Related papers: The Fourier-Mukai Transform in String Theory
A polemical article evaluating string theory from the point of view of a quantum field theorist working in a mathematics department. Comments to the author are encouraged.
Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.
This article surveys some of the highlights in the development of string theory through the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string…
This is a survey of M-regularity for coherent sheaves on abelian varieties and its applications, based on lectures given by the second author at the Seattle conference, in August 2005, and at the Luminy GAC workshop in October 2005. Section…
We consider, in a string theory framework, physical processes of phenomenological interest in models with a low string scale. The amplitudes we study involve tree-level virtual gravitational exchange, divergent in a field-theoretical…
We argue that the light particles in string theory obey an effective quantum mechanics modified by the inclusion of a quantum-gravitational friction term, induced by unavoidable couplings to unobserved massive string states in the…
We give an overview of moduli stabilization in compactifications of string theory. We summarize current methods for construction and analysis of vacua with stabilized moduli, and we describe applications to cosmology and particle physics.…
We study how canonical transfomations in first quantized string theory can be understood as gauge transformations in string field theory. We establish this fact by working out some examples. As a by product, we could identify some of the…
In the present paper, we deal with Fourier-transformation of Frobenius-Euler polynomials. We shall give its applications by using infinite series. Our applications possess interesting properties which we state in this paper.
We provide an overview of recent work which aims to understand patterns of vanishing Yukawa couplings that arise in models of particle physics derived from string theory. These patterns are seemingly linked to a plethora of different…
The analytical solving dynamic problems of elasticity theory for piecewise homogeneous half-space is found. The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The…
This is an invited contribution to the Special Issue of "Foundations of Physics" titled "Forty Years Of String Theory: Reflecting On the Foundations". I have been asked to assess string theory as an outsider, and to compare it with the…
This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
Mathematical diffraction theory is concerned with the analysis of the diffraction measure of a translation bounded complex measure $\omega$. It emerges as the Fourier transform of the autocorrelation measure of $\omega$. The mathematically…
The goal of identifying the Standard Model of particle physics and its extensions within string theory has been one of the principal driving forces in string phenomenology. Recently, the incorporation of artificial intelligence in string…
This paper is an introductory text to the theory of $q$-deformed Fourier transforms, as first discussed by Rogov and Olshanetsky. We derive the well-known results in detail, present them in a format that suits our needs, and include some…
This is a brief review of the present status, of some recent developments and of the open challenges in string/M theory.
We give a condition for an exact functor between triangulated categories to be an equivalence. Applications to Fourier-Mukai transforms are discussed. In particular, we obtain a large number of such transforms for K3 surfaces.
This article contains a summary of the author's contributions, one in collaboration with K. Bardakci, to dual models and string theory prior to the mid-seventies. Other workers' contributions, during and subsequent to this period, are…