# Electroweak Theory

*118*articles on

the Psi Epsilon Wikia

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 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 TheoryHiggs 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 | |

**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 **L**eft-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 DensityEdit this section

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 EquationEdit this section

From the result of the last section, we see that

## Electroweak Symmetry BreakingEdit this section

*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.