Related papers: Aspects of Dualities

We argue that duality symmetries can be manifestly realised when theories with these symmetries are quantised using phase space quantum theory. In particular, using background fields and phase space quantum theory, we quantise the bosonic…

We review some convexity inequalities for Hermitian matrices an add one more to the list.

The differential geometric aspects of Geometric Phases are reviewed.

We investigate some connections between two different ways of defining Poincar\'e Duality, and relate them geometrically to the level curve mapping.

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…

Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…

We study certain double--series inequalities, which are motivated by weighted Hardy inequalities.

In this paper we establish two symmetric identities on sums of products of Euler polynomials.

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

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…

The symmetries of Unimodular Gravity are clarified somewhat.

A variant of the divergence theory for vacuum-condensation developed in a previous communication is analyzed from the viewpoint of a 'time' asymmetric law in vacuum. This law is found to establish a substantial distinction between…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.

Field theories with p-form gauge potentials can possess ``hidden'' symmetries leaving the field strengths invariant on-shell without being gauge symmetries on-shell. The relevance of such symmetries to supersymmetric models is discussed.…

This paper discusses the distributions of missing sums and differences.

Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.