    where g[itex]_{\alpha\beta}[/itex] is the metric tensor.

    I am struggling to understand the last equality.

    Many thanks for any assistance.
     
  2. jcsd
  3. Dec 26, 2013 #2

    Dick

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    Homework Helper

    Look up the definition of the metric tensor you are using and insert the values of the g components.
     
  4. Dec 26, 2013 #3

    HallsofIvy

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    If you are using the standard metric tensor for relativity then [itex]g^{11}= g^{22}= g{33}= -1[/itex] while [itex]g^{00}= 1[/itex].
     
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