A unifying perspective on the Moyal and Voros products and their physical meanings

Understand

The Moyal and Voros formulations of non-commutative quantum field theory has been a point of controversy in the recent past.

• Here we address this issue in the context of non-commutative non-relativistic quantum mechanics.
• In particular we show that the two formulations simply correspond to two different representations associated with two different choices of basis on the quantum Hilbert space.
• From a mathematical perspective the two formulations are therefore completely equivalent, but we also argue that only the Voros formulaton admits a consistent physical interpretation.