Related papers: Notes on correlation functions in (0,2) theories
Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…
Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work…
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
We establish the sharp estimate <<_d N^{2/d} for the number of rational points of height at most N on an irreducible projective curve of degree d. We deduce this from a result for general hypersurfaces that is sensitive to the coefficients…
In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the…
Compton scattering offers in principle an intriguing new window on nucleon structure. Existing experiments and future programs are discussed and the state of theoretical understanding of such measurements is explored.
The perturbative contribution to the correlator of two HQET heavy-light currents expanded in light-quark masses up to quadratic terms is calculated up to 4 loops. The leading large-$\beta_0$ limit is also considered, so that terms with the…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
This is a survey of the rationality problem in invariant theory. It also contains some new results, in particular in Chapter 2 on moduli spaces of plane curves with a theta-characteristic, and a detailed account of the relation of the…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
We enumerate the connected graphs that contain a linear number of edges with respect to the number of vertices. So far, only the first term of the asymptotics was known. Using analytic combinatorics, i.e. generating function manipulations,…
We give a survey of recent joint work with E. M. Stein (Princeton University) concerning the application of suitable versions of the T(1)-theorem technique to the study of orthogonal projections onto the Hardy and Bergman spaces of…
We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge…
After a review of some topics concerning the phenomenological applications of perturbative string theory, I discuss to what extent all of it is affected by the recent developements in string dualities.
In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input…
In a series of papers we classify the possible torsion structures of rational elliptic curves base-extended to number fields of a fixed degree. In this paper we turn our attention to the question of how the torsion of an elliptic curve with…
We have dealt with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and showed some evidence to indicate the hypothesis. We briefly…
We summarize recent results connecting multiloop Feynman diagram calculations to different parts of mathematics, with special attention given to the Hopf algebra structure of renormalization.