Related papers: Singular spinors and their connection
In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes…
When a millimetric body is placed atop a vibrating liquid bath, the relative motion between the object and interface generates outward propagating waves with an associated momentum flux. Prior work has shown that isolated chiral objects,…
The plate trick or belt trick is a striking physical demonstration of properties of the double cover of the three-dimensional rotation group by the sphere of unit quaternions or spinors. The two ends of a flexible object are continuously…
One of the most important mathematical tools necessary for Quantum Field Theory calculations is the field propagator. Applications are always done in terms of plane waves and although this has furnished many magnificent results, one may…
Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.
The present study is the first such attempt to examine rigorously and comprehensively the spectral properties of a three-dimensional ultracold atom when both the spin-orbit interaction and the Zeeman field are taken into account. The model…
We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems…
It has been demonstrated, in a number of special situations, that the spin coefficients of a canonical spinor dyad can be used to define a Lanczos potential of the Weyl curvature spinor. In this paper we explore some of these potentials and…
We show how the space spinor formalism for 2-component spinors can be used to construct estimates for spinor fields satisfying first order equations. We discuss the connection of the approach presented in this article with other strategies…
Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum…
Gravitational waves provide us with a new window into our Universe, and have already been used to place strong constrains on the existence of light scalar fields, which are a common feature in many alternative theories of gravity. However,…
We construct the Wightman function for symmetric traceless tensors and Dirac fermions in dS$_{d+1}$ in a coordinate and index free formalism using a $d+2$ dimensional ambient space. We expand the embedding space formalism to cover spinor…
Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.
Relying on the mathematical analogy of the pure states of a two-qubit system with four-component Dirac spinors, we provide an alternative consideration of quantum entanglement using the mathematical formulation of Cartan's pure spinors. A…
We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into…
As a means of examining the section condition and its possible solutions and relaxations, we perform twistor transforms related to versions of exceptional field theory with Minkowski signature. The spinor parametrisation of the momenta…
A massless spinor field is quantized in the background of a singular static magnetic vortex in 2+1-dimensional space-time. The method of self-adjoint extensions is employed to define the most general set of physically acceptable boundary…
In a series of recent papers, we have introduced an object that was constructed on the connection but which was proven to be a tensor: this object, thus called tensorial connection, has been defined and some of its properties have been…