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The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction.
The main example is the case that the real vector space V is a hermitian vector space (V, h), i.e., V is equipped with a complex structure J that is an orthogonal transformation with respect to the inner product g on V. Then splits in the ±i eigenspaces of J.
Spin is the fundamental property that distinguishes the two types of elementary particles: fermions, with half-integer spins; and bosons, with integer spins. Photons, which are the quanta of light, have been long recognized as spin-1 gauge bosons. The polarization of the light is commonly accepted as its “intrinsic” spin degree of freedom ...
A spin model is a mathematical model used in physics primarily to explain magnetism. Spin models may either be classical or quantum mechanical in nature. Spin models have been studied in quantum field theory as examples of integrable models. Spin models are also used in quantum information theory and computability theory in theoretical computer ...
Many pieces of the Standard Model of physics are non-chiral, which is traceable to anomaly cancellation in chiral theories. Quantum chromodynamics is an example of a vector theory, since both chiralities of all quarks appear in the theory, and couple to gluons in the same way.
The spin magnetic moment of the electron is =, where is the spin (or intrinsic angular-momentum) vector, is the Bohr magneton, and = is the electron-spin g-factor. Here μ {\displaystyle {\boldsymbol {\mu }}} is a negative constant multiplied by the spin , so the spin magnetic moment is antiparallel to the spin.
In particle physics the spin–statistics theorem implies that the wavefunction of an uncharged fermion is a section of the associated vector bundle to the spin lift of an SO(N) bundle E. Therefore, the choice of spin structure is part of the data needed to define the wavefunction, and one often needs to sum over these choices in the partition ...
Spin- 1 / 2 particles can have a permanent magnetic moment along the direction of their spin, and this magnetic moment gives rise to electromagnetic interactions that depend on the spin. One such effect that was important in the discovery of spin is the Zeeman effect , the splitting of a spectral line into several components in the ...