Related papers: On the Spinor Representation
We show that gauge invariant composites in the fermionic realization of $SU(N)_1$ conformal field theory explicitly exhibit the holomorphic factorization of the corresponding WZW primaries. In the $SU(2)_1$ case we show that the holomorphic…
We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S^3 and H^3. The main…
We give a complete classification of topological field theories with reflection structure and spin-statistics in one and two spacetime dimensions. Our answers can be naturally expressed in terms of an internal fermionic symmetry group $G$…
The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus…
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 article is dedicated to q-deformed versions of spinor calculus. As a kind of review, the most relevant properties of the two-dimensional quantum plane are summarized. Additionally, the relationship between the quantum plane and…
Manifestly covariant formulation of discrete-spin, real-mass unitary representations of the Poincar\'e group is given. We begin with a field of spin-frames associated with 4-mometa p and use them to simplify the eigenvalue problem for the…
Bearing in mind the Lounesto spinor classification, we connect the expansion coefficients of well behaved fermionic quantum field, i.e., a local field within a full Lorentz covariant theory, with and only with a given subclass of Type-2…
We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This…
We present a classification of bilinear Majorana representations for spin-$S$ operators, based on the real irreducible matrix representations of SU(2). We identify two types of such representations: While the first type can be…
We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space $\Delta \textstyle{\bigotimes \bigotimes^k V}$. Here $\Delta$ is the fundamental representation of…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a…
A covariant spinor representation of $iosp(d,2/2)$ is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state…
In this paper we study weakly irreducible holonomy representations of the normal connection of a spacelike submanifold in a pseudo-Riemannian space from. We associate screen representations to weakly irreducible normal holonomy groups and…
Quaternionic and octonionic spinors are introduced and their fundamental properties (such as the space-times supporting them) are reviewed. The conditions for the existence of their associated Dirac equations are analyzed. Quaternionic and…
This is the second part of an article about q-deformed analogs of spinor calculus. The considerations refer to quantum spaces of physical interest, i.e. q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We study a holomorphic representation for spinfoams. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann coherent state transform. We derive the expression of the 4d spinfoam vertex for Euclidean and for…
We show that the attempt to introduce all of the discrete space-time transformations into the spinor representation of the Lorentz group as wholly independent transformations (as in the vectorial representation) leads to an 8-component…
We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the…