Relation To Representation Theory of The Lorentz Group
Since the Lorentz group has no non-trivial unitary representation of finite dimension, it naively seems that one cannot construct a state with finite, non-zero spin and positive, Lorentz-invariant norm.
For a state of integer spin the negative norm states (known as "unphysical polarization") are set to zero, which makes the use of gauge symmetry necessary.
For a state of half-integer spin the argument can be circumvented by having fermionic statistics.
Read more about this topic: Spin-statistics Theorem
Famous quotes containing the words relation to, relation, theory and/or group:
“... a worker was seldom so much annoyed by what he got as by what he got in relation to his fellow workers.”
—Mary Barnett Gilson (1877–?)
“When needs and means become abstract in quality, abstraction is also a character of the reciprocal relation of individuals to one another. This abstract character, universality, is the character of being recognized and is the moment which makes concrete, i.e. social, the isolated and abstract needs and their ways and means of satisfaction.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.”
—H.L. (Henry Lewis)
“Instead of seeing society as a collection of clearly defined “interest groups,” society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)