Jean Charles Athanase Peltier: Difference between revisions

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{{Expert-subject|Physics|date=July 2009}}
{{Unreferenced|date=July 2009}}
}}
 
'''Left–right symmetry''' is a general principle in [[physics]] which holds that valid physical laws must not produce a different result for a motion that is left-handed than motion that is right-handed. The most common application is expressed as equal treatment of clockwise and counter-clockwise rotations from a fixed frame of reference.
 
The general principle is often referred to by the name '''[[Chirality (physics)|chiral]] symmetry'''. The rule is absolutely valid in the [[classical mechanics]] of [[Isaac Newton|Newton]] and [[Albert Einstein|Einstein]], but results from [[quantum mechanics|quantum mechanical]] experiments show a difference in the behavior of left-chiral versus right-chiral [[subatomic particles]].
 
==Particle Physics==
In [[theoretical physics]], the [[electroweak]] model breaks [[parity (physics)|parity]] maximally. All its [[fermion]]s are [[chirality (physics)|chiral]] [[Weyl fermion]]s, which means that the charged [[W and Z bosons|weak gauge bosons]] only couple to left-handed quarks and leptons. (Note that the neutral electroweak Z boson already couples to left ''and'' right-handed fermions.)  Some theorists found this objectionable, and so proposed a [[Grand unification theory|GUT]] extension of the [[weak force]] which has new, high energy [[W' and Z' bosons]] which couple with right handed quarks and leptons.
 
:<math>{[SU(2)_W\times U(1)_Y]\over \mathbb{Z}_2}</math>
 
to
 
:<math>{SU(2)_L\times SU(2)_R\times U(1)_{B-L}\over \mathbb{Z}_2}.</math>
 
Here, SU(2)<sub>L</sub> (pronounced SU(2) left) is none other than SU(2)<sub>W</sub> and [[B−L]] is the [[baryon number]] minus the [[lepton number]]. An advantage of this model over the Standard Model is that the electric charge formula in this model is given by
 
:<math> Q= I_{3L}+I_{3R}+\frac{B-L}{2}</math>;
 
where <math>\! I_{3L,R}</math> are the [[weak isospin]] values of the fields in the theory.
 
There is also the [[chromodynamic]] SU(3)<sub>C</sub>. The idea was to restore parity by introducing a '''left-right symmetry'''. This is a [[group extension]] of '''Z'''<sub>2</sub> (the left-right symmetry) by
 
:<math>{SU(3)_C\times SU(2)_L \times SU(2)_R \times U(1)_{B-L}\over \mathbb{Z}_6}</math>
 
to the [[semidirect product]]
 
:<math>{SU(3)_C\times SU(2)_L \times SU(2)_R \times U(1)_{B-L}\over \mathbb{Z}_6} \rtimes \mathbb{Z}_2.</math>
 
This has two [[connected space|connected component]]s where '''Z'''<sub>2</sub> acts as an [[automorphism]], which is the composition of an [[Involution (mathematics)|involutive]] [[outer automorphism]] of SU(3)<sub>C</sub> with the interchange of the left and right copies of SU(2) with the reversal of U(1)<sub>B−L</sub>. It was shown by Rabindra N. Mohapatra and [[Goran Senjanovic]] in 1975 that [[left-right symmetry]] can be [[spontaneous symmetry breaking|spontaneously broken]] to give a chiral low energy theory, which is the Standard Model of Glashow, Weinberg and Salam and it also connects the small observed neutrino masses to the breaking of left-right symmetry via the [[seesaw mechanism]].
 
In this setting the chiral [[quark]]s
 
:(3,2,1)<sub>1/3</sub>
 
and
 
:<math>(\bar{3},1,2)_{-{1\over 3}}</math>
 
are unified into an [[irreducible representation|irrep]]
 
:<math>(3,2,1)_{1\over 3}\oplus(\bar{3},1,2)_{-{1\over 3}}.</math>
 
The [[lepton]]s are also unified into an irrep
 
:<math>(1,2,1)_{-1}\oplus(1,1,2)_1.</math>
 
The Higgs bosons needed to implement the breaking of left-right symmetry down to the Standard Model
are
 
:<math>(1,3,1)_{2}\oplus(1,1,3)_{2}.</math>
 
This then predicts three [[sterile neutrino]]s, which is perfectly consistent with {{As of|2005|alt=current}} [[neutrino oscillation]] data. Within the seesaw mechanism, the sterile neutrinos become superheavy without affecting physics at low energies.
 
Because the left-right symmetry is spontaneously broken, left-right models predict [[Domain wall (string theory)|domain wall]]s.
 
This left-right symmetry idea first appeared in the [[Pati-Salam model]] (1974), Mohapatra-Pati models (1975) and later in [[trinification]] (1984).
 
{{DEFAULTSORT:Left-Right Symmetry}}
[[Category:Particle physics]]
[[Category:Symmetry]]

Latest revision as of 02:15, 23 September 2014

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