Results 191 to 200 of about 2,501 (221)

Linear Algebra and the Dirac Notation

2006
We assume the reader has a strong background in elementary linear algebra. In this section we familiarize the reader with the algebraic notation used in quantum mechanics, remind the reader of some basic facts about complex vector spaces, and introduce some notions that might not have been covered in an elementary linear algebra course.
Phillip Kaye, Raymond Laflamme, Michele Mosca   +2 more
openaire   +1 more source

Algebraic properties of the Dirac oscillator

Journal of Physics A: Mathematical and General, 1991
Summary: An algebraic (representation-independent) analysis is presented for the Dirac oscillator in an angular momentum basis. The analysis is based on shift operators for energy and angular momentum, and it is similar to that for a nonrelativistic isotropic harmonic oscillator.
openaire   +1 more source

A Dirac algebraic approach to supersymmetry

Foundations of Physics, 1983
The power of the Dirac algebra is illustrated through the Kahler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5, 1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields.
openaire   +1 more source

Effect of the Wigner–Dunkl algebra on the Dirac equation and Dirac harmonic oscillator

Modern Physics Letters A, 2018
In this work, we study the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra. By using Dunkl derivative, we solve the momentum operator and Hamiltonian that include the reflection symmetry. Based on the concept of the Wigner–Dunkl algebra and the functional analysis method, we have obtained the energy eigenvalue ...
Sargolzaeipor, S., Hassanabadi, H., Chung, W. S.   +2 more
openaire   +1 more source

Algebraic properties of the Dirac equation

Soviet Physics Journal, 1972
The first-order symmetry operators of the Dirac equation are classified according to their tensor properties under transformations of the homogeneous Lorentz group; a minimal system of generators for the ring of symmetry operators of the free Dirac equation is obtained, and the physical meaning of the spin operators is considered; fields are found ...
openaire   +1 more source

Dirac’s Bra and Ket Algebra

2004
In this chapter we will introduce Dirac’s bra and ket algebra in which the states of a dynamical system will be denoted by certain vectors (which, following Dirac, will be called as bra and ket vectors) and operators representing dynamical variables (like position coordinates, components of momentum and angular momentum) by matrices.2 In the following ...
Ajoy Ghatak, S. Lokanathan
openaire   +1 more source

Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl–Dirac operator

Journal of Algebra, 2022
Hendrik de Bie, Alexis Langlois-Rémillard, Roy Oste   +2 more
exaly  

The Dihedral Dunkl–Dirac Symmetry Algebra with Negative Clifford Signature

Springer Proceedings in Mathematics and Statistics, 2023
Alexis Langlois-Rémillard
exaly  

Real Dirac Algebra

2006
openaire   +2 more sources

The Dirac-Algebra

1974
openaire   +1 more source