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Exchange interaction is the main physical effect responsible for ferromagnetism, and has no classical analogue. For bosons, the exchange symmetry makes them bunch together, and the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation.
In relativistic quantum mechanics, relativistic wave equations predict a remarkable symmetry of nature: that every particle has a corresponding antiparticle. This is mathematically contained in the spinor fields which are the solutions of the relativistic wave equations. Charge conjugation switches particles and antiparticles.
There is actually an exception to this rule, which will be discussed later. On the other hand, it can be shown that the symmetric and antisymmetric states are in a sense special, by examining a particular symmetry of the multiple-particle states known as exchange symmetry. Define a linear operator P, called the exchange operator. When it acts ...
In quantum mechanics, the exchange operator ^, also known as permutation operator, [1] is a quantum mechanical operator that acts on states in Fock space. The exchange operator acts by switching the labels on any two identical particles described by the joint position quantum state | x 1 , x 2 {\displaystyle \left|x_{1},x_{2}\right\rangle } . [ 2 ]
(It is a non-trivial result of quantum field theory [2] that the exchange of even-spin bosons like the pion (spin 0, Yukawa force) or the graviton (spin 2, gravity) results in forces always attractive, while odd-spin bosons like the gluons (spin 1, strong interaction), the photon (spin 1, electromagnetic force) or the rho meson (spin 1, Yukawa ...
The vector symmetry, U B (1) corresponds to the baryon number of quarks and is an exact symmetry. The axial symmetry U A (1) is exact in the classical theory, but broken in the quantum theory, an occurrence called an anomaly. Gluon field configurations called instantons are closely related to this anomaly.
A solution to the lack of anti-symmetry in the Hartree method came when it was shown that a Slater determinant, a determinant of one-particle orbitals first used by Heisenberg and Dirac in 1926, trivially satisfies the antisymmetric property of the exact solution and hence is a suitable ansatz for applying the variational principle.
The standard model is a quantum field theory, meaning its fundamental objects are quantum fields, which are defined at all points in spacetime. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. These fields are