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String Theory. Volume 1, Introduction to the Bosonic String
String Theory. Volume 1, Introduction to the Bosonic String

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... The development of quantum cascade lasers operating at terahertz frequencies is proceeding at a very rapid pace. For their successful practical implementation, specific requirements have now to be addressed, particularly concerning the properties of the emitted radiation. Single-mode THz lasers with ...
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... matter of the macroscopic mass M be made up of, since M  M  2m  52 m  2m  12 m ??? In a classical analysis of the inelastic collision of two relativistic macroscopic lumps of clay {each of mass m} the composite / stuck-together single lump of clay of mass M  52 m  2m would be very hot – it w ...
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... wouldn’t have made it to the end of this PhD — let alone had so much fun along the way. I am greatly indebted to George Booth for the huge amount of knowledge and advice he has (tried) to pass on to me, and to Alex Thom who has made a habit of turning up just when my attempts to solve problems appea ...
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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.
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