Interpolating Between the Gauge and Schr\"odinger Pictures of Quantum Dynamics

• URL: http://arxiv.org/abs/2307.02369v1
• Date: Wed, 5 Jul 2023 15:33:20 GMT
• Title: Interpolating Between the Gauge and Schr\"odinger Pictures of Quantum Dynamics
• Authors: Sayak Guha Roy, Kevin Slagle
• Abstract summary: spatial locality is not explicit in the Schr"odinger picture equations of motion. The gauge picture is a modification of Schr"odinger's picture such that locality is explicit in the equations of motion.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schr\"odinger picture equations of motion. The gauge picture is a modification of Schr\"odinger's picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schr\"odinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schr\"odginer picture wavefunction (and the connections approach the identity).

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