On the Invariant Regularization in Relativistic Quantum Theory

Pauli, Wolfgang; Villars, F.

doi:10.1103/revmodphys.21.434

Cited by 776 publications

(464 citation statements)

References 13 publications

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“…In the present paper we compute the pion distribution amplitude and the pion light-cone wave function within the Nambu-Jona-Lasinio (NJL) model [32,33] in a semibosonized form using the Pauli-Villars (PV) regularization method [34]. This method has been introduced in Refs.…”

Section: Introductionmentioning

confidence: 99%

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

Arriola

Broniowski

2002

Phys. Rev. D

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We compute the pion light-cone wave function and the pion quark distribution amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars regularization method and as a result the distribution amplitude satisfies proper normalization and crossing properties. In the chiral limit we obtain the simple results, namely ϕπ(x) = 1 for the pion distribution amplitude, andfor the second moment of the pion light-cone wave function, where M is the constituent quark mass and fπ is the pion decay constant. After the QCD Gegenbauer evolution of the pion distribution amplitude good end-point behavior is recovered, and a satisfactory agreement with the analysis of the experimental data from CLEO is achieved. This allows us to determine the momentum scale corresponding to our model calculation, which is close to the value Q0 = 313 MeV obtained earlier from the analogous analysis of the pion parton distribution function. The value of k 2 ⊥ is, after the QCD evolution, around (400 MeV) 2 . In addition, the model predicts a linear integral relation between the pion distribution amplitude and the parton distribution function of the pion, which holds at the leading-order QCD evolution.

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Section: Introductionmentioning

confidence: 99%

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

Arriola

Broniowski

2002

Phys. Rev. D

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“…I have also shown that such a model is equivalent to a variation of Linde's model (where the universe consists of the usual universe plus a ghost one). There may be some relation between this scheme and the Pauli-Villars regularization scheme [23] (that employs ghost-like auxiliary fields for regularization), and also between this scheme and Lee-Wick quantum theory [24]. In my opinion all these points need further and detailed studies in future.…”

Section: Resultsmentioning

confidence: 99%

“…where I have used (23) and taken y = y 2 , z = z 2 and φ mn = φ AA mn in (46). After using the antisymmetry of φ AA mn under both of n → −n m → −m, (A.3) may be written in a simplified form as (46).…”

Section: Appendix a Calculation Of S φKmentioning

confidence: 99%

A way to get rid of cosmological constant and zero-point energy problems of quantum fields through metric reversal symmetry

Erdem¹

2008

J. Phys. A: Math. Theor.

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In this paper, a framework is introduced to remove the huge discrepancy between the empirical value of the cosmological constant and the contribution to the cosmological constant predicted from the vacuum energy of quantum fields. An extra-dimensional space with metric reversal symmetry and R 2 gravity (that reduces to the usual R gravity after integration over extra dimensions) is considered to this end. The resulting four-dimensional energy-momentum tensor (obtained after integration over extra dimensions) consists of terms that contain off-diagonally coupled pairs of Kaluza-Klein modes. This, in turn, generically results in the vanishing of the vacuum expectation value of the energy-momentum tensor for quantum fields, and offers a way to solve the problem of huge contribution of quantum fields to the vacuum energy density.

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“…57 Schwinger recalled later that he viewed this paper, in part, as a reaction to the "invariant regularization" of Pauli and Villars. 58 It was this paper, with its mathematical manipulation, without physical insight particularly about questions such as photon mass and so forth, which was the direct inspiration for 'Gauge Invariance and Vacuum Polarization.' The whole point is that if you have a propagation function, it has a certain singularity when the two points coincide.…”

Section: "Gauge Invariance and Vacuum Polarization"mentioning

confidence: 99%

In Appreciation Julian Schwinger: From Nuclear Physics and Quantum Electrodynamics to Source Theory and Beyond

Milton

2007

Phys. perspect.

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Julian Schwinger's influence on twentieth century science is profound and pervasive. Of course, he is most famous for his renormalization theory of quantum electrodynamics, for which he shared the Nobel Prize with Richard Feynman and Sin-itiro Tomonaga. But although this triumph was undoubtedly his most heroic work, his legacy lives on chiefly through subtle and elegant work in classical electrodynamics, quantum variational principles, proper-time methods, quantum anomalies, dynamical mass generation, partial symmetry, and more. Starting as just a boy, he rapidly became the pre-eminent nuclear physicist in the late 1930s, led the theoretical development of radar technology at MIT during World War II, and then, soon after the war, conquered quantum electrodynamics, and became the leading quantum field theorist for two decades, before taking a more iconoclastic route during his last quarter century.

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On the Invariant Regularization in Relativistic Quantum Theory

Cited by 776 publications

References 13 publications

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

A way to get rid of cosmological constant and zero-point energy problems of quantum fields through metric reversal symmetry

In Appreciation Julian Schwinger: From Nuclear Physics and Quantum Electrodynamics to Source Theory and Beyond

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