Related papers: Chiral Splitting at Work
The equations of motion that must be satisfied by fields that constitute realizations of the Poincare group algebra, for integral spin, and mass m, are obtained. For the case of massive spin 2 these equations are satisfied by the selfdual,…
The Dirac equation with chiral symmetry is derived using the irreducible representations of the Poincar\'{e} group, the Lagrangian formalism, and a novel method of projection operators that takes as its starting point the minimal assumption…
We show that the chiral partition function of two-dimensional Yang-Mills theory on the sphere can be mapped to the partition function of the homogeneous six-vertex model with domain wall boundary conditions in the ferroelectric phase. A…
Results of our previous note, "Gerbes of chiral differential operators" (Math. Res. Letters, 7(2000), 55-66), are discussed in the algebraic category.
The chiral phase transition at finite temperature is investigated in the linear sigma model, which is regarded as a low energy effective theory of QCD with three momentum cutoff, in the variational method with the Gaussian approximation in…
The consistent chiral kinetic theory accurate to the second order in electromagnetic and pseudoelectromagnetic fields is derived for a relativistic matter with two Weyl fermions. By making use of such a framework, the properties of…
In two-dimensional Euclidean plane, existence of second-order integrals of motion is investigated for integrable Hamiltonian systems involving spin (\emph{e.g.,} those systems describing interaction between two particles with spin 0 and…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
Incorporating its most relevant global symmetry, chiral effective models are aimed at investigating, in a simplified framework, important aspects of the yet unsolved QCD. We review some recent results obtained in these models on the…
We present a formulation for the construction of first order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant evolution parameter; one obtains a consistent…
It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
Generalizing Karoubi's multiplicative K-theory and multiplicative cohomology groups for smooth manifolds we define secondary theories and characteristic classes for smooth etale groupoids. As special cases we obtain versions of the groups…
We study left-invariant Killing forms of arbitrary degree on simply connected $2-$step nilpotent Lie groups endowed with left-invariant Riemannian metrics, and classify them when the center of the group is at most two-dimensional.
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general…
We describe how chiral matter charged under SU(N) and SO(2N) gauge groups arises from codimension seven singularities in compactifications of M-theory on manifolds with G(2) holonomy. The geometry of these spaces is that of a cone over a…
The talk contains a short introduction to mesonic Chiral Perturbation Theory (ChPT). In addition four disparate areas where some progress has been made in recent years are discussed. These are the last fit of the order $p^4$…
This thesis is about the study of Lie groupoids endowed with a compatible (multiplicative) differential 1-form. The motivation and scope of the present work is to study the geometry of PDEs using the formalism of Lie groupoids and…