Related papers: On classical string configurations
The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of…
In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental…
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
Some connections between classical and nonclassical symmetries of a partial differential equation (PDE) are given in terms of determining equations of the two symmetries. These connections provide additional information for determining…
We give a mathematical perspective on string compactifications. Submitted as a chapter in the Encyclopedia of Mathematical Physics.
Canonical framings and stable framings for the tangent bundle of a spin 3-manifold are introduced, and illustrated by a number of familiar examples. Methods for constructing canonical framings, and for comparing them with other naturally…
We estimate the proportion of several classes of elements in finite classical groups which are readily recognised algorithmically, and for which some power has a large fixed point subspace and acts irreducibly on a complement of it. The…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
On objects of a triangulated category with a stability condition, we construct a topology.
Let $\mathscr{C}$ be a classical group defined over a finite field. We present comprehensive theoretical solutions to the following closely related problems: 1) List a representative for each conjugacy class of $\mathscr{C}$. 2) Given $x…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We discuss a formal system of mathematics. We use it to construct the natural numbers.
Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable…
We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical…
We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…
We review the current status of the singularity problem in string theory for non-experts. After the problem is discussed from the point of view of supergravity, we discuss classic examples and recent examples of singularity resolution in…
String geometry theory is a candidate of the non-perturbative formulation of string theory. In order to determine the string vacuum, we need to clarify how superstring backgrounds are described in string geometry theory. In this paper, we…
We review some aspects of moduli in string theory. We argue that one should focus on {\it approximate moduli spaces}, and that there is evidence that such spaces exist non-perturbatively. We ask what it would mean for string theory to…
Although the Standard Model of particle physics is usually formulated in terms of fields, it can be equivalently formulated in terms of particles and strings. In this picture particles and open strings are always coupled. This offers an…