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arXiv · 2307.02369

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

Sayak Guha Roy·Kevin Slagle
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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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Sayak Guha Roy, Kevin Slagle. 2023-07-05. Interpolating Between the Gauge and Schr\"odinger Pictures of Quantum Dynamics. https://doi.org/10.21468/scipostphyscore.6.4.081

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