Quantum Field Theory | ||
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... no spooky action at a distance (Einstein) | ||
Early Results
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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
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From a framework to a model | Yang-Mills Theory Quantum Electrodynamics Quantum Chromodynamics Electroweak Theory Higgs Mechanism Standard Model |
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Semi-Classical Gravity and the Dark Age | Hawking Radiation Chandrashekhar Limit Inflation Problems with the Standard Model |
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Outlook
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Beyond the Standard Model | Beyond the Standard Model Quantum Gravity Theory of Everything |
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Related
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Related | De Donder-Weyl Theory | |
Electroweak Theory is a Quantum Field Theory which unifies Electromagnetism and the Weak Nuclear Force in a single Gauge Field with gauge group , where acts only on Left-Handed Fermions, and is "hypercharge". The Higgs Mechanism gives mass to the W and Z components of this gauge field, and breaks the symmetry to , as described by Quantum Electrodynamics.
Lagrangian Density[]
It can be easily shown like as for other Quantum Field Theoryies, that the Dirac Equation for Electroweak Theory is:
The Lagrangian Density excluding field strength is given by:
Here, is the mass of the W/Z boson, is the Weak Field, is the Photon Field, and is the Weak Hypercharge.
If one lets
and
then the Lagrangian Density (with a field strength
Dirac Equation[]
From the result of the last section, we see that
Electroweak Symmetry Breaking[]
- Main Article: Higgs Mechanism
As per Experimental Results, Photons are massless, whereas Weak Force mediating W and Z Bosons are massive. If these W and Z Bosons are massive, then this means that Electroweak Symmetry is broken. This Electroweak Symmetry Breaking is the result of the Higgs Mechanism.