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| {{Renormalization and regularization}}
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| 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>
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| 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.
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| 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]].
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| [[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.
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| ==Examples==
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| 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>
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| * Bjorken, J.D., Drell, S.D. ''Relativistic Quantum Mechanics'', McGraw-Hill Book Company, New York City, New York 1964.
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| * Collins, John. ''Renormalization'', Cambridge University Press, Cambridge, England, 1984.
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| * Hatfield, Brian. ''Quantum Field Theory of Point Particles and Strings'', Addison-Wesley Publishing Company, Redwood, California, 1992.
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| * Itzykson, C., Zuber, J-B. ''Quantum Field Theory'', McGraw-Hill Book Company, New York City, New York, 1980.
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| * 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)].
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| == See also ==
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| * [[Regularization (physics)]]
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| * [[Dimensional regularization]]
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| {{DEFAULTSORT:Pauli-Villars regularization}}
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| [[Category:Quantum field theory]]
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| {{quantum-stub}}
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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.
Also visit my homepage: walremal.com