Symplectic Dirac Operator and its Higher Spin Analogues

2008 ◽  
Author(s):  
Svatopluk Krýsl
Keyword(s):  
Dirac Operator ◽  
Symplectic Dirac Operator ◽  
Higher Spin

scholarly journals The Polynomial Null Solutions of a Higher Spin Dirac Operator in Two Vector Variables

2010 ◽  
Vol 21 (3) ◽  
pp. 455-476 ◽  
Author(s):  
F. Brackx ◽  
D. Eelbode ◽  
L. Van de Voorde
Keyword(s):  
Dirac Operator ◽  
Higher Spin

scholarly journals Self-interacting mass-dimension one fields for any spin

2015 ◽  
Vol 30 (11) ◽  
pp. 1550048 ◽  
Author(s):  
Cheng-Yang Lee
Keyword(s):  
Dirac Equation ◽  
Dirac Operator ◽  
Momentum Space ◽  
Conjugation Operator ◽  
Massive Spin ◽  
Mass Dimension ◽  
Higher Spin ◽  
Klein Gordon ◽  
Expansion Coefficients ◽  
Dimension One

According to Ahluwalia and Grumiller, massive spin-half fields of mass-dimension one can be constructed using the eigenspinors of the charge-conjugation operator (Elko) as expansion coefficients. In this paper, we generalize their result by constructing quantum fields from higher-spin Elko. The kinematics of these fields are thoroughly investigated. Starting with the field operators, their propagators and Hamiltonians are derived. These fields satisfy the higher-spin generalization of the Klein–Gordon but not the Dirac equation. Independent of the spin, they are all of mass-dimension one and are thus endowed with renormalizable self-interactions. These fields violate Lorentz symmetry. The violation can be characterized by a non-Lorentz-covariant term that appears in the Elko spin-sums. This term provides a decomposition of the generalized higher-spin Dirac operator in the momentum space thus suggesting a possible connection between the mass-dimension one fields and the Lorentz-invariant fields.

scholarly journals Basic Aspects of Symplectic Clifford Analysis for the Symplectic Dirac Operator

2016 ◽  
Vol 27 (2) ◽  
pp. 1103-1132 ◽  
Author(s):  
Hendrik De Bie ◽  
Marie Holíková ◽  
Petr Somberg
Keyword(s):  
Dirac Operator ◽  
Clifford Analysis ◽  
Symplectic Dirac Operator

scholarly journals Higher symmetries of symplectic Dirac operator

2020 ◽  
Vol 209 (1) ◽  
pp. 177-198
Author(s):  
Petr Somberg ◽  
Josef Šilhan
Keyword(s):  
Dirac Operator ◽  
Higher Symmetries ◽  
Symplectic Dirac Operator

A Rare Low Spin Co(IV) Bis-Silyldiamide with High Thermal Stability: Exploring the Origin of an Unusual S = 1/2 Configuration

2020 ◽  
Author(s):  
David Zanders ◽  
Goran Bačić ◽  
Dominique Leckie ◽  
Oluwadamilola Odegbesan ◽  
Jeremy M. Rawson ◽  
...  
Keyword(s):  
Thermal Stability ◽  
Density Functional ◽  
Atomic Layer ◽  
Epr Spectrum ◽  
Functional Theory ◽  
Cluster Calculations ◽  
Layer Deposition ◽  
Starting Point ◽  
Higher Spin ◽  
Surface Saturation

Attempted preparation of a chelated Co(II) β-silylamide re-sulted in the unprecedented disproportionation to Co(0) and a spirocyclic cobalt(IV) bis(β-silyldiamide): [Co[(NtBu)2SiMe2]2] (1). Compound 1 exhibits a room temperature magnetic moment of 1.8 B.M and a solid state axial EPR spectrum diagnostic of a rare S = 1/2 configuration. Semicanonical coupled-cluster calculations (DLPNO-CCSD(T)) revealed the doublet state was clearly preferred (–27 kcal/mol) over higher spin configurations for which density functional theory (DFT) showed no energetic preference. Unlike other Co(IV) complexes, 1 had remarkable thermal stability, and was demonstrated to form a stable self-limiting monolayer in initial atomic layer deposition (ALD) surface saturation tests. The ease of synthesis and high-stability make 1 an attractive starting point to begin investigating otherwise inaccessible Co(IV) intermediates and synthesizing new materials.

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