One-Loop Renormalization of Non-Abelian Gauge Theory and Β Function Based on Loop Regularization Method

Cui, Jianwei; Wu, Yonggang

doi:10.1142/s0217751x08040305

Cited by 16 publications

(15 citation statements)

References 48 publications

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“…In this sense, we would like to emphasize that the concept of ILIs is a crucial point in the LORE method to realize the interesting symmetry-preserving regularization scheme. In particular, the introduction of two intrinsic energy scales without spoiling symmetries of original theory is an advantage in the LORE method to avoid the infinities of divergent Feynman integrals [3][4][5][6][7][8][9][10][11][12][13][14]. For the effective theories, the intrinsic UV 'cutoff' scale M c plays the role as the characteristic energy scale below which the physics can be well described by the effective quantum field theory [10][11][12][13][14].…”

Section: Concept Of Ilis and Brief Outline On The Lore Methodsmentioning

confidence: 99%

“…To overcome such limitations in the dimensional regularization is our main purpose to look for a possible alternative consistent regularization scheme, which will be helpful for understanding deeply the applicability and consistency of QFTs. In this sense, the LORE method has been a step forward, as already shown in [5][6][7][8][9][10][11][12][13][14] at one loop level. It is worthwhile to go further and make an explicit check at higher loop level, which is our main goal in the present paper.…”

Section: Introductionmentioning

confidence: 97%

“…For short, here we may use 'LORE' as an abbreviation of the loop regularization. It has been proved with explicit calculations at one loop level that the LORE method can preserve non-Abelian gauge symmetry [5] and supersymmetry [6]. It can provide a consistent calculation for the chiral anomaly [7] and the radiatively induced Lorentz and CPT-violating Chern-Simons term in QED [8] as well as the QED trace anomaly [9].…”

Section: Introductionmentioning

confidence: 99%

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Consistency and advantage of loop regularization method merging with Bjorken–Drell’s analogy between Feynman diagrams and electrical circuits

Huang

2012

Eur. Phys. J. C

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The consistency of loop regularization (LORE) method is explored in multiloop calculations. A key concept of the LORE method is the introduction of irreducible loop integrals (ILIs) which are evaluated from the Feynman diagrams by adopting the Feynman parametrization and ultravioletdivergence-preserving(UVDP) parametrization. It is then inevitable for the ILIs to encounter the divergences in the UVDP parameter space due to the generic overlapping divergences in the 4-dimensional momentum space. By computing the so-called αβγ integrals arising from two loop Feynman diagrams, we show how to deal with the divergences in the parameter space with the LORE method. By identifying the divergences in the UVDP parameter space to those in the subdiagrams, we arrive at the Bjorken-Drell's analogy between Feynman diagrams and electrical circuits. The UVDP parameters are shown to correspond to the conductance or resistance in the electrical circuits, and the divergence in Feynman diagrams is ascribed to the infinite conductance or zero resistance. In particular, the sets of conditions required to eliminate the overlapping momentum integrals for obtaining the ILIs are found to be associated with the conservations of electric voltages, and the momentum conservations correspond to the conservations of electrical currents, which are known as the Kirchhoff's laws in the electrical circuits analogy. As a practical application, we carry out a detailed calculation for one-loop and two-loop Feynman diagrams in the massive scalar φ 4 theory, which enables us to obtain the well-known logarithmic running of the coupling constant and the consistent power-law running of the scalar mass at two loop level. Especially, we present an explicit demonstration on the general procedure of applying the LORE method to the multiloop calculations of Feynman diagrams when merging with the advantage of Bjorken-Drell's circuit analogy.

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Section: Concept Of Ilis and Brief Outline On The Lore Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Consistency and advantage of loop regularization method merging with Bjorken–Drell’s analogy between Feynman diagrams and electrical circuits

Huang

2012

Eur. Phys. J. C

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“…The development of LORE method is not for working out a much simpler regularization scheme, but for finding out whether there exists in principle a symmetry-preserving and infinity-free regularization method without modifying the original theory, so as to overcome the shortages and limitations in the widely-used regularization schemes and answer to the criticisms raised by Dirac and Feynman on the treatment of infinities via a renormalization scheme to remove the divergences. The consistency and applicability of the LORE method have been demonstrated in a series of works [38][39][40][41][42][43][44][45][46][47]. It has explicitly been shown at one loop level that the LORE method can preserve non-Abelian gauge symmetry [38] and supersymmetry [39].…”

Section: Introductionmentioning

confidence: 99%

“…The consistency and applicability of the LORE method have been demonstrated in a series of works [38][39][40][41][42][43][44][45][46][47]. It has explicitly been shown at one loop level that the LORE method can preserve non-Abelian gauge symmetry [38] and supersymmetry [39]. It can lead to a consistent result for the chiral anomaly [40] and radiatively induced Lorentz and CPT-violating Chern-Simons term in an extended QED [41] as well as QED trace anomaly [42].…”

Section: Introductionmentioning

confidence: 99%

Quantum Structure of Field Theory and Standard Model Based on Infinity-Free Loop Regularization/Renormalization

2014

Proceedings of the Conference in Honour of the 90th Birthday of Freeman Dyson

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To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cut-off M c and infrared cut-off µ s to avoid infinities. As M c can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales M c and µ s in LORE become physically meaningful as the characteristic energy scale and sliding energy scale respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet-divergence-preserving (UVDP) parametrization naturally leads to Bjorken-Drell's analogy between Feynman diagrams and electric circuits, which enables us to treat systematically the divergences of Feynman diagrams and understand better the divergence structure of QFTs. The LORE method has been shown to be applicable to both underlying and effective QFTs. Its consistency and advantages have been demonstrated in a series of applications, which includes the Slavnov-Taylor-Ward-Takahaski identities of gauge theories and supersymmetric theories, quantum chiral anomaly, renormalization of scalar interaction and power-law running of scalar mass, quantum gravitational effects and asymptotic free power-law running of gauge couplings.

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Gravitational contributions to gauge Green’s functions and asymptotic free power-law running of gauge coupling

Tang

2011

J. High Energ. Phys.

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We perform an explicit one-loop calculation for the gravitational contributions to the two-, threeand four-point gauge Green's functions with paying attention to the quadratic divergences. It is shown for the first time in the diagrammatic calculation that the Slavnov-Taylor identities are preserved even if the quantum graviton effects are included at one-loop level, such a conclusion is independent of the choice of regularization schemes. We also present a regularization scheme independent calculation based on the gauge condition independent background field framework of Vilkovisky-DeWitt's effective action with focusing on both the quadratic divergence and quartic divergence that is not discussed before. With the harmonic gauge condition, the results computed by using the traditional background field method can consistently be recovered from the Vilkovisky-DeWitt's effective action approach by simply taking a limiting case, and are found to be the same as the ones yielded by the diagrammatic calculation. As a consequence, in all the calculations, the symmetry-preserving and divergent-behavior-preserving loop regularization method can consistently lead to a nontrivial gravitational contribution to the gauge coupling constant with an asymptotic free power-law running at one loop near the Planck scale.

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One-Loop Renormalization of Non-Abelian Gauge Theory and Β Function Based on Loop Regularization Method

Cited by 16 publications

References 48 publications

Consistency and advantage of loop regularization method merging with Bjorken–Drell’s analogy between Feynman diagrams and electrical circuits

Consistency and advantage of loop regularization method merging with Bjorken–Drell’s analogy between Feynman diagrams and electrical circuits

Quantum Structure of Field Theory and Standard Model Based on Infinity-Free Loop Regularization/Renormalization

Gravitational contributions to gauge Green’s functions and asymptotic free power-law running of gauge coupling

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