Path integral approach to the full Dicke model

► We study the Dicke model with the rotating and counter-rotating coupling terms. ► Considering only rotating or counter-rotating term there is a continuous symmetry. ► Considering both rotating and counter-rotating terms there is a discrete symmetry. ► There is a phase transition related with the respective spontaneous symmetry breaking. ► We identify a Goldstone mode when the continuous symmetry is spontaneously broken.