principle of extremal action, Euler-Lagrange equations, de Donder-Weyl formalism
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
field theory: classical, pre-quantum, quantum, perturbative quantum
Euler-Lagrange form, presymplectic current?
quantum mechanical system, quantum probability
state on a star-algebra, expectation value
collapse of the wave function?/conditional expectation value
quasi-free state?,
canonical commutation relations, Weyl relations?
normal ordered product?
interacting field quantization
equality (definitional, propositional, computational, judgemental, extensional, intensional, decidable)
isomorphism, weak equivalence, homotopy equivalence, weak homotopy equivalence, equivalence in an (∞,1)-category
Examples.
In variational calculus the Euler-Lagrange equations of a nonlinear functional arising from transgression of a local Lagrangian density characterize the extrema of that functional, hence its critical locus (the “shell”).
This originates from and is mainly used in physics, specifically in Lagrangian field theory, where the functional in question is the action functional of a physical system, and where its critical points encode the physically realized field histories by the principle of extremal action.
See at A first idea of quantum field theory this def.
The Euler-Lagrange equations of the Einstein-Hilbert action are Einstein's equations of gravity.
Wikipedia, Euler-Lagrange equation.
Robert Bryant, Phillip Griffiths, Daniel Grossman, Exterior differential systems and Euler-Lagrange partial differential equations, Chicago Lectures in Mathematics 2003, 205+xiv pp. math.DG/0207039 bookpage
Higher prequantum geometry II: The principle of extremal action – comonadically
Last revised on January 7, 2018 at 05:09:42. See the history of this page for a list of all contributions to it.