Two- and Three-Loop Amplitudes in Covariant Loop Calculus

机译：协变环微积分中的二环和三环振幅

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We study 2- and 3-loop vacuum-amplitudes for the closed bosonic string. We compare two sets of expressions for the corresponding density on moduli space: One, based on the covariant Reggeon loop calculus (where modular invariance is not manifest). The other, based on analytic geometry. We want to prove identity between the two sets of expressions. Quite apart from demonstrating modular invariance of the Reggeon results, this would in itself be a remarkable mathematical feature. Identity is established to 'high' order in some moduli and exactly in others. The expansions reveal an essentially number-theoretical structure. Agreement is found only by exploiting the connection between the 4 Jacobi theta-functions and number theory. (ERA citation 14:012227)

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Roland, K.;
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年度 1988
页码 1-23
总页数 23
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
String Models; Bosons; Conformal Invariance; Conformal Mapping; Jacobian Function; Regge Calculus; Regge Poles; Riemann Function; Transition Amplitudes; Vacuum States;

机译：弦乐模型;玻色子;共形不变性;共形映射;雅可比函数;回归微积分;回归极点;黎曼函数;跃迁幅度;真空态;

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1. Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory - art. no. 056113 [J] . Kleinert H., Van den Bossche B. Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics . 2001,第5aPta2期

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2. The Adler D-function for N=1 SQCD regularized by higher covariant derivatives in the three-loop approximation [J] . Kataev A. L., Kazantsev A. E., Stepanyantz K. V. Nuclear physics, B . 2018,第期

机译：用于n = 1 sqcd的Adler D-函数在三环近似下通过更高的协变衍生物进行规则化
3. The Adler D-function for N = 1 SQCD regularized by higher covariant derivatives in the three-loop approximation [J] . A.L. Kataev, A.E. Kazantsev, K.V. Stepanyantz Nuclear physics, B . 2018,第1期

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4. THE THREE-LOOP CONTRIBUTION TO β-FUNCTION QUARTIC IN THE YUKAWA COUPLINGS FOR THE N = 1 SUPERSYMMETRIC YANG-MILLS THEORY WITH THE HIGHER COVARIANT DERIVATIVE REGULARIZATION [C] . Vikentii Shakhmanov Lomonosov Conference on Elementary Particle Physics . 2019

机译：在N = 1超对对称阳磨机理论中的yukawa联轴器中的三环对β-函数间的贡献与更高的协变衍生物正则化
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6. Restorative proctocolectomy with a three-loop ileal reservoir for ulcerative colitis and familial adenomatous polyposis. Clinical results in 66 patients followed for up to 6 years. [O] . J Nicholls, M Pescatori, R W Motson, 1984

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7. Beyond Reggeization for two- and three-loop QCD amplitudes [O] . Del Duca, Vittorio, Falcioni, Giulio, Magnea, Lorenzo, 2013

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机译：Bosonic弦理论中的二环和三环振幅

Two- and Three-Loop Amplitudes in Covariant Loop Calculus

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