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The holy grail of theoretical physics is to find the theory of everything that combines all the forces of nature, including gravity. This book addresses the question: how far are we from such discovery? Over the last few decades, multiple roads to finding a quantum theory of gravity have been proposed but no obvious description of nature has emerged in this domain. What is to be made of this situation? This volume probes the state-of-the art in this daunting quest of theoretical physics by collecting critical interviews with nearly forty leading theorists in this field. These broad-ranging conversations give important insights and candid opinions on the various approaches to quantum gravity, including string theory, loop quantum gravity, causal set theory and asymptotic safety. This unique, readable overview provides a gateway into cutting edge research for students and others who wish to engage with the open problem of quantum gravity.
Multiverse theories are physical theories according to which we have empirical access only to a tiny part of reality that may not be representative of the whole. The idea that we might live in a multiverse is often suggested as a response to the finding that various parameters seem fine-tuned for life. The combination of string theory and inflationary cosmology is taken to propose a specific implementation of the multiverse idea: the landscape multiverse. I review these lines of thought and outline the structure of the book. I also highlight its central theses and ideas.
In this paper, we analyze Fourier coefficients of automorphic forms on a finite cover G of an adelic split simply-laced group. Let
be a minimal or next-to-minimal automorphic representation of G. We prove that any
$\eta \in \pi $
is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro–Shalika formula for cusp forms on
. We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient, in terms of these Whittaker coefficients. A consequence of our results is the nonexistence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for G of type
with a view toward applications to scattering amplitudes in string theory.