dc.contributor.author Pitts, J Brian dc.date.accessioned 2021-11-22T14:45:02Z dc.date.available 2021-11-22T14:45:02Z dc.date.issued 2021-12 dc.date.submitted 2020-10-01 dc.identifier.issn 0015-9018 dc.identifier.other s10701-021-00509-x dc.identifier.other 509 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/330882 dc.description.abstract AbstractIn General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. By construing change as essential time dependence (lack of a time-like Killing vector field), one can find change locally in vacuum GR in the Hamiltonian formulation just where it should be. But what if spinors are present? This paper is motivated by the tendency in space-time philosophy tends to slight fermionic/spinorial matter, the tendency in Hamiltonian GR to misplace changes of time coordinate, and the tendency in treatments of the Einstein-Dirac equation to include a gratuitous local Lorentz gauge symmetry along with the physically significant coordinate freedom. Spatial dependence is dropped in most of the paper, both restricting the physical situation and largely fixing the spatial coordinates. In the interest of including all and only the coordinate freedom, the Einstein-Dirac equation is investigated using the Schwinger time gauge and Kibble-Deser symmetric triad condition are employed as a $$3+1$$ 3 + 1 version of the DeWitt-Ogievetsky-Polubarinov nonlinear group realization formalism that dispenses with a tetrad and local Lorentz gauge freedom. Change is the lack of a time-like stronger-than-Killing field for which the Lie derivative of the metric-spinor complex vanishes. An appropriate $$3+1$$ 3 + 1 -friendly form of the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first class-constraints, is shown to change the canonical Lagrangian by a total derivative, implying the preservation of Hamilton’s equations. Given the essential presence of second-class constraints with spinors and their lack of resemblance to a gauge theory (unlike, say, massive photons), it is useful to have an explicit physically interesting example. This gauge generator implements changes of time coordinate for solutions of the equations of motion, showing that the gauge generator makes sense even with spinors. dc.language en dc.publisher Springer Science and Business Media LLC dc.subject Article dc.subject Constrained Hamiltonian dynamics dc.subject General relativity dc.subject Problem of time dc.subject Quantum gravity dc.subject Variational principles dc.subject Spinors dc.subject Geometric objects dc.subject Lie derivatives dc.subject Einstein–Dirac equations dc.subject Nonlinear group realizations dc.title Change in Hamiltonian General Relativity with Spinors dc.type Article dc.date.updated 2021-11-22T14:45:01Z prism.issueIdentifier 6 prism.publicationName Foundations of Physics prism.volume 51 dc.identifier.doi 10.17863/CAM.78325 dcterms.dateAccepted 2021-10-08 rioxxterms.versionofrecord 10.1007/s10701-021-00509-x rioxxterms.version VoR rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ dc.contributor.orcid Pitts, J Brian [0000-0002-7299-5137] dc.identifier.eissn 1572-9516 pubs.funder-project-id National Science Foundation (USA) (1734402) cam.issuedOnline 2021-11-03
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