4 ms·

I've had the same question for ages. Shouldn't there be an equation in "Schroedinger form" with some relativistic Hamiltonian?

• colanderman 2y ago
  https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Free_fields https://en.wikipedia.org/wiki/Mathematical_formulation_of_th... I think at least provides the field evolution equations for the free fields. But I can't find the equivalent for the interaction terms. E.g. the path integral formation I can only find Lagrangians for.
• pdonis 2y ago
  > Shouldn't there be an equation in "Schroedinger form" with some relativistic Hamiltonian? Writing it this way goes against the basic idea of QFT, which is that, in a relativistic context, quantum systems can no longer be described as "wave functions evolving in time", which is what the Schrodinger/Hamiltonian formulation describes.
  • colanderman 2y ago
    For those of us interested in non-relativistic field equations of the Standard Model, what are the right keywords to chase?
    • pdonis 2y ago
      > non-relativistic field equations of the Standard Model If you're using the non-relativistic approximation, most of the Standard Model is irrelevant since you're limited to interaction energies much less than the rest mass of the lightest particle involved. You're basically looking at the low energy regime of QED, or straightforward non-relativistic QM with an appropriate potential in the Hamiltonian and no pretense of even trying to derive things from an underlying QFT model.
      • colanderman 2y ago
        Ah thank you for the clear answer! My Wikipedia excursions have left me missing all of this context.
        • pdonis 2y ago
          You're welcome! :-)