I know that the terms in the Lagrangian needs to be scalars (with respect to Lorentz symmetry etc.). Also I know that [see C. G. Tully (EPP) p. 85]
in general, for ψ in the fundamental representation and →λ the generators of the group, then ψ†→λψ will behave like a vector in the adjoint representation and can be dotted into a multiplet of fields in the adjoint representation to form a scalar.
So suppose I want to describe the dynamics or interactions of some particles say π,Σ∗,Λ. What would be the first steps here to build a Lagrangian? I want to work with SU(3) here.
The Λ and Σ∗ belong to the octet and decuplet respectively.
So the questions are:
- What would be the first steps in writing this Lagrangian?
- What shall I take for ψ in this case?
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