I am looking to design an amplifier for the phono output on my turntable. The output is presented as two RCA jacks on the back of the unit. Is it safe to assume that the ground of both the left and right signal are the same, or should they each be treated as separate differential signals (with the positive signal being the center of the jack and the negative being the casing)?
It is safe to assume that for the audio signal, those two RCA shells are common.
Where life can get interesting, especially with a mains-powered turntable and mains powered amplifier, is control of leakage currents at AC line frequencies, due to unintentional coupling of mains to ground through proximity capacitance, and intentional coupling of mains to ground through input filter devices.
To this end, most turntables and amplifiers are provided with a chassis earth screw connection on the back. This can be used to divert most of the leakage current to where you want it to flow, which is not in the shield of your audio coax cables. As turntables and amplifiers are not built to any given standard, you may need to experiment with connecting these chassis terminals, or not, to reduce any mains-related hum.
RCA leads treat them as separate and so do higher quality amplifiers - but RCA leads that convert to 3.5mm jacks combine them.
So it seems to be a choice especially as some amps have two completely separate mono amps in a housing and the controls are common.
Other systems use multiple mono amps for each speaker - one system a friend has contains 6 amplifiers driving each speaker unit - sounds divine...