Related papers: Strichartz's conjecture for the spinor bundle over…
In this paper, following Sullivan, Kusner, and Schmitt, we study conformal immersions of Riemann surfaces into the three-dimensional Euclidean space. Regarding such immersions as special bundle maps from the tangent bundle of the surface to…
The canonical quantization of a field theory for spin-$1/2$ massive bosons that satisfy the Klein-Gordon equation is presented. The breakdown of the usual spin-statistics connection is due to the redefinition of the dual field, rendering…
Let $X= G/K$ symmetric space of non compact type, where $G$ is a rank-one connected semisimple Lie group with finite center. We shall look at the transform $ P_\lambda f(x) = f \ast \varphi_\lambda(x)$, where, $\lambda \in \mathbb C$ and…
Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2) group of space-time symmetries as fundamental, one can consistently gauge one SU(2) factor to get a chiral spin connection formulation of general relativity, the other…
In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly…
We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat…
This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global well-posedness results for…
In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the…
This paper studies spaces of generalized theta functions for odd orthogonal bundles with nontrivial Stiefel-Whitney class and the associated space of twisted spin bundles. In particular, we prove a Verlinde type formula and a dimension…
We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten bundle, we show that the moduli space is a…
On a compact Riemann surface $\Sigma$ of genus $g>1$, equipped with a complex vector bundle $E$ of rank $2$ and degree zero let $M_H$ be the moduli space of Higgs bundles. $M_H$ admits a $\mathbb C^{\star}$-action and to each stable…
The moduli space of $G$-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links…
Relativistic invariant projectors of states in a complex bispinor space on a complex spinor space are constructed. An expression for sections of bundle with connection on group SU(4) in an explicit form has been obtained. Within the…
We investigate the spin-statistics connection in arbitrary dimensions for hermitian spinor or tensor quantum fields with a rotationally invariant bilinear Lagrangian density. We use essentially the same simple method as for space dimension…
We prove that for a wide class of quantum spin systems with isotropic Heisenberg coupling the energy eigenvalues which belong to a total spin quantum number S have upper and lower bounds depending at most quadratically on S. The only…
We describe a sufficient condition for actions constructed in projective superspace to possess an SU(2) R-symmetry. We check directly that this condition implies that the corresponding hyperkahler varieties, constructed by means of the…
Let $P_{\lambda\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\lambda$ of the standard symplex $\Sigma_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold…
Suppose that $\Sigma=\partial\Omega$ is the $n$-dimensional boundary, with positive (inward) mean curvature $H$, of a connected compact $(n+1)$-dimensional Riemannian spin manifold $(\Omega^{n+1},g)$ whose scalar curvature $R\ge…
By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…