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:
“By an application of the theory of relativity to the taste of readers, to-day in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!”
—Albert Einstein (1879–1955)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“The little toy dog is covered with dust,
But sturdy and stanch he stands;
And the little toy soldier is red with rust,
And the musket moulds in his hands.
Time was when the little toy dog was new,
And the soldier was passing fair;
And that was the time when our Little Boy Blue
Kissed them and put them there.”
—Eugene Field (1850–1895)
“The theory [before the twentieth century] ... was that all the jobs in the world belonged by right to men, and that only men were by nature entitled to wages. If a woman earned money, outside domestic service, it was because some misfortune had deprived her of masculine protection.”
—Rheta Childe Dorr (1866–1948)