மறு சீராக்கல் (ரீ நார்மலைசேஷன்)

 

மறு சீராக்கல்  (ரீ நார்மலைசேஷன்)

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எல்லையின்மைகள்  என்பவை உண்மையில் தொல்லைமைகள் தான்.கணித வியலில் எண்ணியலில் நமக்குத்தெரியும் இவை ஏதோ ஒரு எட்டாத தொலைவில் இருப்பதாயும் அதனால் நாம் அதை எட்டிவிட முடியாத ஒரு நிலையில் இருப்பதாகும் மாயம் காட்டிக்கொண்டிருக்கும். இயற்பியல் மற்றும் கணிதவியலாளர்களாலும் எப்படி அணுகப்படுகிறது என்பதை நாம் இப்போது பார்க்கலாம். இயற்பியலில் எலக்ட்ரான் எனும் துகள் இயக்கத்தின் இடைசெயல்களில் அவை "தனக்குத்தானே இடைச்செயல் "( செல்ஃப் இன்டர் ஆக்ஷன்) புரிந்து கொள்ளும் கணக்கீடுகள் இந்த எல்லையின்மைகளில் வந்து 

மோதியும் மோதாமலும் நிற்கிற ஒரு நிலைப்பாட்டுக்கு வரலாம்.அதாவது தன்னைப்போலவே ஒரு வடிவ கணித கட்டமைப்புக்குள் அது அடைபட்டு போகலாம். இதை "ஃப்ராக்டல் ஜியாமெட்ரி "என்பார்கள்.இப்போது ஒரு "பூ"

வடிவம் அதே வடிவை அதன் மேல் அடுக்கி அடுக்கி வருவதாக பார்ப்போம்.

ஒரே வடிவம் பலவடிவங்களாய் அதே போல் வருவதை "பின்ன வடிவங்கள்"

என்கிறோம்.இது எல்லையில்லாமல் பெருக்கிக்கொண்டே  போனால் அதாவது நுண்ணுயிரிகள் அதே போல் பெருக்கிக்கொண்டே போவது போல் இருந்தால் 

அதை எப்படி எதிர்கொள்வது?

Renormalization is a collection of techniques in quantum field theory, statistical field theory, and the theory of

மறு சீராக்கல்  (ரீ நார்மலைசேஷன்)geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian.^[1]

For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in this example, mathematically replaces the initially postulated mass and charge of an electron with the experimentally observed mass and charge. Mathematics and experiments prove that positrons and more massive particles such as protons exhibit precisely the same observed charge as the electron – even in the presence of much stronger interactions and more intense clouds of virtual particles.

Renormalization specifies relationships between parameters in the theory when parameters describing large distance scales differ from parameters describing small distance scales. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in further infinities. When describing spacetime as a continuum, certain statistical and quantum mechanical constructions are not well-defined. To define them, or make them unambiguous, a continuum limit must carefully remove "construction scaffolding" of lattices at various scales. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values. That is, the experimental value of the physical quantity yields practical applications, but due to their empirical nature the observed measurement represents areas of quantum field theory that require deeper derivation from theoretical bases.

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. Despite his later skepticism, it was Paul Dirac who pioneered renormalization.^[2][3]

Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Nikolay Bogolyubov and 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. Wilson clarified which variables of a system are crucial and which are redundant.

Renormalization is distinct from regularization, another technique to control infinities by assuming the existence of new unknown physics at new scales.

Self-interactions in classical physics

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Figure 1. Renormalization in quantum electrodynamics: The simple electron/photon interaction that determines the electron's charge at one renormalization point is revealed to consist of more complicated interactions at another.

The problem of infinities first arose in the classical electrodynamics of point particles in the 19th and early 20th century.

The mass of a charged particle should include the mass–energy in its electrostatic field (electromagnetic mass). Assume that the particle is a charged spherical shell of radius r_e. The mass–energy in the field is

${\displaystyle m_{\text{em}}=\int \frac{1}{2}{E}^{2}dV={\int }_{r_{\text{e}}}^{\mathrm{\infty }}\frac{1}{2}{\left(\frac{q}{4\pi r^2}\right)}^{2}4\pi r^{2}dr=\frac{q^2}{8\pi r_{\text{e}}},}$

which becomes infinite as r_e → 0. This implies that the point particle would have infinite inertia and thus cannot be accelerated. Incidentally, the value of r_e that makes ${\displaystyle m_{\text{em}}}$ equal to the electron mass is called the classical electron radius, which (setting ${\displaystyle q=e}$ and restoring factors of c and ${\displaystyle {\epsilon }_0}$) turns out to be

${\displaystyle r_{\text{e}}=\frac{e^2}{4\pi {\epsilon }_0{m}_{\text{e}}{c}^2}=\alpha \frac{\hslash }{m_{\text{e}}c}\approx 2.8\times {10}^{-15}\text{m},}$

where ${\displaystyle \alpha \approx 1/137}$ is the fine-structure constant, and ${\displaystyle \hslash /(m_{\text{e}}c)}$ is the reduced Compton wavelength of the electron.

Renormalization: The total effective mass of a spherical charged particle includes the actual bare mass of the spherical shell (in addition to the mass mentioned above associated with its electric field). If the shell's bare mass is allowed to be negative, it might be possible to take a consistent point limit.^{[citation needed]} This was called renormalization, and Lorentz and Abraham attempted to develop a classical theory of the electron this way. This early work was the inspiration for later attempts at regularization and renormalization in quantum field theory.

(See also regularization (physics) for an alternative way to remove infinities from this classical problem, assuming new physics exists at small scales.)

When calculating the electromagnetic interactions of charged particles, it is tempting to ignore the back-reaction of a particle's own field on itself. (Analogous to the back-EMF of circuit analysis.) But this back-reaction is necessary to explain the friction on charged particles when they emit radiation. If the electron is assumed to be a point, the value of the back-reaction diverges, for the same reason that the mass diverges, because the field is inverse-square.

The Abraham–Lorentz theory had a noncausal "pre-acceleration". Sometimes an electron would start moving before the force is applied. This is a sign that the point limit is inconsistent.

The trouble was worse in classical field theory than in quantum field theory, because in quantum field theory a charged particle experiences Zitterbewegung due to interference with virtual particle–antiparticle pairs, thus effectively smearing out the charge over a region comparable to the Compton wavelength. In quantum electrodynamics at small coupling, the electromagnetic mass only diverges as the logarithm of the radius of the particle.