Minimum requisite to generalize Proca action

[JuanC97]

Hello guys,
In 90% of the papers I've read about diferent ways to achieve generalizations of the Proca action I've found there's a common condition that has to be satisfied, i.e: The number of degrees of freedom allowed to be propagated by the theory has to be three at most (two if the fields are massless).

I wonder... why is so?, two hypothesis I bare in my mind after discussions with my thesis director were:
1. Proca propagates three degrees of freedom hence, it would be unphysical to pretend to generalize this action at our energy levels including extra degrees of freedom that hasn't been observed in experiments.
2. There could be a fundamental reason related to the representations of the Poincaré group which, as far as I've seen (not much), tell you that two degrees of freedom (2 out of the 4 componets of the vector) are redundant if the vector field is massless and 1 more degree of freedom arises if the mass is non-zero.

The second idea follows from this slides: http://bit.do/UCslides, and this PF post: http://bit.do/PFpost.

Which idea is the most accurate for you guys?
and where could I find more info about it?

 

[Vanadium 50]

How do you have a Proca Lagrangian with massless fields? I thought the whole point was to generalize massless fields to fields with mass.

 

[JuanC97]

How do you have a Proca Lagrangian with massless fields? I thought the whole point was to generalize massless fields to fields with mass.

Well, you're right, the massless case shouldn't be called 'proca' but mathematically, it exists and corresponds to a lagrangian of the form (kinetic term) - (potential).

Also, when I said I was interested in 'generalizing proca', I should've said it was in the sense of adding extra terms to the lagrangian to incorporate aditional kinds of interactions between the fields nothing diferent than this), and basically the way you do it is adding terms composed by products of the fields and their first derivative.