nLab space of field histories



Algebraic Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT



In physics, given a physical system then its space of field histories (e.g.trajectories_ for sigma models) is the space of all ways that the system may be configured in space and time, hence in spacetime.

For a field theory over a spacetime Σ\Sigma and defined by a field bundle EfbΣE \overset{fb}{\to} \Sigma, the space of trajectories is the space of field configurations over spacetimes, which is the space of sections of the field bundle.

For Lagrangian field theories this space of trajectories carries a canonical presymplectic form and it comes with an equation of motion that picks some of the trajectories as being the “physically realizable ones”. The subspace of trajectories solving the equations of motion (the “shell”) equipped with this presymplectic form is called the covariant phase space of the system.

For the moment see at field theory for more details.


Discussion in the convenient context of smooth sets:

Last revised on April 13, 2024 at 07:35:09. See the history of this page for a list of all contributions to it.