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Albert Petrov - Quantum Superfield Supersymmetry

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Albert Petrov Quantum Superfield Supersymmetry
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Book cover of Quantum Superfield Supersymmetry Volume 202 Fundamental - photo 1
Book cover of Quantum Superfield Supersymmetry
Volume 202
Fundamental Theories of Physics
Series Editors
Henk van Beijeren
Utrecht, The Netherlands
Philippe Blanchard
Bielefeld, Germany
Bob Coecke
Oxford, UK
Dennis Dieks
Utrecht, The Netherlands
Bianca Dittrich
Waterloo, ON, Canada
Detlef Drr
Munich, Germany
Ruth Durrer
Geneva, Switzerland
Roman Frigg
London, UK
Christopher Fuchs
Boston, MA, USA
Domenico J. W. Giulini
Hanover, Germany
Gregg Jaeger
Boston, MA, USA
Claus Kiefer
Cologne, Germany
Nicolaas P. Landsman
Nijmegen, The Netherlands
Christian Maes
Leuven, Belgium
Mio Murao
Tokyo, Japan
Hermann Nicolai
Potsdam, Germany
Vesselin Petkov
Montreal, QC, Canada
Laura Ruetsche
Ann Arbor, MI, USA
Mairi Sakellariadou
London, UK
Alwyn van der Merwe
Greenwood Village, CO, USA
Rainer Verch
Leipzig, Germany
Reinhard F. Werner
Hanover, Germany
Christian Wthrich
Geneva, Switzerland
Lai-Sang Young
New York City, NY, USA

The international monograph series Fundamental Theories of Physics aims to stretch the boundaries of mainstream physics by clarifying and developing the theoretical and conceptual framework of physics and by applying it to a wide range of interdisciplinary scientific fields. Original contributions in well-established fields such as Quantum Physics, Relativity Theory, Cosmology, Quantum Field Theory, Statistical Mechanics and Nonlinear Dynamics are welcome. The series also provides a forum for non-conventional approaches to these fields. Publications should present new and promising ideas, with prospects for their further development, and carefully show how they connect to conventional views of the topic. Although the aim of this series is to go beyond established mainstream physics, a high profile and open-minded Editorial Board will evaluate all contributions carefully to ensure a high scientific standard.

More information about this series at http://www.springer.com/series/6001

Albert Petrov
Quantum Superfield Supersymmetry
1st ed. 2021
Logo of the publisher Albert Petrov Departamento de Fisica Universidade - photo 2
Logo of the publisher
Albert Petrov
Departamento de Fisica, Universidade Federal da Paraiba, Joo Pessoa, Brazil
ISSN 0168-1222 e-ISSN 2365-6425
Fundamental Theories of Physics
ISBN 978-3-030-68135-7 e-ISBN 978-3-030-68136-4
https://doi.org/10.1007/978-3-030-68136-4
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This review represents itself as a collection of lecture notes on superfield supersymmetry based on lectures given at Instituto de Fsica, Universidade de So Paulo (So Paulo), Instituto de Fsica, Universidade Federal do Rio Grande do Sul (Porto Alegre), and Departamento de Fsica, Universidade Federal da Paraiba (Joo Pessoa). The book includes many examples of explicit quantum calculations performed with use of the superfield formalism and is intended for students at levels of undergraduate and graduate studies in quantum field theory and theory of elementary particles and for researchers working in related subjects.

Author is grateful to C. A. S. Almeida, E. A. Asano, L. C. T. Brito, I. L. Buchbinder, M. Cvetic, A. F. Ferrari, F. S. Gama, H. O. Girotti, M. Gomes, S. M. Kuzenko, A. C. Lehum, R. V. Maluf, J. R. Nascimento, P. Porfirio, A. A. Ribeiro, V. O. Rivelles, A. J. da Silva, and E. O. Silva for fruitful collaboration and interesting discussions. The work has been partially supported by CNPq.

Albert Petrov
Joo Pessoa, Brazil
Contents
The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
A. Petrov Quantum Supereld Supersymmetry Fundamental Theories of Physics https://doi.org/10.1007/978-3-030-68136-4_1
1. Introduction
Albert Petrov
(1)
Departamento de Fisica, Universidade Federal da Paraiba, Joo Pessoa, Brazil
Albert Petrov
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We prove, once and for all, that people who dont use superspace are really out of it.

Stuperspace

The idea of supersymmetry is now considered as one of the basic concepts of theoretical high energy physics (see e.g. [1]). The supersymmetry, being a fundamental symmetry allowing to relate bosons and fermions, provides possibilities to construct theories with much better renormalization properties since some bosonic and fermionic divergent contributions in supersymmetric theories cancel each other. Moreover, there are essentially finite four-dimensional supersymmetry theories without higher derivatives, e.g. super-Yang-Mills SYM theory the detailed discussion of the finiteness of - photo 3 super-Yang-Mills (SYM) theory (the detailed discussion of the finiteness of this theory is presented in [2]), and, probably, supergravity 3 In the three-dimensional case and - photo 4 supergravity [3]. In the three-dimensional case, and supersymmetric Chern-Simons theories are known to be finite 4 Due to - photo 5 and supersymmetric Chern-Simons theories are known to be finite 4 Due to this - photo 6 supersymmetric Chern-Simons theories are known to be finite [4]. Due to this essential improvement of renormalization properties, there is a common expectation that the expected unified theory of all fundamental interactions must be supersymmetric (see e.g. [5] and references therein).

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