scholarly journals Triality, biquaternion and vector representation of the Dirac equation

2002 ◽  
Vol 12 (2) ◽  
pp. 109-124 ◽  
Author(s):  
Liu Yu-Fen
Keyword(s):  
Dirac Equation ◽  
Vector Representation

scholarly journals Dirac equation based on the vector representation of the Lorentz group

2020 ◽  
Vol 135 (10) ◽  
Author(s):  
Eckart Marsch ◽  
Yasuhito Narita
Keyword(s):  
Gauge Theory ◽  
Dirac Equation ◽  
Lorentz Group ◽  
Degrees Of Freedom ◽  
Lagrangian Density ◽  
Degree Of Freedom ◽  
Vector Representation ◽  
Massive Fermion

AbstractIn this paper, we derive an expanded Dirac equation for a massive fermion doublet, which has in addition to the particle/antiparticle and spin-up/spin-down degrees of freedom explicity an isospin-type degree of freedom. We begin with revisiting the four-vector Lorentz group generators, define the corresponding gamma matrices and then write a Dirac equation for the fermion doublet with eight spinor components. The appropriate Lagrangian density is established, and the related chiral and SU(2) symmetry is discussed in detail, as well as applications to an electroweak-style gauge theory. In “Appendix,” we present some of the relevant matrices.

scholarly journals CPTM Symmetry for the Dirac Equation and Its Extended Version Based on the Vector Representation of the Lorentz Group

2021 ◽  
Vol 9 ◽  
Author(s):  
E. Marsch ◽  
Y. Narita
Keyword(s):  
Dirac Equation ◽  
Lorentz Group ◽  
Essential Role ◽  
Fundamental Equation ◽  
Extended Version ◽  
Vector Representation ◽  
Massive Fermion ◽  
The Standard Model ◽  
Cpt Theorem ◽  
Extended Dirac Equation

We revisit the CPT theorem for the Dirac equation and its extended version based on the vector representation of the Lorentz group. Then it is proposed that CPTM may apply to this fundamental equation for a massive fermion a s a singlet or a doublet with isospin. The symbol M stands here for reversing the sign of the mass in the Dirac equation, which can be accomplished by operation on it with the so-called gamma-five matrix that plays an essential role for the chirality in the Standard Model. We define the CPTM symmetry for the standard and extended Dirac equation and discuss its physical implications and some possible consequences for general relativity.

Dirac equation

2018 ◽  
pp. 515-522
Keyword(s):  
Dirac Equation

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws

SPIN-SPIN INTERACTION IN ONE PARTICLE DIRAC EQUATION

1999 ◽  
Vol 4 (0) ◽  
pp. 66-68
Author(s):  
І. І. Гайсак ◽  
В. С. Морохович
Keyword(s):  
Dirac Equation ◽  
Spin Interaction

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

scholarly journals Virial identity and weak dispersion for the magnetic Dirac equation

2011 ◽  
Vol 95 (2) ◽  
pp. 137-150 ◽  
Author(s):  
Nabile Boussaid ◽  
Piero D'Ancona ◽  
Luca Fanelli
Keyword(s):  
Dirac Equation ◽  
Virial Identity

scholarly journals Photonic realization of the κ -deformed Dirac equation

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
P. Majari ◽  
E. Sadurní ◽  
M. R. Setare ◽  
J. A. Franco-Villafañe ◽  
T. H. Seligman
Keyword(s):  
Dirac Equation

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation

scholarly journals Mudirac: A Dirac equation solver for elemental analysis with muonic X‐rays

2020 ◽  
Author(s):  
Simone Sturniolo ◽  
Adrian Hillier
Keyword(s):  
Dirac Equation ◽  
Elemental Analysis ◽  
X Rays
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