Epigram (programming language) - Revision history

en>BD2412: minor fixes, mostly disambig links using AWB

2014-10-13T04:16:42Z

minor fixes, mostly disambig links using AWB

← Older revision		Revision as of 06:16, 13 October 2014
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	~~{{Renormalization and regularization}}~~		Family Help Worker Mervin from Delta, spends time with pastimes including cryptography, new launch property singapore and coin collecting. Finds motivation by making a journey to Lumbini.<br><br>Also visit my homepage: [http://www.walremal.com/social/index.php?do=/profile-14820/info/ walremal.com]

	~~In [[theoretical physics]], '''Pauli–Villars regularization''' is a procedure that isolates divergent terms~~ from finite parts in loop calculations in [[field theory (physics)\|field theory]] in order to [[renormalization\|renormalize]] the theory. [[Wolfgang Pauli]] and [[Felix Villars]] published the method in 1949, ~~based on earlier work by [[Richard Feynman]]~~, ~~[[Ernst Stueckelberg]]~~ and ~~[[Dominique Rivier]]~~.~~<ref name="Schweber">{{cite book\|title=QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga\|publisher=Princeton University Press\|location=Princeton, N.J.\|year=1994}}</ref>~~

	~~In this treatment, a [[divergence]] arising from a [[loop integral]] (such as [[vacuum polarization]] or [[electron self-energy]]) is modulated~~ by a spectrum of auxiliary particles added to the [[Lagrangian]] or [[propagator]]. When the [[mass]]es of the fictitious particles are taken as an infinite limit (i.e., once the regulator is removed) one expects to recover the original theory.

	This [[regularization (physics)\|regulator]] is [[gauge invariance\|gauge invariant]] due to the auxiliary particles being minimally coupled to the photon field through the [[gauge covariant derivative]]. It is not gauge covariant, though, so Pauli–Villars regularization cannot be used in QCD calculations. P-V serves as an alternative to the more favorable [[dimensional regularization]] in specific circumstances, such as in chiral phenomena, where a change of dimension alters the properties of the [[gamma matrices\|Dirac gamma matrices]].

	~~[[Gerard 't Hooft]] and [[Martinus J. G. Veltman]] invented, in addition to [[dimensional regularization]], the method of unitary regulators,~~<~~ref~~>~~G. 't Hooft, M. Veltman, Diagrammar, CERN report 73-9 (1973), see Secs. 2 and 5-8; reprinted in G. 't Hooft, Under the Spell of Gauge Principle, World Scientific, Singapore (1994).~~<~~/ref~~> ~~which is a Lagrangian-based Pauli-Villars method with a discrete spectrum of auxiliary masses, using the path-integral formalism.~~

	~~==Examples==~~
	Pauli-Villars regularization consists of introducing a fictitious mass term. For example, we would replace a photon propagator <math> \frac{1}{k^2 + i \epsilon} </math>, by <math> \frac{1}{k^2 + i \epsilon} - \frac{1}{k^2 - \Lambda^2+ i \epsilon} </math>, where <math>\Lambda</math> can be thought of as the mass of a fictitious heavy photon, whose contribution is subtracted from that of an ordinary photon. <ref>Peskin, Shroeder "An Introduction to Quantum Field Theory" Westview Press; Reprint edition (October 2, 1995) </ref>

	~~==Notes==~~
	~~{{Reflist}}~~

	~~==References==~~
	* Bjorken, J.D., Drell, S.D. ''Relativistic Quantum Mechanics'', McGraw-Hill Book Company, New York City, New York 1964.
	* Collins, John. ''Renormalization'', Cambridge University Press, Cambridge, England, 1984.
	* Hatfield, Brian. ''Quantum Field Theory of Point Particles and Strings'', Addison-Wesley Publishing Company, Redwood, California, 1992.
	* Itzykson, C., Zuber, J-B. ''Quantum Field Theory'', McGraw-Hill Book Company, New York City, New York, 1980.
	* Pauli, W., Villars, F. ''On the Invariant Regularization in Relativistic Quantum Theory'', [http://~~link~~.~~aps~~.~~org~~/~~abstract~~/~~RMP~~/~~v21~~/~~p434 Rev~~. ~~Mod. Phys, 21, 434-444 (1949)~~].

	~~== See also ==~~
	* [[Regularization (physics)]]
	* [[Dimensional regularization]]

	~~{{DEFAULTSORT:Pauli-Villars regularization}}~~
	~~[[Category:Quantum field theory]]~~


	~~{{quantum-stub}}~~

en>Control.valve: Fixed link to Conor McBride

2013-10-13T19:05:55Z

Fixed link to Conor McBride

← Older revision		Revision as of 21:05, 13 October 2013
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	My name: ~~Dinah Beyer~~<br>~~My age: 35~~<br>~~Country: Belgium~~<br>~~Home town: Bertem~~ <br>~~Post code: 3060~~<br>~~Street: Kerkstraat 189~~<br><br>~~Also visit my blog post~~ ... [http://~~socialthat~~.~~extor~~.org/~~blogs~~/~~145872~~/~~130428~~/~~dog~~-~~training~~-~~how~~-~~to-train-your-pit-bull dog training dallas]~~		{{Renormalization and regularization}}

			In [[theoretical physics]], '''Pauli–Villars regularization''' is a procedure that isolates divergent terms from finite parts in loop calculations in [[field theory (physics)\|field theory]] in order to [[renormalization\|renormalize]] the theory. [[Wolfgang Pauli]] and [[Felix Villars]] published the method in 1949, based on earlier work by [[Richard Feynman]], [[Ernst Stueckelberg]] and [[Dominique Rivier]].<ref name="Schweber">{{cite book\|title=QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga\|publisher=Princeton University Press\|location=Princeton, N.J.\|year=1994}}</ref>

			In this treatment, a [[divergence]] arising from a [[loop integral]] (such as [[vacuum polarization]] or [[electron self-energy]]) is modulated by a spectrum of auxiliary particles added to the [[Lagrangian]] or [[propagator]]. When the [[mass]]es of the fictitious particles are taken as an infinite limit (i.e., once the regulator is removed) one expects to recover the original theory.

			This [[regularization (physics)\|regulator]] is [[gauge invariance\|gauge invariant]] due to the auxiliary particles being minimally coupled to the photon field through the [[gauge covariant derivative]]. It is not gauge covariant, though, so Pauli–Villars regularization cannot be used in QCD calculations. P-V serves as an alternative to the more favorable [[dimensional regularization]] in specific circumstances, such as in chiral phenomena, where a change of dimension alters the properties of the [[gamma matrices\|Dirac gamma matrices]].

			[[Gerard 't Hooft]] and [[Martinus J. G. Veltman]] invented, in addition to [[dimensional regularization]], the method of unitary regulators,<ref>G. 't Hooft, M. Veltman, Diagrammar, CERN report 73-9 (1973), see Secs. 2 and 5-8; reprinted in G. 't Hooft, Under the Spell of Gauge Principle, World Scientific, Singapore (1994).</ref> which is a Lagrangian-based Pauli-Villars method with a discrete spectrum of auxiliary masses, using the path-integral formalism.

			==Examples==
			Pauli-Villars regularization consists of introducing a fictitious mass term. For example, we would replace a photon propagator <math> \frac{1}{k^2 + i \epsilon} </math>, by <math> \frac{1}{k^2 + i \epsilon} - \frac{1}{k^2 - \Lambda^2+ i \epsilon} </math>, where <math>\Lambda</math> can be thought of as the mass of a fictitious heavy photon, whose contribution is subtracted from that of an ordinary photon. <ref>Peskin, Shroeder "An Introduction to Quantum Field Theory" Westview Press; Reprint edition (October 2, 1995) </ref>

			==Notes==
			{{Reflist}}

			==References==
			* Bjorken, J.D., Drell, S.D. ''Relativistic Quantum Mechanics'', McGraw-Hill Book Company, New York City, New York 1964.
			* Collins, John. ''Renormalization'', Cambridge University Press, Cambridge, England, 1984.
			* Hatfield, Brian. ''Quantum Field Theory of Point Particles and Strings'', Addison-Wesley Publishing Company, Redwood, California, 1992.
			* Itzykson, C., Zuber, J-B. ''Quantum Field Theory'', McGraw-Hill Book Company, New York City, New York, 1980.
			* Pauli, W., Villars, F. ''On the Invariant Regularization in Relativistic Quantum Theory'', [http://link.aps.org/abstract/RMP/v21/p434 Rev. Mod. Phys, 21, 434-444 (1949)].

			== See also ==
			* [[Regularization (physics)]]
			* [[Dimensional regularization]]

			{{DEFAULTSORT:Pauli-Villars regularization}}
			[[Category:Quantum field theory]]


			{{quantum-stub}}

130.208.69.54 at 14:18, 31 July 2012

2012-07-31T14:18:07Z

New page

My name: Dinah Beyer My age: 35 Country: Belgium Home town: Bertem Post code: 3060 Street: Kerkstraat 189 Also visit my blog post ... [http://socialthat.extor.org/blogs/145872/130428/dog-training-how-to-train-your-pit-bull dog training dallas]