Related papers: Aspects of $\sigma$ Models
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
We derive gradient and energy estimates for critical points of the full supersymmetric sigma model and discuss several applications.
Matrix models have wide applications in nuclear theory, condensed matter theory and quantum field theory. I discuss supersymmetric extensions of matrix models and their applications to branched polymers, the meander problem, and…
A brief review of some selected topics in p-adic mathematical physics is presented.
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We review some theoretical and experimental issues in unparticle physics, focusing mainly on collider signatures.
Quality of approximations is an important issue in modelling nuclear matter. It is shown that the Pad{\' e} approximation provides a useful tool for describing the symmetry energy in highly asymmetric systems. The focus is on the symmetry…
Some personal reminiscences are followed by a brief illustration of how effective field theories are used in condensed matter physics. Examples include Landau's Fermi liquid, sigma models with topological terms, Dirac fermions and the Gross…
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
Studies on the dynamical properties of the $\sigma$ meson are reviewed and discussed. The important role of fundamental principles such as analyticity, unitarity and crossing symmetry played in the studies are stressed.
Symmetry distills the simplicity of natural laws from the complexity of physical phenomena. The symmetry principle is of vital importance in various aspects of modern physics, including analyzing atomic spectra, determining fundamental…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
In connection with the contribution "Quantum Condensates in Nuclear Matter" some problems are given to become more familiar with the techniques of many-particle physics.
In these Lectures I review possible constraints on particle physics models, obtained by means of combining the results of collider measurements with astrophysical data. I emphasize the theoretical-model dependence of these results. I…
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
This paper reviews the new highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The paper highlights several relevant examples of recent advances in the field and provides a roadmap…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…
In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.