Two-state quantum systems revisited: a Clifford algebra approach

DOI10.1007/s00006-020-01116-1zbMath1460.81118arXiv2001.00656OpenAlexW2996956475MaRDI QIDQ2661150

Hernan Castillo, Pedro Amao

Publication date: 1 April 2021

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.00656

zbMATH Keywords

Clifford algebrasgeometric algebratwo-state quantum systems

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Eigenvalues, singular values, and eigenvectors (15A18) Atomic physics (81V45) Spinor and twistor methods applied to problems in quantum theory (81R25) Clifford algebras, spinors (15A66) Electro- and magnetostatics (78A30) Diagonalization, Jordan forms (15A20)

Uses Software

• GeometricAlgebra

Cites Work

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• Geometric roots of \(-1\) in Clifford algebras \(C \ell_{p,q}\) with \(p + q \leq 4\)
• Quantum/classical interface: classical geometric origin of fermion spin
• Idempotent structure of Clifford algebras
• Calculation of quantum eigens with geometrical algebra rotors
• The construction of spinors in geometric algebra
• The Standard Model of Quantum Physics in Clifford Algebra
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• An Introduction to Clifford Algebras and Spinors
• Real Quaternionic Calculus Handbook
• Modern Quantum Mechanics
• Quantenmechanik
• Space-Time Algebra

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