Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators
SciPost Physics Proceedings, 2023 In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold.
Guner Muarem
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Covariantization of quantized calculi over quantum groups [PDF]
Mathematica Bohemica, 2020 We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$.
Seyed Ebrahim Akrami, Shervin Farzi
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The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe
Universe, 2021 We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua.
Vadim Monakhov
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The generalized relativistic harmonic oscillator with the Snyder-de Sitter algebra
Results in Physics, 2023 The Snyder-de Sitter (SdS) algebra is a model of non-commutative space–time admitting three fundamental parameters: the speed of light, the Planck mass and the cosmological constant, and therefore can be seen as an example of triply special relativity ...
A. Andolsi +3 more
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Internal quark symmetries and colour SU(3) entangled with Z3-graded Lorentz algebra
Nuclear Physics B, 2021 In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the SU(3) colour, the SU(2) flavour, and broken SU(3) providing the family triplets.
Richard Kerner, Jerzy Lukierski
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"Minimal geometric data" approach to Dirac algebra, spinor groups and field theories [PDF]
, 2007 The first three sections contain an updated, not-so-short account of a partly original approach to spinor geometry and field theories introduced by Jadczyk and myself [3–5]; it is based on an intrinsic treatment of 2-spinor geometry in which the needed ...
D. Canarutto
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Seminormal systems of operators in Clifford environments [PDF]
Opuscula Mathematica, 2017 The primary goal of our article is to implement some standard spin geometry techniques related to the study of Dirac and Laplace operators on Dirac vector bundles into the multidimensional theory of Hilbert space operators.
Mircea Martin
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Physics Letters B, 2014 In this Letter, 2D Dirac oscillator in the quantum deformed framework generated by the κ-Poincaré–Hopf algebra is considered. The problem is formulated using the κ-deformed Dirac equation. The resulting theory reveals that the energies and wave functions
Fabiano M. Andrade, Edilberto O. Silva
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Construction of Discrete Symmetries Using the Pauli Algebra Form of the Dirac Equation
Physical Sciences Forum, 2023 Two equations whose variables take values in the Pauli algebra of complex quaternions are shown to be equivalent to the standard Dirac equation and its Hermitian conjugate taken together.
Avraham Nofech
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Relating the topology of Dirac Hamiltonians to quantum geometry: When the quantum metric dictates Chern numbers and winding numbers [PDF]
SciPost Physics, 2021 Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play complementary roles:
B. Mera, Anwei Zhang, N. Goldman
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