A massless interacting Fermionic Cellular Automaton exhibiting bound states

Abstract

We present a Fermionic Cellular Automaton model which describes massless Dirac fermion in 1+1 dimension coupled with local, number preserving interaction. The diagonalization of the two particle sector shows that specific values of the total momentum and of the coupling constant allows for the formation of bound states. Furthermore, we present a classification of the local number-preserving interactions that are invariant under the isotropy group of the cellular automaton which simulates the Weyl equation.

10 pages, 5 figures

References in corpus (5)

• Universal computation by quantum walk
• Chiral Floquet Phases of Many-body Localized Bosons
• Isotropic quantum walks on lattices and the Weyl equation
• A relativistic discrete spacetime formulation of 3+1 QED
• Chirality from quantum walks without quantum coin

Cited by in corpus (3)

• Quantum Electrodynamics from Quantum Cellular Automata, and the Tension Between Symmetry, Locality and Positive Energy
• A perturbative approach to the solution of the Thirring quantum cellular automaton
• Bounds on QCA Lattice Spacing from Data on Lorentz Violation