|Quantum Field Theory|
|... no spooky action at a distance (Einstein)|
|Relativistic Quantum Mechanics|| Klein-Gordon Equation|
|The Dawn of QFT|| Spinors|
Feynman Slash Notation
Conformal Field Theory
Countdown to the Standard Model
|From a framework to a model|| Yang-Mills Theory|
|Semi-Classical Gravity and the Dark Age|| Hawking Radiation|
Problems with the Standard Model
|Beyond the Standard Model|| Beyond the Standard Model|
Theory of Everything
|Related||De Donder-Weyl Theory|
Mathematical FormulationEdit this section
Starting PointEdit this section
The Hamiltonian in Physics is generally strongly tied to the idea of time, as opposed to space, since it is trivial that the Hamiltonian describes the Time-Evolution. This can be seen in, for example, Noether's Theorem and Schrodinger's Equation.
For similar reasons, in Quantum Field Theory,
We thus see, that this is a rather irritating statement for someone who is comfortable with the world of manifestly Lorentz-Invariant creatures.
Therefore, we may instead define the so - called "Polymomenta", as De-Donder and Weyl called it, so that
De Donder-Weyl EquationsEdit this section
The result of this is rather trivially the "De Donder-Weyl Equations":
ReferencesEdit this section
- ↑ Paufler, Cornelius; Romer, Hartmann. (2002). "De Donder–Weyl equations and multisymplectic geometry". Reports on Mathematical Physics 49 (2 - 3): 325 - 334. http://wwwthep.physik.uni-mainz.de/~paufler/publications/DWeqMultSympGeom.pdf.