Interpolating between the gauge and Schrödinger pictures of quantum dynamics
Sayak Guha Roy, Kevin Slagle
SciPost Phys. Core 6, 081 (2023) · published 24 November 2023
- doi: 10.21468/SciPostPhysCore.6.4.081
- Submissions/Reports
Abstract
Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger'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 Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).