Related papers: Spinor Parallel Propagator and Green's Function in…
We prove estimates for the Green's function of the discrete bilaplacian in squares and cubes in two and three dimensions which are optimal except possibly near the corners of the square and the edges and corners of the cube. The main idea…
We consider the Sp(2n) invariant formulation of higher spin fields on flat and curved backgrounds of constant curvature.In this formulation an infinite number of higher spin fields are packed into single scalar and spinor master fields…
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar $S$ and a vector $V$ quadratic potentials in the radial coordinate, as well as a tensor potential $U$ linear in $r$.…
A variant for the superspin one-half massive superparticle in $ 4D $, $ \mathcal{N}=1 $, based on Dirac superfields, is offered. As opposed to the current known models that use spinor chiral superfields, the propagating fields of the…
In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley…
We propose a description of %manifestly supersymmetric continuous spin representations in $4D,\mathcal{N}=1$ Minkowski superspace at the level of equations of motions. The usual continuous spin wave function is promoted to a chiral or a…
We consider a free massive spinor field in Euclidean Anti-de Sitter space. The usual Dirac action in bulk is supplemented by a certain boundary term. The boundary conditions of the field are parametrized by a spinor on the boundary, subject…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
We show a nice symmetric/antisymmetric relation between the four vector Lorentz transformation and the Dirac spinor one in the Majorana representation. From the spinor one, we exhibit the antisymmetric pending of the symmetric Minkowski…
Penrose's spinor calculus of 4-dimensional Lorentzian geometry is extended to the case of 5-dimensional Lorentzian geometry. Such fruitful ideas in Penrose's spinor calculus as the spin covariant derivative, the curvature spinors or the…
Possible quantum mechanical corollaries of changing the vectorial geometrical model of the physical space, extending it twice, in order to describe its spinor structure (in other terminology and emphasis it is known as the Hopf's bundle)…
We give new simple direct proofs in all spacetimes for the existence of asymmetric $(n,m+1)$-spinor potentials for completely symmetric $(n+1,m)$-spinors and for the existence of symmetric $(n,1)$-spinor potentials for symmetric…
This paper constructs a family of conformally invariant differential operators acting on spinor densities with leading part a power of the Dirac operator. The construction applies for all powers in odd dimensions, and only for finitely many…
Some new expressions are found, concerning the effective action as a regularized path-integral for Dirac's spinors in {\it 3+1} dimensions, in the presence of general uniform (i.e., constant and homogeneous) electric and magnetic fields.…
We present different non-perturbative calculations within the context of Migdal's representation for the propagator and effective action of quantum particles. We first calculate the exact propagators and effective actions for Dirac, scalar…
Several estimates for singular integrals, maximal functions and the spherical summation operator are given in the spaces $L^p_{\text{rad}}L^2_{\text{ang}}(\mathbb{R}^n)$, $n\geq 2$.
The symmetries of a scalar field theory in multifractional spacetimes are analyzed. The free theory realizes the Poincar\'e algebra, and the associated symmetries are modifications of ordinary translations and Lorentz transformations. In…
We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges…
We present a new description of the spectrum of the (spin-) Dirac operator $D$ on lens spaces. Viewing a spin lens space $L$ as a locally symmetric space $\Gamma\backslash \operatorname{Spin}(2m)/\operatorname{Spin}(2m-1)$ and exploiting…
Propagators approximated by a meromorphic functions with complex conjugated poles are widely used to model infrared behavior of QCD Green's functions. In this paper, analytical solutions for two point correlator made out of functions with…