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+ 2 like - 0 dislike

I'm not sure such a thing exists. Usually reps only helps you classify the kind of particles you have (i.e the quantum numbers that identify them) and how they transform under the corresponding group. I believe how to represent this particles mathematically and what is their dynamics is a different matter.

The only thing similar I know about is that some of the Poincare group reps, or actually the vector spaces that carry them, have a correspondence with the Hilbert space of solutions of some wave equation

  • spin 0 : Klein-Gordon equation

  • spin 1/2 : Dirac equation

  • spin 3/2 : Rarita-Schwinger

  • etc

and you may be able to construct a Lagrangian/Action which gives these as the dynamics. But this is just the usual problem of finding a Hilbert space isomorphic to the Hilbert space of quantum states.

If the solutions can be properly quantised and interpreted as quantum fields is another issue and usually problems appear. For instance, if you try to couple Rarita-Schwinger fields to electromagnetism you encounter superluminal propagation.

Anyone else have any ideas?

This post imported from StackExchange Physics at 2014-03-11 07:58 (UCT), posted by SE-user Julio Parra
answered Mar 7, 2014 by Julio Parra (20 points) [ no revision ]
There is a subfamily of irreps of the Poincaré group - namely, the zero-mass, "continuous-helicity" representations - which does not admit any Lagrangian formulation whatsoever.

This post imported from StackExchange Physics at 2014-03-11 07:58 (UCT), posted by SE-user Pedro Lauridsen Ribeiro
You can make a much stronger statement: The representations do not uniquely determine a Lagrangian. You have to add other assumptions to get dynamical laws.

This post imported from StackExchange Physics at 2014-03-11 07:58 (UCT), posted by SE-user user1504
@user1504 - Sorry if I'm picky, but that would be a(n important!) "non-uniqueness" statement, whereas my counter-example is rather a "non-existence" one, so both statements deal with different issues.

This post imported from StackExchange Physics at 2014-03-11 07:58 (UCT), posted by SE-user Pedro Lauridsen Ribeiro
@PedroLauridsenRibeiro: My comment was directed at Julio. I'm not arguing that representations determine a Lagrangian. This fails even for the 2d chiral boson.

This post imported from StackExchange Physics at 2014-03-11 07:58 (UCT), posted by SE-user user1504




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