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# Do we need Feynman diagrams for higher orders perturbation theory?

Physics Letters B (Impact Factor: 4.57). 02/2012; 713(3). DOI: 10.1016/j.physletb.2012.05.047

Source: arXiv

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**ABSTRACT:**The monograph is composed on the basis of courses on field theory and particle physics which have been taught by the author at Columbia University, New York City. Besides exposition of the basic topics in quantum field theory (QFT) it illustrates also various applications of the methods of this theory chosen in accordance with the author’s preferences. The general part (Chapters 1–12) includes canonical quantization, S-matrix, functional integral representation, renormalization, gauge theory, symmetry and spontaneous symmetry breaking. This first part of the book can be used for a general course on field theory. However, some more specific questions are touched upon: connection of QFT with General Relativity, light-cone quantization, conformal invariance, loop expansion, BRST symmetry, Ward-Takahasi identities. In Chapters 13–20 more modern developments or specific topics are considered: anomalies, differential-geometric methods, path integrals, finite temperature QFT, nonperturbative approaches to gauge theory, elements of geometric quantization. The introduction given to the mathematical basis of this part is necessarily brief, and these chapters should be accompanied by books on the relevant mathematical topics as indicated in the bibliography. One of the author’s goals was to give in this part a better understanding of the standard model. There is no discussion of supersymmetry, supergravity, developments in field theory inspired by string theory. There is also no detailed discussion of the renormalization group. The discussion of each topic given in the present book is accompanied by references to other publications which can give a more comprehensive perspective of the corresponding subject. The book will be useful for those students and researchers who are familiar with non-relativistic quantum mechanics and wish to have acquaintance with QFT.Quantum Field Theory: A Modern Perspective, Graduate Texts in Contemporary Physics. ISBN 978-0-387-21386-6. Springer Science+Business Media, Inc., 2005. 01/2005; - [Show abstract] [Hide abstract]

**ABSTRACT:**We have calculated the value of the Callan-Symanzik beta function to order g5 for non-Abelian gauge theories with fermions. We discuss internal consistency of the calculation, and consider the approach to the aymptotic energy range in such theories.Physical Review Letters 01/1974; 33:244-246. · 7.73 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The analytic calculation of the three-loop QCD β-function and anomalous dimensions within the minimal subtraction scheme in an arbitrary covariant gauge is presented. The result for the β-function coincides with the previous calculation [O.V. Tarasov, A.A. Vladimirov and A. Yu. Zharkov, Phys. Lett. B 93 (1980) 429].Physics Letters B 01/1993; · 4.57 Impact Factor

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