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Electromagnetic Tensor with (-+++) convention

  1. Dec 18, 2015 #1
    Hi there,

    Over the last couple of weeks, I have been learning about the relativistic description of electromagnetism through Leonard Susskind's Theoretical Minimum lectures, and although I have managed to follow it, there are some parts which I am becoming increasingly confused by, not helped by the fact Susskind uses the (-+++) convention rather than the seemingly more popular (+---).

    Is the definition of the electromagnetic tensor different depending on the convention? I am aware that the matrix changes (the contravariant and covariant forms are multiplied by -1 when moving between conventions), but does the definition of each component in terms of the vector potential change?

    The reason I ask this is because when deriving the relativistic Lorentz force from the Lagrangian:
    L=-m√(-dXϑ/dt dXϑ/dt)-qAϑ dXϑ/dt
    I always seem to get the following answer (using the (-+++) convention):
    Which is the negative of what I would expect from the definition of the Electromagnetic Tensor.

    Any help would be appreciated, and thanks in advance.
  2. jcsd
  3. Dec 19, 2015 #2
  4. Dec 19, 2015 #3


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    Note that there are also conventions regarding the index structure of F...
    the ;-notation vs the ∇-notation.
  5. Dec 19, 2015 #4
    Maybe the Lagrangian should be:
    L=-m√(-dXϑ/dt dXϑ/dt)+qAϑ dXϑ/dt
    when using the (-+++) convention?
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