field history

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

**quantum mechanical system**, **quantum probability**

**interacting field quantization**

Given a Lagrangian field theory with field bundle $E \overset{fb}{\to} \Sigma$ over spacetime $\Sigma$, then a *field history* is a smooth section of this field bundle $\Phi \in \Gamma_\Sigma(E)$.

For every Cauchy surface $\Sigma_p \hookrightarrow \Sigma$ the restriction $\Phi\vert_{\Sigma_p}$ of $\Phi$ to $\Sigma_p$ may be thought of as the *field configuration* “at that time” and hence the change of $\Phi\vert_{\Sigma_p}$ as the choice of Cauchy surface changes reflects the “history” of these configurations, whence the name.

For a sigma model field theory a field history may be thought of as a *trajectory*.

For more see at *geometry of physics – perturbative quantum field theory* the chapter *Fields*.

Last revised on August 1, 2018 at 08:23:32. See the history of this page for a list of all contributions to it.