Change in Hamiltonian General Relativity with Spinors
dc.contributor.author  Pitts, J Brian  
dc.date.accessioned  20211122T14:45:02Z  
dc.date.available  20211122T14:45:02Z  
dc.date.issued  202112  
dc.date.submitted  20201001  
dc.identifier.issn  00159018  
dc.identifier.other  s1070102100509x  
dc.identifier.other  509  
dc.identifier.uri  https://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 firstclass constraints and a boundary term and thus supposedly generates gauge transformations. By construing change as essential time dependence (lack of a timelike 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 spacetime 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 EinsteinDirac 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 EinsteinDirac equation is investigated using the Schwinger time gauge and KibbleDeser symmetric triad condition are employed as a <jats:inlineformula><jats:alternatives><jats:texmath>$$3+1$$</jats:texmath><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:inlineformula> version of the DeWittOgievetskyPolubarinov nonlinear group realization formalism that dispenses with a tetrad and local Lorentz gauge freedom. Change is the lack of a timelike strongerthanKilling field for which the Lie derivative of the metricspinor complex vanishes. An appropriate <jats:inlineformula><jats:alternatives><jats:texmath>$$3+1$$</jats:texmath><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:inlineformula>friendly form of the RosenfeldAndersonBergmannCastellani gauge generator <jats:italic>G</jats:italic>, a tuned sum of first classconstraints, is shown to change the canonical Lagrangian by a total derivative, implying the preservation of Hamilton’s equations. Given the essential presence of secondclass 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.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  20211122T14:45:01Z  
prism.issueIdentifier  6  
prism.publicationName  Foundations of Physics  
prism.volume  51  
dc.identifier.doi  10.17863/CAM.78325  
dcterms.dateAccepted  20211008  
rioxxterms.versionofrecord  10.1007/s1070102100509x  
rioxxterms.version  VoR  
rioxxterms.licenseref.uri  http://creativecommons.org/licenses/by/4.0/  
dc.contributor.orcid  Pitts, J Brian [0000000272995137]  
dc.identifier.eissn  15729516  
pubs.funderprojectid  National Science Foundation (USA) (1734402)  
cam.issuedOnline  20211103 
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