Quote:
Originally Posted by CraigS
Hi Steven;
Whereabouts does this occur ? (Ie: which theory etc?)
Cheers
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Craig,
Are you familiar with use of Hamiltonians in Quantum Mechanics?
http://en.wikipedia.org/wiki/Hamilto...ntum_mechanics)
The Hamiltonian is an operator which defines the total energy of a system (the sum of it's kinetic and potential energies).
In Quantum Field Theory the definition of a Hamiltonian is not as straigthtforward and is based on the creation and destruction of virtual particles in a field.
The experimental verification of this concept is the Casimir effect
http://en.wikipedia.org/wiki/Casimir_effect
When the Hamiltonian is applied to a vacuum, the total energy is found to be infinite. A vacuum should in fact be a system in it's lowest energy state.
http://en.wikipedia.org/wiki/Vacuum_energy
The way out of this conumdrum is to define a renormalized Hamiltonian where the term in the Hamiltonian that produces the infinite term is chopped out. The physical significance of this operation is vague.
In other applications of renormalization such as Quantum Electrodynamics or the attachment in this thread, renormalization has a physical significance. The divergence is caused by out of scale or non quantum mechanical effects which can be removed without destroying the integrity of the theory.
Regards
Steven