Simple question.

Simple question.
 

In this sentence, "quiero estar feliz", you don't need to use "a", correct?

Is this because the "a" is included in the infinitive? I'm just not quite sure when to use "a" to connect words together.

I hope I explained my problem clearly.

"Quiero ser feliz", yes, no "a" needed nor included. "Ser" much more used than "estar" in this sense, no matter "la felicidad" can be a temporary state.

Quiero ser feliz.
Quiero estar contento.
Quiero sentirme dichoso.