Quantum Field Theory
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... no spooky action at a distance (Einstein)
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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 MechanismStandard Model | |

Semi-Classical Gravity and the Dark Age
| Hawking Radiation Chandrashekhar Limit Inflation Problems with the Standard Model | |

Outlook
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Beyond the Standard Model
| Beyond the Standard Model Quantum Gravity Theory of Everything | |

Related
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Related
| De Donder-Weyl Theory | |

The **Higgs Mechanism** is a process whereby the spin-1 bosons of a gauge field can acquire mass without spoiling the theory's renormalisability.

In its simplest form (as in the Standard Model), a scalar field (the Higgs Field), charged under the Gauge Field that is to be "higgsed" (e.g. $ SU(2)\times U(1) $, in the Standard Model), acquires a nonzero Vacuum Expectation Value (a nonzero energy density for the field, even in its zero-particle ground state) thanks to a self-interaction potential. The Goldstone Bosons of this charged condensate add a third, spin-0 component to the two degrees of freedom of the massless spin-1 bosons, creating a massive spin-1 boson with three spin states, -1, 0, and +1.

Such a charged condensate is also capable of giving a mass to Chiral fermions in a Gauge-Invariant way, through an interaction term in which a left-handed fermion and a right-handed Fermion couple to the scalar field, e.g. as in the Yukawa Interaction terms in the Standard Model Lagrangian Density.

## In Electroweak theory and Quantum ChromodynamicsEdit this section

The Electroweak Lagrangian Density is given by: $ \mathcal{L} -\frac{1}{4}{{I}^{\mu \nu \rho }}{{I}_{\mu \nu \rho } }+i\hbar {{c}_{0}}\bar{\psi }{{\not{\nabla }} }\psi -\bar{\psi }{{m} }c_{0}^{2}\psi $

As you can see, a more natural description of the mass can be given by using a "*Higgs Field*" $ \phi $ such that the following:

$ {{\mathsf{\mathcal{L}}} }=-\frac{1}{4}{{I}^{\mu \nu \rho }}{{I}_{\mu \nu \rho }}+i\hbar {{c}_{0}}\bar{\psi }{{\not{\nabla }} }\psi +{{c}_{0}}\bar{\psi }\phi \psi $

## Lagrangian Density for the HiggsEdit this section

The Higgs Field is a Scalar Field, also known as a Klein-Gordon Field, and it consequently satisfies the Klein-Gordon Equation. Like any other Klein-Gordon Field, it has the following/ Lagrangian Density:

$ \mathcal{L}=| \nabla^2 \phi | - V(\phi) $ . \

## Electroweak Symmetry BreakingEdit this section

The **Higgs Mechanism** makes W & Z Bosons massive, leaving photons massless by breaking Electroweak Symmetry, i.e. by breaking the $ SU(2)\times U(1) $ symmetry.

## The Higgs BosonEdit this section

The Higgs Boson is an excitation of the Higgs Field.

It was experimentally detected at the LHC in 2011 at a mass of 125 Giga-electron-Volts. This experimental finding was again re-confirmed in 2012, and finally finalised in 2013, also thereby confirming a prediction of the Minimal Supersymmetric Standard Model. It is a popular myth that it confirms a prediction of the Non-Supersymmetric Standard Model.