Results 181 to 190 of about 2,501 (221)

Complexes of Dirac operators in Clifford algebras

Mathematische Zeitschrift, 2002
In this paper the following is studied: The Cauchy-Fueter operator in the quaternionic case was obtained by the Moisil-Theodorescu product (the case of the Dirac operator in the Clifford algebra \({\mathcal C}_3\). Thus it is motivated the choice of Dirac operators in the Clifford algebra \({\mathcal C}_m\) only in the case when \(m>4\) or \(m=4 ...
SABADINI, IRENE MARIA, STRUPPA DC, SOMMEN F, VAN LANCKER P.   +3 more
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A Dirac–Dunkl Equation on S 2 and the Bannai–Ito Algebra

Communications in Mathematical Physics, 2016
The Dirac–Dunkl operator on the two-sphere associated to the Z_2^3 reflection group is considered. Its symmetries are found and are shown to generate the Bannai–Ito algebra.
Hendrik de Bie, Vincent X Genest, Luc Vinet   +2 more
exaly   +3 more sources

Algebra of the Dirac-Matrices

Proceedings of the Indian Academy of Sciences - Section A, 1945
Not ...
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Lie algebras for the Dirac–Clifford ring

Journal of Mathematical Physics, 1993
It is shown in general that the Dirac–Clifford ring formed by the Dirac matrices and all their products, for all even and odd space–time dimensions D, span the commutation algebras su(2D/2) for even D and su(2(D−1)/2)⊕su(2(D−1)/2) for odd D. Some physical consequences of these results are discussed herein.
Mignaco, Juan Alberto, Linhares, Cesar Augusto   +1 more
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Algebra of Dirac Bilinears

Journal of Mathematical Physics, 1964
All of the possible quadratic relations among the Dirac bilinear covariants which one may construct using both the usual bispinor and its charge-conjugate are given. Many interesting purely algebraic results are found for a general Dirac field.
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On the Dirac equation in the algebraic approximation

Theoretica Chimica Acta, 1986
It is shown that the restrictive conditions of Wood et al. [1] are not necessary to reach the conclusion that the Dirac hamiltonian, projected onto the space of the large component, exhibits variational properties. The eigenvalue spectrum of matrix approximations to the partitioned hamiltonian (obtained by matrix partitioning) converges to the exact ...
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Computer algorithms for dirac algebra

Journal of Computational Physics, 1969
We present a collection of algorithms written in ALGOL 60 to illustrate the manipulation techniques used in machine language programs designed for symbolic evaluation of algebraic expressions. Such algorithms have been used by theoretical physicists in quantum electrodynamics calculations.
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Pauli’s identities in the Dirac algebra

Proceedings of the Indian Academy of Sciences - Section A, 1945
It is shown in this paper that by choosing suitable forms for 4×4 matrices as products of Dirac matrices and matrices of rank unity (i.e., products of 4×1 and 1×4 matrices), and expressing them as linear combinations of the sixteen elementsγ A of the basis of the Dirac algebra, one can derive the generalized identities of Pauli which ...
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Spurious Roots in the Algebraic Dirac Equation

Physica Scripta, 2003
Summary: The nature of spurious roots discovered by \textit{G. W. F. Drake} and \textit{S. P. Goldman} [Phys. Rev. A 23, 2093 (1981)] among solutions of the algebraic Dirac Hamiltonian eigenvalue problem is discussed. It is shown that the spurious roots represent the positive spectrum states of the Dirac Hamiltonian and that each of them has its ...
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The Dirac equation in the algebraic approximation

Physica Scripta, 1987
The construction of variational approximations to the solutions of the Dirac equation is discussed. The importance of imposing the physical boundary conditions for both the point- and finite-nuclear models on the set of trial functions is emphasised.
H M Quiney, I P Grant, S Wilson
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