Lagrangian field theories: ind/pro-approach and L∞-algebra of local observables
Lagrangian field theories: ind/pro-approach and L∞-algebra of local observables
View/Type of Scholarly Publication
DissertationDate of Exam
04.05.2018Date of Publication
11.05.2018Advisor
Teichner, PeterCo-Referee
Ballmann, WernerMetadata
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Abstract
Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to different topological and Frechét structures on it. A category of local (insular) manifolds has been constructed. Noether's second theorem is reviewed and the notion of Lie pseudogroups is explored using these concepts.
The L∞-algebra of local observables is defined depending only on the cohomology of the Lagrangian (using a result in multisymplectic manifold which has been extended to the local category). That local pre-multisymplectic form, called the Poincaré-Cartan can be thought of as a coordinate free, cohomological version of other similar structures in the field.
The L∞-algebra of local observables is defined depending only on the cohomology of the Lagrangian (using a result in multisymplectic manifold which has been extended to the local category). That local pre-multisymplectic form, called the Poincaré-Cartan can be thought of as a coordinate free, cohomological version of other similar structures in the field.
Subjects
Mathematical physics, Symplectic geometry, Differential geometry, Higher differential geometry, L-infinity algebra, Variational calculus, Lagrangian Field theory, Observables, Frechet geometry
Classification (DDC)
510 MathematikLeón Delgado, Néstor: Lagrangian field theories: ind/pro-approach and L∞-algebra of local observables. - Bonn, 2018. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-50257
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-50257
@phdthesis{handle:20.500.11811/7534,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-50257,
author = {{Néstor León Delgado}},
title = {Lagrangian field theories: ind/pro-approach and L∞-algebra of local observables},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2018,
month = may,
note = {Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to different topological and Frechét structures on it. A category of local (insular) manifolds has been constructed. Noether's second theorem is reviewed and the notion of Lie pseudogroups is explored using these concepts.
The L∞-algebra of local observables is defined depending only on the cohomology of the Lagrangian (using a result in multisymplectic manifold which has been extended to the local category). That local pre-multisymplectic form, called the Poincaré-Cartan can be thought of as a coordinate free, cohomological version of other similar structures in the field.},
url = {https://hdl.handle.net/20.500.11811/7534}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-50257,
author = {{Néstor León Delgado}},
title = {Lagrangian field theories: ind/pro-approach and L∞-algebra of local observables},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2018,
month = may,
note = {Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to different topological and Frechét structures on it. A category of local (insular) manifolds has been constructed. Noether's second theorem is reviewed and the notion of Lie pseudogroups is explored using these concepts.
The L∞-algebra of local observables is defined depending only on the cohomology of the Lagrangian (using a result in multisymplectic manifold which has been extended to the local category). That local pre-multisymplectic form, called the Poincaré-Cartan can be thought of as a coordinate free, cohomological version of other similar structures in the field.},
url = {https://hdl.handle.net/20.500.11811/7534}
}
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