Feynman Integral Calculus by Vladimir A. Smirnov

Feynman Integral Calculus Contents

1. Introduction
2. Feynman Integrals: Primary Definitions and Instruments
3. Evaluating by Alpha and Feynman Parameters
4. Evaluating by MB Illustration
5. IBP and Discount to Grasp Integrals
6. Discount to Grasp Integrals by Baikov’s Technique
7.  Analysis by Differential Equations

Preface to Feynman Integral Calculus PDF

This can be a textbook model of my earlier ebook [190]. Issues and options have been included, Appendix G has been added, extra particulars have been offered, latest publications on evaluating Feynman integrals have been taken under consideration and the bibliography has been up to date.

The purpose of the ebook is to explain intimately how Feynman integrals1 will be evaluated analytically. The issue of evaluating Lorentz-covariant Feynman integrals over loop momenta originated within the early days of perturbative quantum area principle.

Over a span of greater than fifty years, an incredible number of strategies for evaluating Feynman integrals has been developed. Strongest trendy strategies are described on this ebook.

I perceive that if one other individual – specifically one actively concerned in creating strategies for Feynman integral analysis – wrote a ebook on this topic, she or he would most likely focus on another strategies and would rank the strategies as most essential and fewer essential in a special order.

I imagine, nevertheless, that my alternative is affordable. At the very least I’ve tried to focus on the strategies which have been used lately in probably the most refined calculations, wherein world information within the Feynman integral ‘sport’ have been achieved.

The issue of analysis is essential in the mean time. What may very well be simply evaluated was evaluated a few years in the past. To carry out essential calculations on the two-loop degree and better one wants to decide on satisfactory strategies and mix them in a non-trivial approach.

Within the current scenario – which is likely to be thought-about boring as a result of the Customary Mannequin works roughly correctly and there are not any obtrusive contradictions with experiment – one wants not solely to arrange new experiments but in addition carry out fairly nontrivial calculations for additional essential high-precision checks.

So I hope very a lot that this ebook shall be used as a textbook in sensible calculations. I shall focus on analytical strategies and solely briefly describe numerical ones. Some strategies are additionally characterised as semi-analytical, for instance, the tactic based mostly on asymptotic expansions of Feynman integrals in momenta and lots more and plenty which was described intimately in [186].

On this methodology, it’s also obligatory to use some analytical strategies of analysis which have been described there solely very briefly.

So the current ebook (and/or its earlier model [190]) will be thought-about as Quantity 1 with respect to [186], which is likely to be termed Quantity 2, or the sequel. Though all the required definitions regarding Feynman integrals are supplied within the ebook, it might be useful for the reader to know the fundamentals of perturbative quantum area principle, e.g. by following the primary few chapters of the well-known textbooks by Bogoliubov and Shirkov and/or Peskin and Schroeder.

This ebook relies on the course of lectures which I gave within the two winter semesters of 2003–2004 and 2005–2006 on the College of Hamburg (and in 2003–2004 on the College of Karlsruhe) as a DFG Mercator professor in Hamburg.

It’s my pleasure to thank the scholars, postgraduate college students, postdoctoral fellows and professors who attended my lectures for quite a few stimulating discussions.

Feynman Integral Calculus PDF

Author(s): Vladimir A. Smirnov

Publisher: Springer, Year: 2006

ISBN: 9783540306108,3-540-30610-2

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