Spacetime quantum mechanics for bosonic and fermionic systems

Understand

We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing.

• Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic structure, thereby unifying the axioms that traditionally distinguish the treatment of spacelike and timelike separations.
• Standard quantum evolution can be recovered from timelike correlators, defined by means of a quantum action operator, a quantum version of the action of classical mechanics.
• The corresponding map also provides a novel perspective on the path integral formulation, which, in the case of fermions, yields an alternative to the use of Grassmann variables.