Axial vector ward identities and dimensional regularization

1983 ◽  
Vol 213 (2) ◽  
pp. 241-265 ◽  
Author(s):  
Burt A. Ovrut
Keyword(s):  
Axial Vector ◽  
Dimensional Regularization ◽  
Ward Identities

scholarly journals ANOMALIES IN WARD IDENTITIES FOR THREE-POINT FUNCTIONS REVISITED

2002 ◽  
Vol 17 (15) ◽  
pp. 1979-2017 ◽  
Author(s):  
O. A. BATTISTEL ◽  
O. L. BATTISTEL
Keyword(s):  
Traditional Approach ◽  
Axial Vector ◽  
Dimensional Regularization ◽  
Point Of View ◽  
Ward Identities ◽  
Calculational Method ◽  
Free Fermion Model ◽  
Traditional Work ◽  
Symmetry Relations ◽  
Natural Way

A general calculational method is applied to investigate symmetry relations among divergent amplitudes in a free fermion model. A very traditional work on this subject is revisited. A systematic study of one, two and three-point functions associated to scalar, pseudoscalar, vector and axial-vector densities is performed. The divergent content of the amplitudes are left in terms of five basic objects (external momentum independent). No specific assumptions about a regulator is adopted in the calculations. All ambiguities and symmetry violating terms are shown to be associated with only three combinations of the basic divergent objects. Our final results can be mapped in the corresponding Dimensional Regularization calculations (in cases where this technique could be applied) or in those of Gertsein and Jackiw which we will show in detail. The results emerging from our general approach allow us to extract, in a natural way, a set of reasonable conditions (e.g. crucial for QED consistency) that could lead us to obtain all Ward Identities satisfied. Consequently, we conclude that the traditional approach used to justify the famous triangular anomalies in perturbative calculations could be questionable. An alternative point of view, dismissed of ambiguities, which lead to a correct description of the associated phenomenology, is pointed out.

Axial-vector current and dimensional regularization

1979 ◽  
Vol 20 (12) ◽  
pp. 3378-3389 ◽  
Author(s):  
Steven Gottlieb ◽  
J. T. Donohue
Keyword(s):  
Axial Vector ◽  
Dimensional Regularization ◽  
Vector Current ◽  
Axial Vector Current

scholarly journals Extraction of light quark masses from sum rule analyses of axial vector and vector current Ward identities

1998 ◽  
Vol 57 (9) ◽  
pp. 5455-5467 ◽  
Author(s):  
Tanmoy Bhattacharya ◽  
Rajan Gupta ◽  
Kim Maltman
Keyword(s):  
Light Quark ◽  
Axial Vector ◽  
Vector Current ◽  
Ward Identities ◽  
Sum Rule ◽  
Quark Masses

Transversality of the Rarita-Schwinger self-energy, Ward identities, and dimensional regularization

1980 ◽  
Vol 22 (12) ◽  
pp. 2995-3002 ◽  
Author(s):  
M. K. Fung ◽  
P. van Nieuwenhuizen ◽  
D. R. T. Jones
Keyword(s):  
Dimensional Regularization ◽  
Ward Identities ◽  
Self Energy

scholarly journals ANOMALY AND ANOMALY-FREE TREATMENT OF QFT's BASED ON SYMMETRY-PRESERVING LOOP REGULARIZATION

2006 ◽  
Vol 21 (31) ◽  
pp. 6383-6456 ◽  
Author(s):  
YONG-LIANG MA ◽  
YUE-LIANG WU
Keyword(s):  
Ward Identity ◽  
Axial Vector ◽  
Dimensional Regularization ◽  
Direct Calculation ◽  
Vector Current ◽  
Explicit Calculation ◽  
Abelian Gauge ◽  
Free Treatment ◽  
Definition Of ◽  
Villars Regularization

The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in Refs. 1 and 2. The method is realized in the initial dimension of theory without modifying the original Lagrangian, it preserves symmetries under non-Abelian gauge and Poincaré transformations in spite of the existence of two intrinsic mass scales Mc and μs which actually play the roles of UV- and IR-cutoff respectively. The axial-vector–vector-vector (AVV) triangle diagrams in massless and massive QED are evaluated explicitly by using the loop regularization. It is shown that when the momentum k of external state is soft with [Formula: see text], m2 (m is the mass of loop fermions) and Mc → ∞, both massless and massive QED become anomaly free. The triangle anomaly is found to appear as quantum corrections in the case that m2, [Formula: see text] and Mc → ∞. Especially, it is justified that in the massless QED with μs = 0 and Mc → ∞, the triangle anomaly naturally exists as quantum effects in the axial-vector current when the ambiguity caused by the trace of gamma matrices with γ5 is eliminated by simply using the definition of γ5. It is explicitly demonstrated how the Ward identity anomaly of currents depends on the treatment for the trace of gamma matrices, which enables us to make a clarification whether the ambiguity of triangle anomaly is caused by the regularization scheme in the perturbation calculations or by the trace of gamma matrices with γ5. For comparison, an explicit calculation based on the Pauli–Villars regularization and dimensional regularization is carried out and the possible ambiguities of Ward identity anomalies caused from these two regularization schemes are carefully discussed, which include the ambiguities induced by the treatment of the trace of gamma matrices with γ5 and the action of the external momentum on the amplitude before the direct calculation of the AVV diagram.

scholarly journals Feynman Rules, Ward Identities and Loop Corrections in Very Special Relativity Standard Model

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 16 ◽  
Author(s):  
Jorge Alfaro
Keyword(s):  
Standard Model ◽  
Special Relativity ◽  
Effective Action ◽  
Dimensional Regularization ◽  
External Momentum ◽  
Ward Identities ◽  
Feynman Rules ◽  
Very Special Relativity ◽  
Charged Leptons ◽  
The Masses

In this paper, we want to study one loop corrections in Very Special Relativity Standard Model(VSRSM). In order to satisfy the Ward identities and the S i m ( 2 ) symmetry of the model, we have to specify the Feynman rules, including the infrared regulator. To do this, we adapt the Mandelstam–Leibbrandt (ML) prescription to incorporate external momentum-dependent null vectors. As an example, we use the new S i m ( 2 ) invariant dimensional regularization to compute one loop corrections to the effective action in the subsector of the VSRSM that describe the interaction of photons with charged leptons. New stringent bounds for the masses of ν e and ν μ are obtained.

scholarly journals BARE AND INDUCED LORENTZ AND CPT INVARIANCE VIOLATIONS IN QED

2010 ◽  
Vol 25 (16) ◽  
pp. 3271-3306 ◽  
Author(s):  
J. ALFARO ◽  
A. A. ANDRIANOV ◽  
M. CAMBIASO ◽  
P. GIACCONI ◽  
R. SOLDATI
Keyword(s):  
Finite Temperature ◽  
Lorentz Invariance ◽  
Axial Vector ◽  
Dimensional Regularization ◽  
Large Momentum ◽  
Radiative Corrections ◽  
Photon Mass ◽  
Cpt Invariance ◽  
Physical Role

We consider QED in a constant axial vector background (Æther). Further Lorentz invariance violations (LIV) might occur owing to radiative corrections. The phenomenology of this model is studied, clarifying issues related to the various regularizations employed, with a particular emphasis on the induced photon mass. To this concern, it is shown that in the presence of LIV dimensional regularization may produce a radiatively induced finite photon mass. The possible physical role of the large momentum cutoff is elucidated and the finite temperature radiative corrections are evaluated. Finally, various experimental bounds on the parameters of the model are discussed.

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