Causal fermions in discrete spacetime
Abstract
In this paper, we consider fermionic systems in discrete spacetime evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete spacetime can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete spacetime that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields, and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete spacetime can be efficiently simulated on a quantum computer.
 Publication:

Physical Review A
 Pub Date:
 January 2014
 DOI:
 10.1103/PhysRevA.89.012302
 arXiv:
 arXiv:1303.4652
 Bibcode:
 2014PhRvA..89a2302F
 Keywords:

 03.67.Ac;
 03.70.+k;
 Quantum algorithms protocols and simulations;
 Theory of quantized fields;
 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 16 pages, 1 figure