On the fundamental solution for higher spin Dirac operators

被引：5

作者：

Eelbode, D. ^{[1
]}

Raeymaekers, T. ^{[2
]}

Van Lancker, P. ^{[2
]}

机构：

[1] Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp, Belgium

[2] Univ Ghent, Dept Math Anal, Clifford Res Grp, B-9000 Ghent, Belgium

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 405卷 / 02期

关键词：

Clifford analysis; Fundamental solution; Higher spin; Dirac operator; The Stokes theorem; The Cauchy integral formula;

D O I：

10.1016/j.jmaa.2013.04.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we will determine the fundamental solution for the higher spin Dirac operator Q(lambda), which is a generalisation of the classical Rarita-Schwinger operator to more complicated irreducible (half-integer) representations for the spin group in in dimensions. This will allow us to generalise the Stokes theorem, the Cauchy-Pompeiu theorem and the Cauchy integral formula, which lie at the very heart of the function theory behind arbitrary elliptic higher spin operators. (c) 2013 Elsevier Inc. All rights reserved.

引用

页码：555 / 564

页数：10

共 50 条

[11] On the Dirac and Spin-Dirac Operators
Notte-Cuello, E. A.
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2010, 20 (3-4) : 765 - 780
[12] Polynomial Invariants for General Higher Spin Dirac Operators: A Toy Model
Eelbode, David
Smid, Dalibor
[J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, 2010, 1281 : 1504 - +
[13] On weighted dirac operators and their fundamental solutions
Vanegas, Judith
Vargas, Franklin
[J]. QUAESTIONES MATHEMATICAE, 2020, 43 (03) : 383 - 393
[14] Fundamental operators in Dirac quantum mechanics
Silenko, Alexander J.
Zhang, Pengming
Zou, Liping
[J]. XVIII WORKSHOP ON HIGH ENERGY SPIN PHYSICS, DSPIN-2019, 2020, 1435
[15] Fundamental Solution for Natural Powers of the Fractional Laplace and Dirac Operators in the Riemann–Liouville Sense
A. Di Teodoro
M. Ferreira
N. Vieira
[J]. Advances in Applied Clifford Algebras, 2020, 30
[16] Estimates of the Fundamental Solution for Higher Order Schrodinger Type Operators and Their Applications
Sugano, Satoko
[J]. JOURNAL OF FUNCTION SPACES AND APPLICATIONS, 2013,
[17] On finite difference Dirac operators and their fundamental solutions
K. Gürlebeck
A. Hommel
[J]. Advances in Applied Clifford Algebras, 2001, 11 (Suppl 2) : 89 - 106
[18] Higher Spin Dirac Operators Between Spaces of Simplicial Monogenics in Two Vector Variables
Brackx, F.
Eelbode, D.
Van de Voorde, L.
[J]. MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY, 2011, 14 (01) : 1 - 20
[19] Syzygies of multi-variable higher spin Dirac operators on R3
Damiano, Alberto
[J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2007, 17 (03) : 343 - 355
[20] Higher Spin Dirac Operators Between Spaces of Simplicial Monogenics in Two Vector Variables
F. Brackx
D. Eelbode
L. Van de Voorde
[J]. Mathematical Physics, Analysis and Geometry, 2011, 14 : 1 - 20

← 1 2 3 4 5 →