# Boson

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Standard model with the
gauge bosons (red) and the Higgs boson (yellow)

Bosons (after the Indian physicist Satyendranath Bose ) are all particles that behave according to the Bose-Einstein statistics , in which u. a. several indistinguishable particles can assume the same state. According to the spin statistics theorem , they have an integral angular momentum ( spin ) in units of Planck's${\ displaystyle \ hbar}$ reduced quantum of action  . This is how they can be distinguished from fermions with half-integer spin and anyons with any (also fractional) spin; both types therefore have different statistical properties.

In the standard model of particle physics , the exchange particles that mediate the forces between the fermions are elementary bosons with a spin of 1, such as B. the photon as a transmitter of electromagnetic force . The hypothetical graviton as the carrier of gravitation is also a boson, but with a spin of 2. In addition, with the Higgs boson in the standard model, there is a boson with a spin of 0.

Other bosons are composed of several particles such as B. Cooper pairs of electrons and phonons as charge carriers in the superconductor , atomic nuclei with an even number of nucleons or mesons , i.e. subatomic quark-antiquark pairs. Furthermore, quasiparticles can also show bosonic properties, such as the phonons or spinons already mentioned .

## Classification according to the spin

The elementary bosons are called differently depending on the spin . This designation is based on its transformation behavior under the "actual orthochronous Lorentz transformations" . Elementary particles can, except in a non-local or a string theory , have a maximum spin of 2, because massless particles are subject to the low-energy theorem , which excludes the coupling of high spins to currents of other spins, as well as a ban on self-interactions and for massive particles, the general nonexistence was shown in 2017. Bosons with higher spin are therefore less physically relevant, since they only appear as composite particles.

Spin Boson type Representative
elementary composed
0 Scalar boson Higgs boson Pions , 4 He core
1 Vector boson Photon , W bosons , Z bosons , gluons J / ψ meson , 14 N nucleus
2 Tensor boson Graviton (hypothetical) 36 Cl core, 60 Co core
3 - - 10 B core

## Macroscopic quantum states

A special property of the bosons is that the quantum mechanical wave function does not change when two identical bosons are exchanged ( phase factor +1). In contrast to this, if two identical fermions are exchanged, the sign of the wave function changes. The reason for the invariance of the wave function in the case of boson exchange is based on the relatively complicated spin statistics theorem . After two exchanges (i.e. a mirroring or application of the parity operator ) the original state is clearly obtained again; One-time swapping can only generate a factor of the amount 1, which when squared results in 1 - i.e. either 1 or -1 -, where 1 corresponds to the bosons.

One consequence is that bosons of the same type can be at the same place (within the uncertainty relation ) at the same time ; one then speaks of a Bose-Einstein condensate . Several bosons then assume the same quantum state , they form macroscopic quantum states . Examples are:

## Compound particles

Fermionic or bosonic behavior of composite particles can only be observed from a greater distance (compared to the system under consideration). On closer inspection (on an order of magnitude in which the structure of the components becomes relevant) it becomes apparent that a composite particle behaves according to the properties (spins) of the components. For example, two helium-4 atoms (bosons) cannot occupy the same space if the space under consideration is comparable to the internal structure of the helium atom (≈10 −10  m), since the components of the helium-4 atom are themselves fermions. As a result, liquid helium has a finite density just like an ordinary liquid.

## Supersymmetric bosons

Further elementary bosons exist in the model of elementary particles, which has been expanded to include supersymmetry . Mathematically , for every fermion there is a boson as a supersymmetrical partner particle , a so-called sfermion , so that the spin differs by ± 1/2 in each case. The superpartners of the fermions are generally named with an additional prefix S- . B. the corresponding boson to the electron then selectron .

Strictly speaking, in the interaction picture each fermionic field is initially assigned a bosonic field as a super partner. In the mass image, the observable or predicted particles result as linear combinations of these fields. The number and the relative proportion of the components contributing to the mixtures on the side of the bosonic superpartners do not have to match the proportions on the original fermionic side. In the simplest case (with little or no mixture), however, a particular boson or sfermion (such as the selectron) can be assigned to a fermion (such as the electron).

In addition, the minimal supersymmetric standard model (MSSM), in contrast to the standard model (SM) , already requires several bosonic Higgs fields including their super partners.

So far none of the postulated supersymmetric partner particles has been experimentally proven. They should therefore have such a high mass that they do not arise under normal conditions. It is hoped that the new generation of particle accelerators will be able to detect at least some of these bosons. There are indications that the mass of the lightest supersymmetric particle (LSP) is in the range of a few hundred GeV / c².