We shall introduce the principal symbol for quite a general class of (quasi linear) Euler–Lagrange operators and use them to characterise well-posed initial value problems in gauge covariant field theories. We shall clarify how constraints can arise in covariant Lagrangian theories by extending the standard treatment in GR and without resorting to Hamiltonian formalism. Finally as an example of application, we sketch a quantisation procedure based on what is done in LQG by framing it in a more general context which applies to general gauge covariant field theories.

Principal symbol of Euler-Lagrange operators

FATIBENE, Lorenzo;GARRUTO, SIMON
2016-01-01

Abstract

We shall introduce the principal symbol for quite a general class of (quasi linear) Euler–Lagrange operators and use them to characterise well-posed initial value problems in gauge covariant field theories. We shall clarify how constraints can arise in covariant Lagrangian theories by extending the standard treatment in GR and without resorting to Hamiltonian formalism. Finally as an example of application, we sketch a quantisation procedure based on what is done in LQG by framing it in a more general context which applies to general gauge covariant field theories.
2016
33
14
145012
145029
https://arxiv.org/pdf/1603.04732.pdf
Cauchy problem; EulerLagrange morphism; principal symbol; Physics and Astronomy (miscellaneous)
Fatibene, L.; Garruto, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1621201
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