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The choice of symmetry or antisymmetry is determined by the species of particle. For example, symmetric states must always be used when describing photons or helium-4 atoms, and antisymmetric states when describing electrons or protons. Particles which exhibit symmetric states are called bosons. The nature of symmetric states has important ...
Such a state is either completely symmetric under exchange of all identical bosons or completely antisymmetric under exchange of all identical fermions of the system. To do so for fermions, for example, the antisymmetrizer builds such a completely antisymmetric state. In 2 dimensions, the adiabatic exchange of particles is not necessarily possible.
Exchanging and gives either a symmetric combination of the states ("plus") or an antisymmetric combination ("minus"). Particles that give symmetric combinations are called bosons; those with antisymmetric combinations are called fermions. The two possible combinations imply different physics.
The discovery of antisymmetric exchange originated in the early 20th century from the controversial observation of weak ferromagnetism in typically antiferromagnetic α-Fe 2 O 3 crystals. [1] In 1958, Igor Dzyaloshinskii provided evidence that the interaction was due to the relativistic spin lattice and magnetic dipole interactions based on Lev ...
It satisfies anti-symmetry requirements, and consequently the Pauli principle, by changing sign upon exchange of two electrons (or other fermions). [1] Only a small subset of all possible fermionic wave functions can be written as a single Slater determinant, but those form an important and useful subset because of their simplicity.
A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (for example, the "preys on" relation on biological species). Antisymmetry is different from asymmetry: a relation is asymmetric if and only if it is antisymmetric and irreflexive.
This article describes the mathematics of the Standard Model of particle physics, a gauge quantum field theory containing the internal symmetries of the unitary product group SU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – the leptons, quarks, gauge bosons and the Higgs boson.
A more rigorous statement is: under the exchange of two identical particles, the total (many-particle) wave function is antisymmetric for fermions and symmetric for bosons. This means that if the space and spin coordinates of two identical particles are interchanged, then the total wave function changes sign for fermions, but does not change ...