NON-HALF PROPAGATING DEGREES OF FREEDOM IN EXTENDED PROCA-NUEVO

Generalized Proca is a theory describing massive spin-1 field which by construction avoids Ostrogradsky ghost by keeping the equation of motion at most second order. Such theory have rich application potential in both cosmology and astrophysics. For a massive spin-1 field in $D$-dimensional spacetime, the degrees of freedom should be $D-1$. Following the same construction way of massive gravity, Proca-Nuevo is proposed as an alternative vector theory that can be shown inequivalent to Generalized Proca. Later Extend Proca-Nuevo is proposed in order to combine both Generalized Proca and Proca-Nuevo, which cover all Proca-Nuevo interaction and part of Generalized Proca. By construction, such theorem should have the same degrees of freedom as Generalized Proca, however, there is a calculation that shows it may be the first counter-example as a Lorentz parity invariant theory propagating half degrees of freedom. In this thesis, the reason why a parity and Lorentz invariant theory cannot propagate half degrees of freedom will be discussed. The primary and secondary constraints of the theory would be calculated both in the Lagrangian and Hamiltonian formalism showing their second class nature. Such two constraints will ensure the correct propagating degrees of freedom. The proof would include a general analysis in two-dimensional spacetime and the minimal model in arbitrary dimension case. The methods used in the proof may have application to the coupling theory of Extended Proca-Nuevo with gravity.

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