Application in Quantum Field Theory
The creation of a particle and anti-particle from a boson is defined similarly but for infinite dimensions. Therefore the Levi-Civita symbol for infinite dimensions is introduced.
The commutation relations are simply carried over to infinite dimensions . is now equal to where n=∞. Its eigenvalue is . Defining the magnetic quantum number, angular momentum projected in the z direction, is more challenging than the simple state of spin. The problem becomes analogous to moment of inertia in classical mechanics and is generalizable to n dimensions. It is this property that allows for the creation and annihilation of bosons.
Read more about this topic: Anti-symmetric Operator
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