The Clifford Algebra of the Density Matrix: An Elementary Approach

This work studies the Clifford algebra approach to the density matrix. We discuss elementary examples of pure and mixed states by writing the density matrix as an element of the Clifford algebra of the three-dimensional space C l 3 . We also revisit the phenomenon of Larmor precession within the fra...

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Bibliographic Details
Published inAdvances in applied Clifford algebras Vol. 34; no. 3
Main Authors Amao, Pedro, Castillo, Hernan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2024
Springer Nature B.V
Subjects
Applications of Mathematics
Density
ICCA23
Larmor precession
Mathematical and Computational Physics
Mathematical Methods in Physics
Matrix algebra
Physics
Physics and Astronomy
Quantum theory
Theoretical
Dynamics of quantum systems
Mixed states
Two-level systems
Secondary 15A66
Larmor precession
Density operator
Density matrix
Primary 81V45
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Summary:This work studies the Clifford algebra approach to the density matrix. We discuss elementary examples of pure and mixed states by writing the density matrix as an element of the Clifford algebra of the three-dimensional space C l 3 . We also revisit the phenomenon of Larmor precession within the framework of Clifford algebra. Additionally, we discuss the geometrical interpretation of the so-called Clifford Density Element (CDE) for pure states in analogy to the Bloch sphere of conventional quantum theory. Finally, we discuss the dynamics of the CDE, which obeys an algebraic form of the Liouville von–Neumann equation.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-024-01337-8