相关论文: Four-Spinor Reference Sheets
In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components and the spin group is…
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…
The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
Recently Z.W.Sun found over hundred conjectured formulas for 1/pi. Many of them were proved by H.H.Chan, J.Wan andW.Zudilin (see [3], [8] in the paper). Here we show that several other formulas in [6] are simple transformations of known…
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright. 3 new formulas are explained.
After commenting on the state of contemporary hadronic physics and spectroscopy, I highlight four areas where the action is: searching for the relevant degrees of freedom, mesons with beauty and charm, chiral symmetry and the D_{sJ} levels,…
A method is presented, and used, for determining any heat-kernel coefficient for the form-valued Laplacian on the $D$-ball as an explicit function of dimension and form order. The calculation is offerred as a particular application of a…
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…
The implementation of tensor sources in Chiral Lagrangians allows the computation of Green functions and form factors involving tensor currents, that is, quark bilinears of the form \bar{q}_i\sigma^{\mu\nu}q_j. Whereas only four new terms…
This papers aims at revisiting Minkowski space-time with a modified outlook and making it more consistent (III.8). The paper scrutinizes the special case of relativistic hypothesis (STR). The paper tries to solve the problems faced by…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
Under certain conditions, we give an estimate from above on the number of differential equations of order $r+1$ with prescribed regular singular points, prescribed exponents at singular points, and having a quasi-polynomial flag of…
In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.
We establish a necessary condition for pseudoprimality and a sufficient condition for primality of Fermat numbers, based on a congruence involving the exponent $(F_n-1)/4$. Moreover, in connection with P\'epin's primality test, we obtain a…
In this paper we prove the entireness of the Spinor L function of certain generic representations of the group GSp(4) over a totally real field.
After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as…