What is Renormalization? G.Peter Lepage
... changing the bare coupling and mass in the Lagrangian in such a way that the low-energy physics of the theory is unaffected. This is the classical result of renormalization theory. Exercise: Sketch out arguments for the validity of this result to two-loop order by examining some simple process like ...
... changing the bare coupling and mass in the Lagrangian in such a way that the low-energy physics of the theory is unaffected. This is the classical result of renormalization theory. Exercise: Sketch out arguments for the validity of this result to two-loop order by examining some simple process like ...
photon particle - wave duality
... 2. From assumption (1) page 47, we see that the energy carried by a quantum of electromagnetic radiation (a photon) is given by E = hν where ν is the frequency of the radiation (and hence of the photon). From considerations of classical electromagnetic theory, the photons should also carry momentum ...
... 2. From assumption (1) page 47, we see that the energy carried by a quantum of electromagnetic radiation (a photon) is given by E = hν where ν is the frequency of the radiation (and hence of the photon). From considerations of classical electromagnetic theory, the photons should also carry momentum ...
In 1913 Bohr proposed his quantized shell model of the atom to
... move in orbits of fixed size and energy. The energy of an electron depends on the size of the orbit and is lower for smaller orbits. Radiation can occur only when the electron jumps from one orbit to another. The atom will be completely stable in the state with the smallest orbit, since there is no ...
... move in orbits of fixed size and energy. The energy of an electron depends on the size of the orbit and is lower for smaller orbits. Radiation can occur only when the electron jumps from one orbit to another. The atom will be completely stable in the state with the smallest orbit, since there is no ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.