Clifford algebra from quantum automata and unitary Wilson fermions

Abstract

We introduce a spacetime discretization of the Dirac equation that has the form of a quantum automaton and that is invariant upon changing the representation of the Clifford algebra, as the Dirac equation itself. Our derivation follows Dirac's original one: We required that the square of the discrete Dirac scheme be what we define as an acceptable discretization of the Klein-Gordon equation. Contrary to standard lattice gauge theory in discrete time, in which unitarity needs to be proven, we show that the quantum automaton delivers naturally unitary Wilson fermions for any choice of Wilson's parameter.

Comments: 5 pages + references, 1 figure, and 9 pages of Supplemental Material. From versions 1 to 4, the preprints contain errors, consult versions only starting from v5