Surface terms and radiative corrections to the<i>VVA</i>triangle diagram

Chowdhury, A. M.; McKeon, Gerry

doi:10.1103/physrevd.33.598

Cited by 23 publications

(26 citation statements)

References 6 publications

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“…(Again, we do not consider the nonAbelian axial current.) Provided an appropriate choice of arbitrary parameters associated with one-loop subdiagrams is made, no two-loop contribution to the anomaly occurs, which is consistent with the Adler-Bardeen result (14)(15)(16). A different choice of arbitrary parameters results in a contribution to the anomaly that is proportional to F*F. (We note that the validity of the Adler-Bardeen result has been shown to be dependent on the regulating technique that has been employed (17), especially in the context of supersymmetric theories.…”

Section: Introductionsupporting

confidence: 73%

Operator regularization and the chiral anomaly

Culumovic¹,

McKeon²

1990

Can. J. Phys.

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Operator regularization is used to compute anomalies in axial gauge theories to one-and two-loop order. To one-loop order, we consider the decay of a U(l) axial current into two, three, and four SU(N) vector currents. This is done first by directly computing the relevant Green functions, and then by a functional approach. The one-loop anomaly is found to be proportional to trF*F. We note that the quadrilinear term in this expression is zero. The Schwinger expansion, employed in operator regularization to generate Green functions, is then used to derive the Schwinger-de Witt WKB (Wentzel-kamersBrillouin) expansion of the heat kernel, recovering the known diagonal elements and also giving the previously unknown off-diagonal elements. For the case of a constant background electromagnetic field, these off-diagonal terms can also be obtained from an exact expression for the heat kernel given by Schwinger. We then use this result, in conjunction with the functional technique originally introduced in one-loop calculations, to compute exactly the amplitude for the decay of the U(l) axial current into both U (1) and O(3) constant gauge fields to two-loop order. With the appropriate choice of mass scale parameters, a vanishing result is obtained, in agreement with the Adler-Bardeen result. Le rCgularisation d'optrateur est utilisCe pour calculer les anomalies dans les thCories de jauge axiales, B I'ordre d'une et de deux boucles. A l'ordre d'une boucle, nous considCrons la dCcomposition d'un courant axial U(l) en deux, trois et quatre courants vectoriels SU(N). Cela est fait d'abord en calculant directement les fonctions de Green appropriCes, et ensuite par une approche fonctionnelle. On trouve que I'anomalie i une boucle est proportionnelle B trF*F. Nous notons que le terme quadrilinkaire dans cette expression est ziro. Le dtveloppement de Schwinger, employ6 en rCgularisation d'opirateur pour gCnCrer des fonctions de Green, est ensuite utilisC pour obtenir le dCveloppement Wentzel-kamers-Brillouin Schwinger-de Witt du noyau de la chaleur, en retroubant les ClCments diagonaux connus et en obtenant aussi les ClCments hors diagonale prCcCdemment inconnus. En prCsence d'un champ ClectromagnCtique constant ces termes hors diagonale peuvent aussi &tre obtenus B partir d'une expression exacte du noyau de la chaleur donnte par Schwinger. Nous utilisons ensuite ce rksultat, en conjonction avec la technique fonctionnelle introduite originellement dans les calculs a une boucle, pour calculer exactement, a l'ordre de deux boucles, I'amplitude pour la transition du courant axial U(1) aux deux champs de jauge constants U(1) et O(3). Avec le choix appropriC des parambtres d'tchelle de masse, on obtient un rCsultat qui s'annule, en accord avec le rksultat Adler-Bardeen.[Traduit par la revue]Can. I.

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Section: Introductionsupporting

confidence: 73%

Operator regularization and the chiral anomaly

Culumovic¹,

McKeon²

1990

Can. J. Phys.

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“…To * h18m1140@hirosaki-u.ac.jp; present an escalator, we construct a two-lane model with a modified totally asymmetric simple exclusion process (TASEP), which is a stochastic process on a onedimensional lattice in which particles are allowed to hop in one direction (left to right in the present study). In the field of nonequilibrium statistical mechanics, researchers have applied TASEP extensively to various themes such as molecular-motor traffic [18][19][20][21], vehicular traffic [22][23][24][25], and exclusive queuing processes [26][27][28], and the process is especially useful since it can be solved exactly [29][30][31]. Our model differs from the original TASEP with open boundaries in two respects.…”

Section: Introductionmentioning

confidence: 99%

Comparison of escalator strategies in models using a modified totally asymmetric simple exclusion process

Yamamoto

Yanagisawa

Nishinari

2020

Physica A: Statistical Mechanics and its Applications

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We develop a modified version of the totally asymmetric simple exclusion process (TASEP) and use it to reproduce flow on an escalator with two distinct lanes of pedestrian traffic. The model is used to compare strategies with two standing lanes and a standing lane with a walking lane, using theoretical analysis and numerical simulations. The results show that two standing lanes are better for smoother overall transportation, while a mixture of standing and walking is advantageous only in limited cases that have a small number of pedestrians. In contrast, with many pedestrians, the individual travel time of the first several entering particles is always shorter with distinct standing and walking lanes than it is with two standing lanes.

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“…The collective movement of multiple RNAPs simultaneously on a DNA track resembles, at least superficially, vehicular traffic on highways [7,8]. Wide varieties of collective traffic-like phenomena in non-living as well as in living systems have been modelled by various appropriate extensions of the totally asymmetric simple exclusion process (TASEP) [7][8][9][10][11]. In the past, RNAP traffic has been modelled theoretically [12][13][14][15][16][17][18] by extending the TASEP [7,[19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Biologically motivated asymmetric exclusion process: Interplay of congestion in RNA polymerase traffic and slippage of nascent transcript

et al. 2019

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We develope a theoretical framework, based on exclusion process, that is motivated by a biological phenomenon called transcript slippage (TS). In this model a discrete lattice repesents a DNA strand while each of the particles that hop on it unidirectionally, from site to site, represents a RNA polymerase (RNAP). While walking like a molecular motor along a DNA track in a step-by-step manner, a RNAP simultaneously synthesizes a RNA chain; in each forward step it elongates the nascent RNA molecule by one unit, using the DNA track also as the template. At some special "slippery" position on the DNA, which we represent as a defect on the lattice, a RNAP can lose its grip on the nascent RNA and the latter's consequent slippage results in a final product that is either longer or shorter than the corresponding DNA template. We develope an exclusion model for RNAP traffic where the kinetics of the system at the defect site captures key features of TS events. We demonstrate the interplay of the crowding of RNAPs and TS. A RNAP has to wait at the defect site for longer period in a more congested RNAP traffic, thereby increasing the likelihood of its suffering a larger number of TS events. The qualitative trends of some of our results for a simple special case of our model are consistent with experimental observations. The general theoretical framework presented here will be useful for guiding future experimental queries and for analysis of the experimental data with more detailed versions of the same model.

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Surface terms and radiative corrections to theVVAtriangle diagram

Cited by 23 publications

References 6 publications

Operator regularization and the chiral anomaly

Operator regularization and the chiral anomaly

Comparison of escalator strategies in models using a modified totally asymmetric simple exclusion process

Biologically motivated asymmetric exclusion process: Interplay of congestion in RNA polymerase traffic and slippage of nascent transcript

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