Note on the Non-Perturbation-Approach to Quantum Field Theory

Gotō, Tetsuo; Imamura, Tsutomu

doi:10.1143/ptp.14.396

Cited by 129 publications

(34 citation statements)

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“…In particular, C − Z −1 3 = C(0) −ā(0) represents the contributions of the so-called GotoImamura-Schwinger term [29,30]. When Z −1 3 = 0, however, this term should also vanish as we have remarked above [31].…”

Section: Conditions F or Color Conf Inement And Their Relationshipmentioning

confidence: 93%

Renormalization constant of the color gauge field as a probe of confinement

Chaichian

Nishijima²

2001

Eur. Phys. J. C

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The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by Z −1 3 = 0 where Z 3 denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it.

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Section: Conditions F or Color Conf Inement And Their Relationshipmentioning

confidence: 93%

Renormalization constant of the color gauge field as a probe of confinement

Chaichian

Nishijima²

2001

Eur. Phys. J. C

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“…Deeply related to anomalies are the socalled Schwinger terms [33] - [35] (for an introduction see e.g. Refs.…”

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Gravitational Anomalies, Schwinger Terms, and Dispersion Relations

2001

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We are dealing with two-dimensional gravitational anomalies, specifically with the Einstein anomaly and the Weyl anomaly, and we show that they are fully determined by dispersion relations independent of any renormalization procedure (or ultraviolet regularization). The origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor. In the zero mass limit the imaginary part of the formfactor approaches a δ-function singularity at zero momentum squared, exhibiting in this way the infrared feature of the gravitational anomalies. We find an equivalence between the dispersive approach and the dimensional regularization procedure. The Schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method. Although all computations are performed in two dimensions the method is expected to work in higher dimensions too. * This work was partly supported by Austria-Czech Republic Scientific collaboration, project KON-TACT 1999-8. † Supported by a Wissenschaftsstipendium der Magistratsabteilung 18 der Stadt Wien.

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“…Up to and including O(k 2 ), there are exactly eight independent terms, T µνα (bN ) (N = 1, · · · , 8), that satisfy all the requirements above, and they are explicitly given in appendix. As in the previous case, one finds that for µ = ν = 0 there are cancellations that reduce d eff of the diagram (b) at least down to −2 so that it does not contribute to the ETC for µ = ν = 0.…”

Section: Diagram (B)mentioning

confidence: 99%

“…During the mathematization of anomalies, especially soon after the works of Stora [4], Zumino [5] and Baulieu [6] in connection to the chiral anomalies, Faddeev [7] succeeded to reveal the relation between the gauge group cohomology and the anomalous Schwinger term [8] in the commutator algebra of the Gauß law operators in chiral Yang-Mills theories.…”

Section: Introductionmentioning

confidence: 99%

An analysis on the convergence of equal-time commutators and the closure of the BRST algebra in Yang-Mills theories

Kubo

1994

Nuclear Physics B

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In renormalizable theories, we define equal-time commutators (ETC'S) in terms of the equal-time limit and investigate its convergence in perturbation theory. We find that the equal-time limit vanishes for amplitudes with the effective dimension d eff ≤ −2 and is finite for those with d eff = −1 but without nontrivial discontinuity. Otherwise we expect divergent equal-time limits. We also find that, if the ETC's involved in verifying an Jacobi identity exist, the identity is satisfied. Under these circumstances, we show in the Yang-Mills theory that the ETC of the 0 component of the BRST current with each other vanishes to all orders in perturbation theory if the theory is free from the chiral anomaly, from which we conclude that [ Q , Q ] = 0, where Q is the BRST charge. For the case that the chiral anomaly is not canceled, we use various broken Ward identities to show that [ Q , Q ] is finite and [ Q , [ Q , Q] ] vanishes at the one-loop level and that they start to diverge at the two-loop level unless there is some unexpected cancellation mechanism that improves the degree of convergence. †

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Note on the Non-Perturbation-Approach to Quantum Field Theory

Cited by 129 publications

References 1 publication

Renormalization constant of the color gauge field as a probe of confinement

Renormalization constant of the color gauge field as a probe of confinement

Two-Dimensional Gravitational Anomalies, Schwinger Terms, and Dispersion Relations

An analysis on the convergence of equal-time commutators and the closure of the BRST algebra in Yang-Mills theories

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