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Infinitesimal transformation of a field

  1. Nov 20, 2015 #1
    Hi,

    Could you please explain me why, under the transformation of a complex valued field Φ→eΦ, for an infinitesimal transformation we have the following relation?

    δΦ=iαΦ

    Thanks a lot
     
  2. jcsd
  3. Nov 20, 2015 #2

    samalkhaiat

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    Science Advisor

    When [itex]\alpha[/itex] is infinitesimal, i.e. [itex]\alpha^{2} = 0[/itex], you can write [itex]e^{i\alpha} = 1 + i\alpha[/itex]. So, [itex]\Phi \to \Phi^{'} = \Phi + i\alpha \Phi[/itex], leads to [itex]\delta\Phi = \Phi^{'} - \Phi = i\alpha \Phi[/itex].
     
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