N-Symplectic Analysis of Field Theory

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dc.contributor.advisor L. K. Norris, Chair en_US
dc.contributor.advisor R. O. Fulp, Member en_US
dc.contributor.advisor A. Kheyfets, Member en_US
dc.contributor.advisor H. J. Charlton, Member en_US
dc.contributor.author McLean, Michael A. en_US
dc.date.accessioned 2010-04-02T18:55:19Z
dc.date.available 2010-04-02T18:55:19Z
dc.date.issued 2001-04-23 en_US
dc.identifier.other etd-20010420-142529 en_US
dc.identifier.uri http://www.lib.ncsu.edu/resolver/1840.16/4515
dc.description.abstract Two techniques for relating n-symplectic geometry tothe jet bundle formulations of classical fieldtheory are presented.The tangent bundle of the frame bundle of a manifoldM is shown to be a principal fiber bundle over thejet bundle of the tangent bundle of M. We are ableto generalize this result to symmetric andantisymmetric tensor bundles of rank p. Using thisGL(m) gauge freedom, we interpret the standard freefield Lagrangian as a symmetric type (0,2) tensor onLM. The adapted frame bundle of an arbitrary fiberbundle PI is shown to be a principal bundle over thejet bundle of PI. Using this GL(m) times GL(k) gaugefreedom we generate a modified m+k-symplecticgeometry from a lifted Lagrangian. The modifiedsoldering form is shown to induce the Cartan-Hamilton-Poincare m-form on the jet bundleof PI. We derive generalized Hamilton-Jacobi andHamilton equations on adapted frame bundle, andshow that the Hamilton-Jacobi and canonicalequations of Caratheodory-Rund and de Donder-Weylare obtained as special cases.These results demonstrate that by introducingadditional gauge freedom into the standard jetbundle formalism one can obtain a great of ofadditional geometric and algebraic structure. Suchadditional structure may be key in achieving agreater understanding of field theory or in attempts at quantization. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.title N-Symplectic Analysis of Field Theory en_US
dc.degree.name PhD en_US
dc.degree.level PhD Dissertation en_US
dc.degree.discipline Mathematics en_US

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