Related papers: World Spinors Revisited
In our previous papers we repeatedly emphasized the special role in Quaternionic Analysis of the conformal group SU(2,2) and other real forms of its complexification SL(4,C). In particular, the natural product map of the left and right…
Linear spinor fields are a generalization of the Dirac field that have transparent cluster decomposability properties needed for classical correspondence of relativistic quantum systems. The algebra of these fields directly incorporate…
Spinor fields are considered in a generally covariant environment where they can be written in the polar form. The polar form is the one in which spinorial fields are expressed as a module times the exponential of a complex pseudo-phase,…
We present new parametrizations of elements of spinor and orthogonal groups of dimension 4 using Grassmann exterior algebra. Theory of spinor groups is an important tool in theoretical and mathematical physics namely in the Dirac equation…
We provide a recipe for building explicit representations of the real Clifford algebras once an explicit family is given in dimensions $1$ through $4$. We further give an explicit construction of spin coordinate systems for a given real…
We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor…
Those fundamental physical properties, such as phase transitions, Weyl fermions, and spin excitation, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has come…
We study the solutions to the Klein-Gordon equation for the massive scalar field in the universal covering space of two-dimensional anti-de Sitter space. For certain values of the mass parameter, we impose a suitable set of boundary…
We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We…
Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the…
We present the dictionary between the one-particle Hilbert spaces of totally symmetric tensor-spinor fields of spin $s={3}/{2}, {5}/{2}$ with any mass parameter on $D$-dimensional ($D \geq 3$) de Sitter space ($dS_{D}$) and Unitary…
Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study…
We relate the Lounesto classification of regular and singular spinors to the orbits of the $Spin(3,1)$ group in the space of Dirac spinors. We find that regular spinors are associated with the principal orbits of the spin group while…
We determine which orthogonal representations V of GL(n,q) lift to the double cover Pin(V ) of the orthogonal group O(V ). We cover all n and prime powers q, except for (n; q) =(3,4).
A systematic presentation of spinors in various dimensions is given.
We show explicitly that a free Lagrangian expressed in terms of scalar, spinor, vector and Rarita-Schwinger (RS) fields is invariant under linear supersymmetry transformations generated by a global spinor-vector parameter. A (generalized)…
We study the conformal window of gauge theories containing fermionic matter fields, where the gauge group is any of the exceptional groups with the fermions transforming according to the fundamental and adjoint representations and the…
Chiral spinors and self dual tensors of the Lie superalgebra $\mathfrak{osp}(m|n)$ are infinite dimensional representations belonging to the class of representations with Dynkin labels $[0,\ldots,0,p]$. We have shown that the superdimension…
Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized ${\cal N}=4$ SYM theory, are considered in some detail. Duality between…
We present a twistor description for null two-surfaces (null strings) in 4D Minkowski space-time. The Lagrangian density for a variational principle is taken as a surface-forming null bivector. The proposed formulation is reparametrization…