Isospin
The isotopic spin is in the theory of elementary a Flavor  quantum number , an inner symmetry of the strong interaction describes and for classifying the hadrons is used. The designation ( iso : “quantitatively equal”, from ancient Greek ἴσος) indicates that the system appears like a spin 1/2 particle , although it is not a spin .
The concept is used more generally (also in solidstate physics ) to describe twostate systems . The two quantum mechanical states are understood as opposing orientations of the isospin (± ). If the system is in a superposition of the two states, this is described by the two other components ( ).
discovery
In scattering processes on mirror cores it was found that the strong interaction does not differentiate between neutral neutrons and positively charged protons , i.e. This means that it acts independently of the charge. With regard to the nuclear force, the neutron and proton are identical, and their slight difference in mass is related to the electrical charge . Werner Heisenberg concluded from this in 1932 that the proton and the neutron are two different charge states of one and the same particle, the nucleon .
For a further description he “borrowed” the quantum mechanical spin formalism from the corresponding behavior of the electrons . They also have two states ( spinup and spindown ) which cannot be distinguished by a certain force  here the purely electrical force.
The name Isospin was coined by Eugene Wigner in 1937 and initially stood for isotopic spin . However, since this can be misinterpreted as an indication of a change in the number of neutrons (cf. isotope ), the term isobaric spin is used today. Murray GellMann combined the properties of isospin and strangeness in the Eightfold Way , a direct precursor of the quark model and quantum chromodynamics .
formalism
up  

Quark / antiquark  u  u 
Isospin  + ½  ½ 
down  
Quark / antiquark  d  d 
Isospin  ½  + ½ 
Like the normal spin of the fundamental fermions (such as the electron), the quantum number of the isospin always has the value 1/2.
The canonically used third component (often also referred to as) of the isospin represents its setting and has the two possible values +1/2 and −1/2. In the quark model, these stand for the two quarks
 u ( up ): and
 d ( down , Eng .: below): .
The quarks s , c , b and t do not have an isospin. For anti quarks the sign changes from .
The number of u and d quarks and the associated antiquarks is thus given as follows :
 .
The difference between protons and neutrons results from their composition:
 Proton p = uud
 Neutron n = udd .
This assignment is done the other way around in some books and is just a convention that doesn't matter as long as consistency is maintained.
Hypercharge
Particle  Components  el. charge 
Isospin 
Hyperldg. 


Quarks  Up  u  +2/3  + ½  +1/3 
Antiup  u  2/3  ½  1/3  
Down  d  1/3  ½  +1/3  
Antidown  d  +1/3  + ½  1/3  
Hadrons  proton  uud  +1  + ½  +1 
neutron  udd  0  ½  +1 
Due to their isospin and their electrical charge , many particles can be assigned a hypercharge using the GellMannNishijima formula :
The hypercharge is
 for up and down quark respectively:
 for antiup and antidown quark:
 for the nucleons ( protons p, neutron n) respectively: .
Quantum field theory
Within the framework of quantum field theory , the isospin is assigned the twodimensional complex vector space in which the quarks u and d can be represented as basis vectors :
This makes it possible to describe the transformation of nucleons as the radioactive decay takes place: . This is a transformation of SU (2) symmetry described in the weak interaction theory.
Mathematically, these transformations are mediated by ladder operators , which are assigned to the gauge bosons of field theory. For example, the transition is described by the matrix equation
literature
 Bogdan Povh et al .: Particles and Cores . Springer, Berlin, Heidelberg 2006, ISBN 9783540366850
Individual evidence
 ^ W. Heisenberg: About the construction of atomic nuclei . In: Journal of Physics . tape 77 , 1932, pp. 1–11 , doi : 10.1007 / BF01342433 , bibcode : 1932ZPhy ... 77 .... 1H .