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{{Short description|Unified quantum field theory describing the electromagnetic and weak interactions via SU(2) × U(1) gauge symmetry}}

{{Quantum book backlink|Quantum field theory}}
'''Electroweak theory''' is the unified quantum field theory that combines the electromagnetic and weak interactions into a single framework based on the gauge symmetry group <math>SU(2)_L \times U(1)_Y</math>.<ref name="weinberg">Weinberg, S. (1967). A model of leptons.</ref> It forms a central part of the Standard Model of particle physics.

<div style="float:right; border:1px solid #ccc; padding:4px; background:#fff8dc; margin:0 0 1em 1em; width:420px;">
[[File:Electroweak_unification_diagram.jpg|400px]]
<div style="font-size:90%;">Electroweak unification: electromagnetic and weak interactions arising from a single gauge structure</div>
</div>

== Unification of forces ==
Electroweak theory shows that the electromagnetic force and weak nuclear force are different manifestations of a single interaction at high energies.

At low energies:
* electromagnetic interaction → long-range force
* weak interaction → short-range force

At high energies, they merge into a unified electroweak interaction.<ref name="peskin">Peskin, M. E.; Schroeder, D. V. ''An Introduction to Quantum Field Theory'' (1995).</ref>

== Gauge symmetry ==
The theory is based on the symmetry group:
<math>
SU(2)_L \times U(1)_Y
</math>

where:

* <math>SU(2)_L</math> acts on left-handed fermions
* <math>U(1)_Y</math> corresponds to weak hypercharge

Gauge fields are introduced to preserve local symmetry, leading to four gauge bosons.<ref name="schwartz">Schwartz, M. D. ''Quantum Field Theory and the Standard Model'' (2014).</ref>

== Gauge bosons ==
The electroweak theory predicts four gauge bosons:

* <math>W^1_\mu, W^2_\mu, W^3_\mu</math> (from <math>SU(2)</math>)
* <math>B_\mu</math> (from <math>U(1)</math>)

These combine to form the physical particles:

* <math>W^+</math> and <math>W^-</math> (charged weak bosons)
* <math>Z^0</math> (neutral weak boson)
* <math>\gamma</math> (photon)

This mixing explains how electromagnetic and weak forces are related.<ref name="weinberg"/>

== Spontaneous symmetry breaking ==
The electroweak symmetry is not directly observed because it is spontaneously broken.

This occurs through the Higgs mechanism, introducing a scalar field whose vacuum expectation value selects a specific ground state:
<math>
\langle \phi \rangle \neq 0
</math>

As a result:

* <math>W^\pm</math> and <math>Z^0</math> acquire mass
* the photon remains massless

This explains the short range of the weak interaction.<ref name="higgs">Higgs, P. W. (1964). Broken symmetries and the masses of gauge bosons.</ref>

== Electroweak Lagrangian ==
The electroweak Lagrangian includes:

* fermion kinetic terms
* gauge field terms
* Higgs field contributions
* interaction terms

These components together describe the full dynamics of the electroweak interaction.

== Weak interactions ==
The weak interaction involves processes such as:

* beta decay
* neutrino interactions
* flavor-changing processes

These are mediated by the <math>W^\pm</math> and <math>Z^0</math> bosons.

== Experimental confirmation ==
Electroweak theory has been confirmed by numerous experiments, including:

* discovery of the <math>W</math> and <math>Z</math> bosons
* precision measurements at particle accelerators
* observation of the Higgs boson

These results strongly support the validity of the theory.<ref name="schwartz"/>

== Role in the Standard Model ==
Electroweak theory, together with quantum chromodynamics, forms the core of the Standard Model.

It unifies two of the fundamental forces and provides a consistent framework for describing particle interactions.

== Conceptual importance ==
Electroweak theory demonstrates how gauge symmetry and spontaneous symmetry breaking combine to produce realistic physical theories.

It is a cornerstone of modern particle physics and a key step toward deeper unification.

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

==References==
{{reflist|3}}
{{Author|Harold Foppele}}

{{Sourceattribution|Quantum field theory (QFT) core|1}}

Physics:Quantum Electroweak theory - Revision history

imported>WikiHarold: Repair Quantum Collection B backlink template

imported>WikiHarold: Repair Quantum Collection B backlink template