Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions
arXiv:2011.05597 · doi:10.1103/PhysRevA.103.052203
Abstract
Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum cellular automata for distinguishable particles based on two different quantum walks, and show that by restricting to the antisymmetric and symmetric subspaces, respectively, a multiparticle theory for free fermions and bosons in three spatial dimensions can be produced. This construction evades a no-go theorem that prohibits the usual fermionization constructions in more than one spatial dimension. In the long-wavelength limit, these recover Dirac field theory and Maxwell field theory, i.e., free QED.
arXiv comment5 pages, two column format
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- 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
- The Dirac Vacuum in Discrete Spacetime
- Bounds on QCA Lattice Spacing from Data on Lorentz Violation