A discrete relativistic spacetime formalism for 1 + 1-QED with continuum limits

Area of Science:

• Quantum physics
• Computational physics
• High-energy physics

Background:

• Quantum electrodynamics (QED) is a fundamental theory describing interactions between light and matter.
• Lattice-based simulations are crucial for studying complex quantum systems.
• Previous models faced challenges in accurately capturing relativistic regimes.

Purpose of the Study:

• To construct a quantum cellular automaton (QCA) that replicates [Formula: see text] QED.
• To verify the QCA's convergence to known continuum limits of QED.
• To validate the QCA's accuracy in the relativistic regime.

Main Methods:

• Development of a one-dimensional lattice QCA using unitary gates.
• Modeling massive fermions interacting with a U(1) gauge field.
• Analysis of the QCA's behavior in continuous-time discrete-space and continuous spacetime limits.

Main Results:

• The QCA exactly preserves U(1) gauge invariance.
• Convergence to the Kogut-Susskind staggered version of [Formula: see text] QED in the continuous-time discrete-space limit.
• Convergence to the Dirac equation in the free one-particle sector, indicating relativistic accuracy.

Conclusions:

• The developed QCA provides a viable and accurate lattice model for [Formula: see text] QED.
• The model's convergence properties confirm its suitability for studying relativistic quantum phenomena.
• This work offers a novel computational tool for exploring fundamental physics.