In theoretical physics, Pauli–Villars regularization (P–V) is a procedure that isolates divergent terms from finite parts in loop calculations in field theory in order to 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. Gerard 't Hooft and Martinus J. G. Veltman invented, in addition to dimensional regularization, the method of unitary regulators, which is a Lagrangian-based Pauli–Villars method with a discrete spectrum of auxiliary masses, using the path-integral formalism.
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| - 파울리-빌라르 조절 (ko)
- Pauli–Villars regularization (en)
- Regularização de Pauli-Villars (pt)
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| - 파울리-빌라르 조절(-調節, 영어: Pauli–Villars regularization)은 실재하지 않는 아주 무거운 입자를 삽입하는, 조절의 한 방법이다. 이 허구의 입자의 질량을 무한대로 보내면, 허구 입자는 관측할 수 없게 된다. 파울리-빌라르 조절은 게이지 불변이지만 게이지 공변이지 않다. 따라서 가환 게이지 이론 (양자전기역학)에서 유용하지만 비가환 게이지 이론 (양자색역학 등)에서는 적절하지 않다. 대체로 더 간편한 차원 조절을 쓸 수 없을 때 (예를 들어 레비치비타 기호를 포함한 손지기 현상)에 쓴다. (ko)
- Em física teórica, regularização de Pauli-Villars (P-V) é um procedimento que isola termos divergentes das partes finitas nos cálculos de loop em teoria de campo, com o fim de renormalizar a teoria. Wolfgang Pauli e Felix Villars publicaram o método em 1949, com base no trabalho anterior de Richard Feynman, Ernst Stueckelberg e . (pt)
- In theoretical physics, Pauli–Villars regularization (P–V) is a procedure that isolates divergent terms from finite parts in loop calculations in field theory in order to 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. Gerard 't Hooft and Martinus J. G. Veltman invented, in addition to dimensional regularization, the method of unitary regulators, which is a Lagrangian-based Pauli–Villars method with a discrete spectrum of auxiliary masses, using the path-integral formalism. (en)
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| - In theoretical physics, Pauli–Villars regularization (P–V) is a procedure that isolates divergent terms from finite parts in loop calculations in field theory in order to 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. 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 masses 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 regulator is gauge invariant in an abelian theory due to the auxiliary particles being minimally coupled to the photon field through the gauge covariant derivative. It is not gauge covariant in a non-abelian theory, 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 Dirac gamma matrices. Gerard 't Hooft and Martinus J. G. Veltman invented, in addition to dimensional regularization, the method of unitary regulators, which is a Lagrangian-based Pauli–Villars method with a discrete spectrum of auxiliary masses, using the path-integral formalism. (en)
- 파울리-빌라르 조절(-調節, 영어: Pauli–Villars regularization)은 실재하지 않는 아주 무거운 입자를 삽입하는, 조절의 한 방법이다. 이 허구의 입자의 질량을 무한대로 보내면, 허구 입자는 관측할 수 없게 된다. 파울리-빌라르 조절은 게이지 불변이지만 게이지 공변이지 않다. 따라서 가환 게이지 이론 (양자전기역학)에서 유용하지만 비가환 게이지 이론 (양자색역학 등)에서는 적절하지 않다. 대체로 더 간편한 차원 조절을 쓸 수 없을 때 (예를 들어 레비치비타 기호를 포함한 손지기 현상)에 쓴다. (ko)
- Em física teórica, regularização de Pauli-Villars (P-V) é um procedimento que isola termos divergentes das partes finitas nos cálculos de loop em teoria de campo, com o fim de renormalizar a teoria. Wolfgang Pauli e Felix Villars publicaram o método em 1949, com base no trabalho anterior de Richard Feynman, Ernst Stueckelberg e . (pt)
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