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Problem Set 1
Problem Set 1

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY

... The Sopwith Camel was a single engine fighter plan flown by the British in WWI (and also by the character Snoopy in the Peanuts comic strip). It was powered by a radial engine, and the entire engine rotated with the propeller. The Camel had an unfortunate property: if the pilot turned to the right, ...
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... where the cj are constants, for substitution of a typical term of (21) reduces (20) to an expression differing from (17) only by a constant factor. Now by (19) the term proportional to cj in (21) simply adds to (15) very approximately the change cjihb( ,IeS/ih)/baj which results in (15) if a, is alt ...
Standard model of particle physics
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< 1 ... 393 394 395 396 397 398 399 400 401 ... 511 >

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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