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In this report, fundamental educational concepts of linear and non-linear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic…
Large gauge symmetries in Minkowski spacetime are often studied in two distinct regimes: either at asymptotic (past or future) times or at spatial infinity. By working in harmonic gauge, we provide a unified description of large gauge…
We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory by including one massless flavor. We write the equations of motion at leading order in the coupling constant and we solve them exactly in the non(anti)commutativity…
We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $\mathbb R\times \mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov…
In this letter, we study the instanton moduli space of the eight-dimensional solutions of the self-duality equation $F\wedge F= \ast F\wedge F$. Using the known ADHM-construction of such instantons, we compute the dimension of the space of…
We prove an energy identity for anti-self-dual connections on the product C\times\Sigma of the complex plane and a Riemann surface. The energy is a multiple of a basic constant that is determined from the values of a corresponding…
It is shown that periodic instanton solutions may have bifurcations which qualitatively change the behaviour of the finite temperature transition rate. These bifurcations are studied numerically in a quantum mechanical model and in the…
A characterization of instanton contributions to gauge field theory is given. The dynamics of instantons with the gluon field is given in terms of 'classical' instanton contributions, i.e. on the same footing as tree amplitudes in field…
We study how instantons arise in the low energy effective theory of the SU(2) Yang-Mills theory in the context of the non-linear sigma model recently propose by Faddeev and Niemi. We find a simple relation between the instanton number $\nu$…
We find classically stable solitons (instantons) in odd (even) dimensional scalar noncommutative field theories whose scalar potential, $V(\ph)$, has at least two minima. These solutions are bubbles of the false vacuum whose size is set by…
On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…
We discuss non-perturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the $U(2)\times U(2)$ model, explicitly, and computing the Euclidean action. The Wick-rotated Lagrangian…
We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is the first in a series…
We study $SU(2)$ lattice gauge theory in small volumes and with twist $\vec{m}=(1,1,1)$. We investigate the presence of the periodic instantons of $Q=\frac{1}{2}$ and determine their free energy and their contribution to the splitting of…
We study the non-perturbative effects induced by stringy instantons on N=2 SU}(N) gauge theories in four dimensions, realized on fractional D3 branes in a C^3/Z_3 orientifold. The stringy instantons, corresponding to D(-1) branes that…
We construct a large class of periodic instantons. Conjecturally we produce all periodic instantons. This confirms a conjecture of Garland and Murray that relates periodic instantons to orbits of the loop group acting on an extension of its…
We describe the modern formalism, ideas and applications of the instanton calculus for gauge theories with, and without, supersymmetry. Particular emphasis is put on developing a formalism that can deal with any number of instantons. This…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
We consider topology changing processes in SU(2)--Higgs theory. In the Standard Model of particle physics they are accompanied by baryon--and lepton--number non--conservation. At fixed energy and multiplicity of initial state, these…
We study stationary rotating topological solitons in (2+1)-dimensional ${\mathbb C}P^2$ non-linear sigma model with a stabilizing potential term. We find families of $U(1)\times U(1)$ symmetric solutions with topological degrees larger than…