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dc.contributor.authorPitts, J Brian
dc.date.accessioned2021-11-22T14:45:02Z
dc.date.available2021-11-22T14:45:02Z
dc.date.issued2021-12
dc.date.submitted2020-10-01
dc.identifier.issn0015-9018
dc.identifier.others10701-021-00509-x
dc.identifier.other509
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/330882
dc.description.abstract<jats:title>Abstract</jats:title><jats:p>In 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$3+1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> 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 <jats:inline-formula><jats:alternatives><jats:tex-math>$$3+1$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>-friendly form of the Rosenfeld-Anderson-Bergmann-Castellani gauge generator <jats:italic>G</jats:italic>, 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.</jats:p>
dc.languageen
dc.publisherSpringer Science and Business Media LLC
dc.subjectArticle
dc.subjectConstrained Hamiltonian dynamics
dc.subjectGeneral relativity
dc.subjectProblem of time
dc.subjectQuantum gravity
dc.subjectVariational principles
dc.subjectSpinors
dc.subjectGeometric objects
dc.subjectLie derivatives
dc.subjectEinstein–Dirac equations
dc.subjectNonlinear group realizations
dc.titleChange in Hamiltonian General Relativity with Spinors
dc.typeArticle
dc.date.updated2021-11-22T14:45:01Z
prism.issueIdentifier6
prism.publicationNameFoundations of Physics
prism.volume51
dc.identifier.doi10.17863/CAM.78325
dcterms.dateAccepted2021-10-08
rioxxterms.versionofrecord10.1007/s10701-021-00509-x
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidPitts, J Brian [0000-0002-7299-5137]
dc.identifier.eissn1572-9516
pubs.funder-project-idNational Science Foundation (USA) (1734402)
cam.issuedOnline2021-11-03


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