相关论文: Nowhere-zero harmonic spinors and their associated…
A set of two-parameter bi-orthogonal eigen-spinors has been constructed from a deformed pseudo- Hermitian extension of Pauli Hamiltonian and its Hermitian conjugate. The Hamiltonians thus obtained are iso-spectral to the original Pauli…
We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for…
It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator…
The Hamiltonian symmetry reduction of the geodesics system on a symmetric space of negative curvature by the maximal compact subgroup of the isometry group is investigated at an arbitrary value of the momentum map. Restricting to regular…
This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a…
We introduce and analyze a Spencer-type elliptic complex on the space of differential forms valued in symmetric powers of an adjoint bundle, $\Omega^\bullet(X)\otimes \mathrm{Sym}^\bullet(G)$. The complex is governed by a total differential…
While general relativity provides a complete geometric theory of gravity, it fails to explain the other three forces of nature, i.e., electromagnetism and weak and strong interactions. We require the quantum field theory (QFT) to explain…
The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…
Starting with a first order in derivatives self-dual model which describes a massive spin-4 mode in $D=2+1$ dimensions, we have obtained a sequence of three more new descriptions, which then give us an interconnected self-dual chain $SD(i)$…
N=1, D=4 non linear sigma models, parametrized by chiral superfields, usually describe Kaehlerian geometries, provided that Einstein frame supergravity is used. The sigma model metric is no longer Kaehler when local supersymmetry becomes…
We study Rarita-Schwinger fields on 6-dimensional compact strict nearly K\"{a}hler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita…
Let $\nabla$ be a metric connection with totally skew-symmetric torsion $\T$ on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad…
I present a construction of real or complex selfdual conformal 4-manifolds (of signature (2,2) in the real case) from a natural gauge field equation on a real or complex projective surface, the gauge group being the group of diffeomorphisms…
In this manuscript we report the flag-dipole spinors dual structure direct definition and analyze the properties behind the corresponding operator which generates such structure. This particular construction may be interesting for…
Let $\mathbf{a}$ be a quadratic form associated with a Schr\"odinger operator $L=-\nabla\cdot(A\nabla)+V$ on a domain $\Omega\subset \mathbb{R}^d$. If $\mathbf{a}$ is nonnegative on $C_0^{\infty}(\Omega)$, then either there is $W>0$ such…
We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $\Omega$-deformation. We compute them by equivariant…
We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary…
We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2 (dim=7)…
Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…
Let $(M^{n}, g)$ denote a Riemannian spin manifold of dimension $n$ with Dirac operator $D$ induced from the Levi-Cevita connection acing on the spinor bundle, $S$ ($D$ is also called the Atiyah-Singer Operator). Let $c: Cl(TM^{n})…