Related papers: Tying up instantons with anti-instantons
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
This paper is a review of the works devoted to understanding and reinterpretation of the theory of quantum integrable models solvable by Bethe ansatz in terms of the theory of purely classical soliton equations. Remarkably, studying…
The validity of dilute gas approximation is explored by making use of the large-sized instanton in quantum mechanical model. It is shown that the Euclidean probability amplitude derived through a dilute gas approximation not only cannot…
The aim of this memoir for "Habilitation \`a Diriger des Recherches" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by…
In this paper we study the global existence and completeness of classical solutions of gravity coupled a scalar field system called Einstein-Klein-Gordon system in higher dimensions. We introduce a new ansatz function to reduce the problem…
Naively, a resolution of the black hole information paradox appears to involve microscopic details of a theory of quantum gravity. However, recent work has argued that a unitary Page curve can be recovered by including novel replica…
We discuss simple vacuum solutions to the Einstein Equations in five dimensional space-times compactified in two different ways. In such spaces, one black hole phase and more then one black string phase may exist. Several old metrics are…
We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented…
We discuss an interrelation between quantum integrable models and classical soliton equations with discretized time. It appeared that spectral characteristics of quantum integrable systems may be obtained from entirely classical set up.…
The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle…
We present and discuss BPS instanton solutions that appear in type II string theory compactifications on Calabi-Yau threefolds. From an effective action point of view these arise as finite action solutions of the Euclidean equations of…
The mechanism of irreversible dynamics in the systems with mixing is analyzed. The procedure of splitting of system on equilibrium subsystems and studying of dynamics of one of them under condition of its interaction with other subsystems…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used.…
Usual gauge fixing procedures in classical general relativity rely on the existence of solutions of a second order wave equation. We propose to use the equation to relate asymptotic symmetries at infinity to asymptotic symmetries of a black…
We propose a simple method that allows, in one dimension, to solve exactly a wide class of classical stochastic many-body systems far from equilibrium. For the sake of illustration and without loss of generality, we focus on a model that…
An often fruitful route to study quantum gravity is the determination and study of quantum mechanical models--that is, models with finite degrees of freedom--that capture the dynamics of a black hole's microstates. An example of such a…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
Collective spin systems -- spin ensembles coupled to a common reservoir and effectively described by a single macrospin -- play an important role in both atomic and solid-state physics. Their intrinsic nonlinearity gives rise to multiple…
Various constructions of the affine Lie algebra action on the homology group of moduli spaces of instantons on 4-manifolds are discussed. The analogy between the local-global principle and the role of mass is also explained. The detailed…