Dual DC power supply from AC heater

[dobrota]

I want to make dual DC supply voltage for operational amp (about +-12V) using voltage doubler from 6.3V AC valve filament without center tap.
It isn't problem, but what about right grounding method AC heater voltage for minimal hum ?
Because of in this case I think one AC heater side have to be connect to ground.

[dobrota]

Here is schematic:



But what about grounding AC filament F1 - F2 without center tap (original circuit uses it) ?
Add next 100R resistors or pot to ground?