Quantum Field Theory
... no spooky action at a distance (Einstein)
Early Results
Relativistic Quantum Mechanics Klein-Gordon Equation
Dirac Equation
The Dawn of QFT Spinors
Feynman Slash Notation
Klein-Gordon Field
Dirac Field
Grassman Variable
Conformal Field Theory
Countdown to the Standard Model
From a framework to a model Yang-Mills Theory
Quantum Electrodynamics
Quantum Chromodynamics
Electroweak Theory
Higgs Mechanism
Standard Model
Semi-Classical Gravity and the Dark Age Hawking Radiation
Chandrashekhar Limit
Problems with the Standard Model
Beyond the Standard Model Beyond the Standard Model
Quantum Gravity
Theory of Everything
Related De Donder-Weyl Theory

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The Yang-Mills Theory describes gluons and other gauge interactions. The Yang-Mills Lagrangian Density is given by:

$ \mathcal{L}=-\frac12\mathrm{tr} \left(F^{\mu\nu}F_{\mu\nu}\right) $

Here, the Tensor $ F_{\mu\nu} $ is given by:

$ F_{\mu\nu}=\frac1{ig} \left[\nabla_\mu,\nabla_\nu\right] $

Here, $ g $ is the coupling constant in question and $ \left[\cdot,\cdot\right] $ is the Commutator Bracket. Here, the Covariant Derivative is given by: $ \nabla_\mu = I \partial_\mu - i g T_a V_\mu^a $

Here, $ I $ is the identity, and $ V $ is the Vector Potential.

Faddeev-Popov GhostsEdit this section