Canonical momentum for Dirac adjoint field

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    Dirac Field Momentum
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Discussion Overview

The discussion revolves around the concept of canonical momentum for the Dirac adjoint field within the context of quantum field theory. Participants explore the implications of the Lagrangian formulation and the treatment of derivatives in relation to the Dirac adjoint field.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that the canonical momentum for the Dirac adjoint field is zero and seeks clarification on this point.
  • Another participant asks for the calculation that leads to this conclusion.
  • A different participant suggests using the symmetrized classical action for the analysis.
  • One participant expresses confusion regarding the treatment of derivatives in the Lagrangian, specifically how they 'act to the right' for ψ and 'act to the left' for ψbarγ0, indicating that resolving this confusion would clarify the zero momentum result.
  • Another participant corrects the terminology, stating that it should be 'acting to the left' for ψbar.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of derivatives and the implications for canonical momentum, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations regarding the assumptions made about the action and the treatment of the Dirac adjoint field, which may affect the conclusions drawn about canonical momentum.

nigelscott
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I read that the canonical momentum for Dirac adjoint field is zero. Why is that?
 
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What does your calculation give you?
 
You should be using the symmetrized „classical” action:
upload_2015-11-25_1-40-38.png
 
I know that π = iψbarγ0. My confusion concerns the notion of the derivative in the Lagrangian 'acting to the right' for ψ or 'acting to the left' for ψbarγ0 . If I ignore that confusion then I can see that the canonical momentum would be 0.
 
should be 'acting to the left' for ψbar
 

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