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We show that geometric locality can be achieved explicitly in the equations of motion by \"gauging\" the global unitary invariance of quantum mechanics into a local gauge invariance. That is, expectation values &#x27E8;<\/mml:mo>&#x03C8;<\/mml:mi>|<\/mml:mo><\/mml:mrow>A<\/mml:mi>|<\/mml:mo><\/mml:mrow>&#x03C8;<\/mml:mi>&#x27E9;<\/mml:mo><\/mml:math> are invariant under a global unitary transformation acting on the wavefunction |<\/mml:mo><\/mml:mrow>&#x03C8;<\/mml:mi>&#x27E9;<\/mml:mo>&#x2192;<\/mml:mo>U<\/mml:mi>|<\/mml:mo><\/mml:mrow>&#x03C8;<\/mml:mi>&#x27E9;<\/mml:mo><\/mml:math> and operators A<\/mml:mi>&#x2192;<\/mml:mo>U<\/mml:mi>A<\/mml:mi>U<\/mml:mi>&#x2020;<\/mml:mo><\/mml:msup><\/mml:math>, and we show that it is possible to gauge this global invariance into a local gauge invariance. To do this, we replace the wavefunction with a collection of local wavefunctions |<\/mml:mo><\/mml:mrow>&#x03C8;<\/mml:mi>J<\/mml:mi><\/mml:msub>&#x27E9;<\/mml:mo><\/mml:math>, one for each patch of space J<\/mml:mi><\/mml:math>. The collection of spatial patches is chosen to cover the space; e.g. we could choose the patches to be single qubits or nearest-neighbor sites on a lattice. Local wavefunctions associated with neighboring pairs of spatial patches I<\/mml:mi><\/mml:math> and J<\/mml:mi><\/mml:math> are related to each other by dynamical unitary transformations U<\/mml:mi>I<\/mml:mi>J<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math>. The local wavefunctions are local in the sense that their dynamics are local. That is, the equations of motion for the local wavefunctions |<\/mml:mo><\/mml:mrow>&#x03C8;<\/mml:mi>J<\/mml:mi><\/mml:msub>&#x27E9;<\/mml:mo><\/mml:math> and connections U<\/mml:mi>I<\/mml:mi>J<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:math> are explicitly local in space and only depend on nearby Hamiltonian terms. (The local wavefunctions are many-body wavefunctions and have the same Hilbert space dimension as the usual wavefunction.) We call this picture of quantum dynamics the gauge picture since it exhibits a local gauge invariance. The local dynamics of a single spatial patch is related to the interaction picture, where the interaction Hamiltonian consists of only nearby Hamiltonian terms. We can also generalize the explicit locality to include locality in local charge and energy densities.<\/jats:p>","DOI":"10.22331\/q-2024-03-21-1295","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T10:53:21Z","timestamp":1711018401000},"page":"1295","update-policy":"http:\/\/dx.doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["The Gauge Picture of Quantum Dynamics"],"prefix":"10.22331","volume":"8","author":[{"given":"Kevin","family":"Slagle","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005 USA"},{"name":"Department of Physics, California Institute of Technology, Pasadena, California 91125, USA"},{"name":"Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA"}]}],"member":"9598","published-online":{"date-parts":[[2024,3,21]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"David Deutsch and Patrick Hayden. ``Information flow in entangled quantum systems''. 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