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Quantum Field Theory
QFT
... no spooky action at a distance (Einstein)
Early Results
Relativistic Quantum Mechanics Klein-Gordon Equation
Dirac Equation
The Dawn of QFT Spinors
Spin
Feynman Slash Notation
Antimatter
Klein-Gordon Field
Dirac Field
Renormalisation
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
Inflation
Problems with the Standard Model
Outlook
Beyond the Standard Model Beyond the Standard Model
Quantum Gravity
Theory of Everything
Related
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.

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