Quantum cosmology -- the supersymmetric perspective. Vol. 2: Advanced topics.
For Vol. 1 see [Lecture Notes in Physics 803. Berlin: Springer (2010; Zbl 1219.83004)]. From the Introduction: ``The key purpose of this book will be to introduce and present the essentials, as well as pertinent details of supersymmetric quantum cosmology (SQC) to the interested fellow explorer. The book is split into two volumes, each divided into four parts. Volume 1 conveys, in essence, the fundamentals of SQC. Part I constitutes a brief overview of the methods and results discussed throughout the two volumes and is provided identically in both books. It contains this introduction as Chapter I. Part II of Vol. 1 presents some basic elements that will be required for the core part of the book. Chapter 2 provides a generic description of the main aspects and methods used in quantum cosmology, namely, minisuperspace quantization. We introduce and explain the basic principles of SUSY and SUGRA in Chapter 3. The Hamiltonian formulation and canonical quantization of SUGRA are analysed in detail in Chapter 4. In Part III, Chapter 5 focuses on supersymmetric cosmological models extracted from \(N = 1\) SUGRA, exploring a fermionic differential operator representation for SQC models, which has proved itself to be a suitable method. The emphasis is on FRW models, and in particular on obtaining physical states for quantum supersymmmetric universes. Bianchi models are also dealt with, and the presence of matter fields is explored. Chapter 6 presents a thorough description of supersymmetric minisuperspaces derived from the bosonic sectors of superstring theories. Some of these models are explored in a context where duality properties can be related to these hidden supersymmetries. Finally, in Part IV, within the context of Vol. 1, we present an appraisal of current accomplishments, and point to subsequent suggestions for investigation in SQC. In more detail, Chapter 7 describes the main results that have been achieved, while Chapter 8 lists several lines of further enquiry. Two appendices conclude the volume, explaining the notation used along with some useful expressions (Appendix A), and describing canonical quantization procedures for theories with constraints (Appendix B). Volume 2 is entitled Advanced Topics. It begins with a carbon copy of Part I from Vol. 1, the intention being to provide a consistent context and broad guidance throughout the book. Part II is entitled Further Essentials. These begin in Chapter 2, which corresponds to Chapter 2 of Vol. 1, focusing again on quantum cosmology and possible semiclassical limits. Chapter 3 provides a brief treatment of SUSY breaking in SUSY and SUGRA theories, placing particular emphasis on supersymmetric quantum mechanics (SQM). Then in Chapter 4, counterpart to Chapter 4 of Vol. 1, we detail a framework suitable for describing the semiclassical limit of quantum SUGRA. Part III of Vol. 2 discusses alternative frameworks for SQC. The presence of supermatter and SUSY breaking is presented in Chapter 5 with regard to supersymmetric cosmological models extracted from \(N = 1\) SUGRA, with a fermionic differential operator representation for SQC. Then in Chapter 6 we describe connection and loop variables in SQC, with emphasis on the interesting developments they have stimulated. Chapter 7 deals with the matrix fermionic representation used in SQC for fermionic momenta. Chapter 8 reports on minisuperspace models extending from those discussed in Chapter 6 of Vol. 1. We conclude with Part IV. Chapter 9 summarizes reported accomplishments concerning the frameworks introduced in Parts II and III of Vol. 2, while Chapter 10 suggests more routes for exploration and investigation that follow on from the contents of Vol. 2. An appendix concludes Vol. 2, with a review of the notation and some further useful expressions.''
scientific article; zbMATH DE number 5690266