Related papers: Chiral Splitting at Work
Two different families of abelian chiral gauge theories on the torus are investigated: the aim is to test the consistency of two-dimensional anomalous gauge theories in the presence of global degrees of freedom for the gauge field. An…
Generalizations of the Korteweg-de Vries equation are considered, and some explicit solutions are presented. There are situations where solutions engender the interesting property of being chiral, that is, of having velocity determined in…
In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…
We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.
This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…
A generic theory of a single real scalar field is considered, and a simple method is presented for obtaining a class of solutions to the equation of motion. These solutions are obtained from a simpler equation of motion that is generated by…
This paper is a continuation of \cite{Lu1}. In Part I, applying the new splitting theorems developed therein we generalize previous some results on computations of critical groups and some critical point theorems to weaker versions. In Part…
We derive the chiral kinetic theory in a non-Abelian gauge field using a self-consistent semiclassical expansion. Within this new expansion scheme, we disentangle the Wigner equations up to second order and demonstrate that they do not…
We use the methods of group theory to reduce the equations of motion of two spin systems in (2+1) dimensions to sets of coupled ordinary differential equations. We present solutions of some classes of these sets and discuss their physical…
The chiral phase transition at a certain critical temperature is a restoration mechanism of the chiral symmetry, broken by the nonzero mass of quarks and mesons. The transition can be studied through several models, among which are the…
General features of microscopic and macroscopic chiral structures can be discussed under the standard of orthogonal group theory. Configuration space of systems, not physical space, is taken into account. This change of perspective allows…
We study linear actions of finite groups in small dimensions, up to equivariant birationality.
A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.
In this letter we uncover a new facet of chiral symmetry and the implications of its breaking in some theories. By generalizing the concept of chiral symmetry, tensor theories naturally arise. This novel approach adds to the known uses of…
Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…
We show that a chiral sector of a symplectic group manifold possesses a symmetry similar to, but somewhat weaker than the Lie--Poisson one.
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
In these lectures notes I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
Expanding upon earlier work of Pouliot and Strassler, we construct chiral magnetic duals to nonchiral supersymmetric electric theories based upon SO(7), SO(8) and SO(9) gauge groups with various numbers of vector and spinor matter…