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Metric and Covariant Derivative

  1. Aug 30, 2009 #1
    I've seen read a lot of books where they use different sign conventions for the metric and the covariant derivative. I'd like to ask the physics community the following questions:

    I've seen both, the (+, -, -, -) and (-, +, +, +), conventions used for the metric, and I've also seen both, [itex]D_\mu = \partial_\mu + i g T^a A_\mu^a[/itex] and [itex]D_\mu = \partial_\mu - i g T^a A_\mu^a[/itex], in the literature.

    1. Which convention, for the metric and the covariant, do you use? and,

    2. Why? Do you find one more convenient over the other? or were you brought up to believe in one convention, and has it stuck with you ever since?
     
  2. jcsd
  3. Aug 30, 2009 #2
    Interesting!
    I use the 'mostly minus' metric: (+, -, -, -), and use the 'plus' covariant derivative. Essentially I use this convention since I was trained to use this one first. But, I've found that the (+, -, -, -) convention is nicer for me in particle physics since the pole structure in the propagators are more transparent.

    In the mostly minus metric, the on-shell condition is [itex]p^2 = m^2[/itex], where as in the mostly plus metric, the on-shell condition is [itex]p^2 = -m^2[/itex].
     
  4. Aug 30, 2009 #3
    I've learned to use both the (+---) and (-+++) conventions. It's not easy at first switching between the two, but after awhile you get used to it. For me it's not preference, but necessity because different books are written in different conventions and I'm not going to not read a book just because of a sign convention.

    There are other conventions that differ from book to book, such as normalization of spinors, normalization of creation and annihilation operators, and normalization of Fock states. Again, I ended up learning all of them. What's nice is that most of the time there are only two different conventions. If there were a bunch then it'd be confusing.
     
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