Bosonic strings: A mathematical treatment (Q2723292)

This book elaborates a mathematical construction of the partition function of the bosonic string. In the author's own words the construction constitutes ``the quantization of Plateau's problem for minimal surfaces'', because it is based on global Riemannian geometry rather than the representation theory of the Virasoro algebra. This approach was first presented in a monograph by \textit{S. Albeverio, J. Jost, S. Paycha} and \textit{S. Scarlatti} [A Mathematical Introduction to String Theory, Cambridge University Press (1997; Zbl 0882.53056)] and has been reworked for the present volume (in particular, harmonic mappings are no longer the centrepiece), which contains additional mathematical connections but leaves out the probabilistic aspects.NEWLINENEWLINENEWLINEFor pedagogical reasons the brief first chapter of the book is devoted to Euclidean path integral techniques for the relativistic point particle which are then generalized for the bosonic string in chapter 2. Here Teichmüller theory is developed and a rigorous version of what is known to physicists as the Polyakov path integral (based on the Dirichlet integral as the world sheet action) is derived for the ``critical dimension'' \(D=26\). A final section discusses -- in more physical terms -- the simplest version of \(T\)-duality and its relevance for the notion of \(D\)-branes.NEWLINENEWLINENEWLINEThe book is written in a clear and concise style and should be of interest to mathematicians seeking an introduction to bosonic string theory. On the other hand it can also be recommended to physicists in search for a rigorous treatment of the same subject, although they may sometimes have to consult the references listed at the end of the book.