Interpolating Between the Gauge and Schr\'odinger Pictures of Quantum Dynamics
| Autor: | Roy, Sayak Guha, Slagle, Kevin |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.21468/SciPostPhysCore.6.4.081 |
| Popis: | 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). Comment: 12+3 pages, 9+1 figures |
| Databáze: | arXiv |
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