Related papers: Relative integral spinor norm groups over dyadic l…
We consider two spacelike separated Dirac particles and construct five invariants under the spinor representations of the local proper orthochronous Lorentz groups. All of the constructed Lorentz invariants are identically zero for product…
The studies of Ram\'irez, Hino-Ram\'irez, and Ariyoshi-Hino showed that an integrated version of Varadhan's asymptotics holds for Markovian semigroups associated with arbitrary strong local symmetric Dirichlet forms. In this paper, we…
The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain…
We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct a differential operator of infinite order D(C)…
We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor…
(2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of…
Dirac field equations are studied for spinor fields without any external interaction and when they are considered on a background having a tensorial connection with a specific non-vanishing structure some solution can be found in polar form…
We consider Dirac-type operators on manifolds with boundary, and set out to determine all local smooth boundary conditions that give rise to (strongly) regular self-adjoint operators. By combining the general theory of boundary value…
It was observed recently that relations between matrix elements of certain operators in the ${\rm SL}(2,\mathbb R)$ spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with ${\rm…
A general set of rules is given how to convert a local kappa-symmetry of a brane action and space-time supersymmetry into the global supersymmetry of the worldvolume. A Killing spinor adapted gauge for quantization of kappa-symmetry is…
Within the scope of a static cylindrically symmetric space-time we study the behavior of a nonlinear spinor field that depends on time and radial coordinates. It is found that the presence of nontrivial non-diagonal components of the…
When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d>1, one obtains a finite group G^d which is often the automorphism group of an abstract regular polytope. Building…
Fix $n\ge3$. For the pure field $K_a=\mathbb Q(\theta)$ with $\theta^n=a$, where $a\neq \pm 1$ is $n$th-power-free, we encode an integral basis in the fixed coordinate $\{1,\theta,\dots,\theta^{n-1}\}$ by its \emph{shape}. We prove a sharp…
In this paper, we formulate and prove a local intertwining relation for metaplectic groups assuming the local intertwining relation for non-quasi-split odd special orthogonal groups.
This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double…
We prove various results about the Local Converse Problem for split reductive groups $G$ over a non-archimedean local field~$F$ of characteristic $0$ and residual characteristic $p$. In particular, we prove that when $G$ is a symplectic or…
Motivated by the challenge of defining twisted quantum field theories in the context of higher categories, we develop a general framework for lax and oplax transformations and their higher analogs between strong $(\infty, n)$-functors. We…
We define the local fundamental group scheme, defined by the F-trivial vector bundles, and give necessary and sufficient conditions for it to base change.
A density dependent relativistic mean-field model is determined to reproduce the components of the nucleon self-energy at low densities. This model is used to investigate spinodal instabilities in isospin asymmetric nuclear matter at finite…
The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given…