標(biāo)題: Titlebook: Anti-Differentiation and the Calculation of Feynman Amplitudes; Johannes Blümlein,Carsten Schneider Book 2021 The Editor(s) (if applicable [打印本頁] 作者: Deflated 時(shí)間: 2025-3-21 19:13
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書目名稱Anti-Differentiation and the Calculation of Feynman Amplitudes讀者反饋學(xué)科排名
作者: 啪心兒跳動 時(shí)間: 2025-3-21 23:21 作者: Alveoli 時(shí)間: 2025-3-22 04:21 作者: constitute 時(shí)間: 2025-3-22 05:11 作者: 放大 時(shí)間: 2025-3-22 09:18 作者: 黃瓜 時(shí)間: 2025-3-22 13:53 作者: 亂砍 時(shí)間: 2025-3-22 17:16 作者: ungainly 時(shí)間: 2025-3-23 00:27
Top-Down Decomposition: A Cut-Based Approach to Integral Reductions,atical object known as the intersection number to define what amounts to an inner product between Feynman integrals, which can be used to project directly unto the basis of master integrals. In particular we will discuss one perspective to this intersection-based method, which we name the top-down a作者: 蟄伏 時(shí)間: 2025-3-23 02:29
Hypergeometric Functions and Feynman Diagrams,ruction of the .-expansion. As an example, we present a detailed discussion of the construction of the .-expansion of the Appell function .. around rational values of parameters via an iterative solution of differential equations. As a by-product, we have found that the one-loop massless pentagon di作者: 復(fù)習(xí) 時(shí)間: 2025-3-23 08:05
Outer Space as a Combinatorial Backbone for Cutkosky Rules and Coactions,o boundary operations: shrinking edges or removing them. Only if the number of spanning trees of a graph . equals its number of internal edges we find that the graphical coaction .. constructed here agrees with the coaction .. proposed by Britto and collaborators. The graphs for which this is the ca作者: Agnosia 時(shí)間: 2025-3-23 12:40
Calculating Four-Loop Corrections in QCD,rs, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as ., designed for large scale computations.作者: 強(qiáng)有力 時(shí)間: 2025-3-23 15:27 作者: FLAX 時(shí)間: 2025-3-23 19:45 作者: Chagrin 時(shí)間: 2025-3-23 22:13 作者: 微枝末節(jié) 時(shí)間: 2025-3-24 04:38 作者: 影響 時(shí)間: 2025-3-24 10:14
Anti-Differentiation and the Calculation of Feynman Amplitudes978-3-030-80219-6Series ISSN 0943-853X Series E-ISSN 2197-8409 作者: flourish 時(shí)間: 2025-3-24 11:50
https://doi.org/10.1007/978-3-663-16044-1hich emerge in higher order perturbative calculations in the Standard Model of elementary particles, its extensions and associated model field theories, including effective field theories of different kind.作者: 不規(guī)則 時(shí)間: 2025-3-24 17:04
https://doi.org/10.1007/978-3-663-16044-1ty and energy discontinuities, and the analytic structure plays a vital role. We first summarize the lessons learned from the study of the remainder functions of the 2?→?4 and the 2?→?5 scattering amplitudes and then present new results for the 2?→?6 amplitude.作者: 人類學(xué)家 時(shí)間: 2025-3-24 20:35 作者: 輕打 時(shí)間: 2025-3-24 23:33
Exkurs: Algebraische Strukturen,s of such systems. We will illustrate the methods developed in Dreyfus and Weil (Computing the Lie algebra of the differential Galois group: The reducible case, ArXiv . 2019) on several examples to reduce the differential system. This will give information on potential algebraic relations between integrals.作者: carotid-bruit 時(shí)間: 2025-3-25 05:29 作者: homocysteine 時(shí)間: 2025-3-25 09:46
Einführung in die Kinderheilkundeen limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Prescriptions of this strategy are formulated in a simple geometrical language and are illustrated through simple examples.作者: 剝皮 時(shí)間: 2025-3-25 12:56
Johannes Blümlein,Carsten SchneiderPresents up-to-date reviews on modular forms and functions and their use in particle physics.Combines knowledge from mathematical physics and mathematics.Written by international authors作者: 吹氣 時(shí)間: 2025-3-25 16:00
Texts & Monographs in Symbolic Computationhttp://image.papertrans.cn/a/image/158329.jpg作者: 抱負(fù) 時(shí)間: 2025-3-25 19:58
Exkurs: Algebraische Strukturen,The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion coefficients are shown, and modern methods based on differential equations are discussed.作者: ODIUM 時(shí)間: 2025-3-26 00:33
https://doi.org/10.1007/978-3-322-83837-7Computer algebra methods within the scope of the holonomic systems approach provide a versatile toolbox to integration problems in the context of Feynman diagrams. This is demonstrated with the aid of several benchmark problems, ranging from hypergeometric series evaluations to Bessel integrals of sunrise diagrams.作者: Cosmopolitan 時(shí)間: 2025-3-26 08:09 作者: 甜得發(fā)膩 時(shí)間: 2025-3-26 11:50
Einführung in die KinderheilkundeA number of aspects of IBP reductions are discussed, indicating some of the major bottlenecks. Potential future developments are indicated, including some in the realm of mathematics and computer algebra.作者: 愚笨 時(shí)間: 2025-3-26 13:38
Differential Equations and Feynman Integrals,The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion coefficients are shown, and modern methods based on differential equations are discussed.作者: 雪上輕舟飛過 時(shí)間: 2025-3-26 16:59
Holonomic Anti-Differentiation and Feynman Amplitudes,Computer algebra methods within the scope of the holonomic systems approach provide a versatile toolbox to integration problems in the context of Feynman diagrams. This is demonstrated with the aid of several benchmark problems, ranging from hypergeometric series evaluations to Bessel integrals of sunrise diagrams.作者: Commission 時(shí)間: 2025-3-26 22:01
Integration-by-Parts: A Survey,We present an overview of the field of Integration-By-Parts with special emphasis on Laporta’s algorithm. We give an overview of the problems associated with Laporta’s algorithm and try to illustrate possible ways out.作者: 小淡水魚 時(shí)間: 2025-3-27 01:40 作者: 上下連貫 時(shí)間: 2025-3-27 07:47 作者: Mere僅僅 時(shí)間: 2025-3-27 11:35
,N =? 4 SYM Gauge Theories: The 2?→?6 Amplitude in the Regge Limit,ty and energy discontinuities, and the analytic structure plays a vital role. We first summarize the lessons learned from the study of the remainder functions of the 2?→?4 and the 2?→?5 scattering amplitudes and then present new results for the 2?→?6 amplitude.作者: 農(nóng)學(xué) 時(shí)間: 2025-3-27 13:53 作者: Folklore 時(shí)間: 2025-3-27 18:11 作者: Malleable 時(shí)間: 2025-3-28 00:08
Calculating Four-Loop Corrections in QCD,rs, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as ., designed for large scale computations.作者: DALLY 時(shí)間: 2025-3-28 03:21
Expansion by Regions: An Overview,en limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Prescriptions of this strategy are formulated in a simple geometrical language and are illustrated through simple examples.作者: Charitable 時(shí)間: 2025-3-28 06:31
https://doi.org/10.1007/978-3-030-80219-6elliptic integrals and functions; iterated modular functions; iterated integrals; massive high loop Fey作者: 浮雕寶石 時(shí)間: 2025-3-28 10:41
978-3-030-80221-9The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl作者: Infraction 時(shí)間: 2025-3-28 16:15 作者: 沒有希望 時(shí)間: 2025-3-28 19:32 作者: 幾何學(xué)家 時(shí)間: 2025-3-29 02:31
https://doi.org/10.1007/978-3-663-16044-1reductions to linear combinations of a basis, with rational or algebraic coefficients. Once a tentative reduction is obtained, confidence in its validity is greatly increased by computing more decimal digits of the terms and verifying the stability of the result. Here we give examples of how the PSL作者: Fresco 時(shí)間: 2025-3-29 04:42 作者: 離開 時(shí)間: 2025-3-29 07:42
Mathematisch-physikalische Bibliothekcle diagrams. We review a variety of results by the authors in which this method, employed with some care, can compute diagrams of up to eight particles and four loops. We also highlight situations in which this method fails due to an algebraic obstruction. In a large number of cases the obstruction作者: Offbeat 時(shí)間: 2025-3-29 11:43 作者: 貪婪的人 時(shí)間: 2025-3-29 16:10 作者: fabricate 時(shí)間: 2025-3-29 20:34 作者: 切掉 時(shí)間: 2025-3-30 01:36 作者: lipids 時(shí)間: 2025-3-30 04:58
https://doi.org/10.1007/978-3-322-83837-7o boundary operations: shrinking edges or removing them. Only if the number of spanning trees of a graph . equals its number of internal edges we find that the graphical coaction .. constructed here agrees with the coaction .. proposed by Britto and collaborators. The graphs for which this is the ca作者: Measured 時(shí)間: 2025-3-30 08:30
Abdomen, Darm, Leber, Milz, Pankreas,rs, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as ., designed for large scale computations.作者: Kernel 時(shí)間: 2025-3-30 14:31
Einführung in die Kinderheilkunde theory of hypergeometric series. In contrast to Takayama’s approach, which for elimination uses non-commutative Gr?bner bases, our framework is based on parameterized telescoping and can be viewed as an extension of Zeilberger’s creative telescoping paradigm based on Gosper’s algorithm. The wide ra作者: reaching 時(shí)間: 2025-3-30 19:53 作者: 聯(lián)想 時(shí)間: 2025-3-30 23:53 作者: 友好關(guān)系 時(shí)間: 2025-3-31 01:24
Einführung in die Kinderheilkundeen limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Prescriptions of this strategy are formulated in a simple geometrical language and are illustrated through simple examples.作者: Esophagitis 時(shí)間: 2025-3-31 06:39 作者: 未成熟 時(shí)間: 2025-3-31 10:18 作者: misanthrope 時(shí)間: 2025-3-31 15:39
Einführung in die Kinderheilkunde (unique) representations and their refinements in the introduced term algebra are explored by utilizing the available difference ring theory. Based on that, precise input-output specifications of the available tools of the summation package . are provided.作者: Banquet 時(shí)間: 2025-3-31 19:29
Nested Integrals and Rationalizing Transformations,holonomic systems approach and the differential field approach. For simplification to rational integrands, we give a comprehensive list of univariate rationalizing transformations, including transformations tuned to map the interval [0, 1] bijectively to itself.作者: Resistance 時(shí)間: 2025-4-1 00:03
Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation, (unique) representations and their refinements in the introduced term algebra are explored by utilizing the available difference ring theory. Based on that, precise input-output specifications of the available tools of the summation package . are provided.作者: 休戰(zhàn) 時(shí)間: 2025-4-1 03:44
Book 2021rmany, in October 2020, and a few additional invited reviews.?.The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function sp作者: 不透明 時(shí)間: 2025-4-1 07:13
Book 2021of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics..作者: 來就得意 時(shí)間: 2025-4-1 10:33
A Geometrical Framework for Amplitude Recursions: Bridging Between Trees and Loops,variable of a differential equation of KZ or KZB type. The parameter interpolates between two associated regularized boundary values, which contain iterated integrals closely related to scattering amplitudes defined on two different geometries.作者: 高度贊揚(yáng) 時(shí)間: 2025-4-1 15:48
Top-Down Decomposition: A Cut-Based Approach to Integral Reductions,pproach. This approach can be seen as an integral level version of the algorithms based on integrand reduction and generalized unitarity cuts, that were revolutionizing NLO scattering computations in the early 2000s.作者: 最高點(diǎn) 時(shí)間: 2025-4-1 21:31 作者: 表示向下 時(shí)間: 2025-4-2 02:33
Mathematisch-physikalische Bibliothekvariable of a differential equation of KZ or KZB type. The parameter interpolates between two associated regularized boundary values, which contain iterated integrals closely related to scattering amplitudes defined on two different geometries.作者: 含糊 時(shí)間: 2025-4-2 04:15 作者: 切碎 時(shí)間: 2025-4-2 07:13
Exkurs: Algebraische Strukturen,agram in dimension .?=?3???2. is not expressible in terms of multiple polylogarithms. Another interesting example is the Puiseux-type solution involving a differential operator generated by a hypergeometric function of three variables. The holonomic properties of the .. hypergeometric functions are briefly discussed.作者: 條街道往前推 時(shí)間: 2025-4-2 12:15 作者: 無孔 時(shí)間: 2025-4-2 17:28
https://doi.org/10.1007/978-3-322-83837-7such graphs simple graphs. The Dunce’s cap graph is the first non-simple graph. The number of its spanning trees (five) exceeds the number of its edges (four). We compare the two coactions which indeed do not agree and discuss this result. We also point out that for kinematic renormalization schemes the coaction .. simplifies.
