Related papers: Pinwheels as Lagrangian barriers
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are…
The sticky particle system is a system of partial differential equations which assert the conservation of mass and momentum of a collection of particles that interact only via inelastic collisions. These equations arise in Zel'dovich's…
The Bargman-Wigner equations are generalized to include chiral symmetry based on the irreps of the Poincar\'{e} group, and the chirial Bargmann-Wigner equations are derived for spin-1 massive fields. By specifying the chiral basis, the…
We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted…
I discuss recent development on the description of heavy-quark (such as charmed and bottom) baryons as one or more heavy mesons "wrapped" by a skyrmion. Amazingly enough, such a description naturally arises when light-quark chiral symmetry…
The equation determining whether a projective structure admits a connection in its given projective class that has skew-symmetric Ricci tensor is an overdetermined system of semi-linear partial differential equations which we call the…
Let $S$ be a closed, orientable surface of genus $g\geq 2$. We consider Delaunay circle patterns on $S$ equipped with a complex projective structure. We prove that the space of complex projective structures on $S$ equipped with a Delaunay…
Chiral perturbation lagrangian in the framework of non-commutative geometry is considered in full detail. It is found that the explicit symmetry breaking terms appear and some relations between the coupling constants of the theory come out…
We compute the p-widths, $\{\omega_p\}$, for the real projective plane with the standard metric.
We define genus zero open Gromov-Witten invariants with boundary and interior constraints for a Lagrangian submanifold of arbitrary even dimension. The definition relies on constructing a canonical family of bounding cochains that satisfy…
We find an upper bound for the Gromov width of coadjoint orbits of compact Lie groups with respect to the Kirillov Kostant Souriau form by computing certain Gromov Witten invariants, the approach presented here is closely related to the one…
We study Gromov-Witten invariants on the blow-up of P^n at a point, which is probably the simplest example of a variety whose moduli spaces of stable maps do not have the expected dimension. It is shown that many of these invariants can be…
In this paper, we employ the loop group method to study the construction of minimal Lagrangian surfaces in the complex projective plane for which the surface is contractible. We present several new classes of minimal Lagrangian surfaces in…
An extension of the Standard Model is proposed, where the Higgs field is valued in the complex projective plane ${\mathbb{CP}}^2$, rather than ${\mathbb{C}}^2$. Its geometry is consistent with $U(2) \simeq (SU(2) \times U(1))/ \mathbb{Z}_2$…
Using obstruction bundles, composition law and the localization formula, we compute certain 3-point genus-0 Gromov-Witten invariants of the Hilbert scheme of 3-points on the complex projective plane. Our results partially verify Ruan's…
The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite…
We obtain plane fronted gravitational waves (PFGWs) in arbitrary dimension in Lovelock gravity, to any order in the Riemann tensor. We exhibit pure gravity as well as Lovelock-Yang-Mills PFGWs. Lovelock-Maxwell and $pp$ waves arise as…
A model is proposed in which quarks, leptons and perhaps gauge bosons are composites of magnetically charged rishons T(q=1/3) and V(q=0) with magnetic charges g=(1,2,-3)g0. Structural formulas of composite particles and their interactions…
The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general {\it{less}} than the number of independent primary…
The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete…