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
Famous quotes containing the words application, quantum, field and/or theory:
“If you would be a favourite of your king, address yourself to his weaknesses. An application to his reason will seldom prove very successful.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“He stung me first and stung me afterward.
He rolled me off the field head over heels
And would not listen to my explanations.”
—Robert Frost (1874–1963)
“The human species, according to the best theory I can form of it, is composed of two distinct races, the men who borrow and the men who lend.”
—Charles Lamb (1775–1834)