On the equivalence of complex and quaternionic quantum mechanics

DOI10.1007/s40509-017-0147-5zbMath1402.81133arXiv1709.07289OpenAlexW2963182216MaRDI QIDQ1621558

Jonathan Gantner

Publication date: 9 November 2018

Published in: Quantum Studies: Mathematics and Foundations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.07289

zbMATH Keywords

quaternionic quantum mechanicsquaternionic operatorsquaternionic Hilbert spacequaternionic quantum systems

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items (9)

A survey on the recent advances in the spectral theory on the S-spectrum ⋮ The fine structure of the spectral theory on the \(S\)-spectrum in dimension five ⋮ Quaternionic triangular linear operators ⋮ Infinite-order differential operators acting on entire hyperholomorphic functions ⋮ An application of the \(S\)-functional calculus to fractional diffusion processes ⋮ An introduction to hyperholomorphic spectral theories and fractional powers of vector operators ⋮ Fractional powers of vector operators with first order boundary conditions ⋮ Perturbation of normal quaternionic operators ⋮ The spectral theorem for normal operators on a Clifford module

Cites Work

• The spectral theorem for unitary operators based on the \(S\)-spectrum
• Slice hyperholomorphic Schur analysis
• Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
• Quantum logic in algebraic approach
• Quaternionic Aharonov-Bohm effect
• A representation of Weyl-Heisenberg Lie algebra in the quaternionic setting
• The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum
• CONTINUOUS SLICE FUNCTIONAL CALCULUS IN QUATERNIONIC HILBERT SPACES
• Coherent state quantization of quaternions
• Functions of the infinitesimal generator of a strongly continuous quaternionic group
• Spectral theory for unitary operators on a quaternionic Hilbert space
• Concerning the state-change due to the measurement process
• Quantum theory in real Hilbert space: How the complex Hilbert space structure emerges from Poincaré symmetry
• Absolute-Valued Algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the equivalence of complex and quaternionic quantum mechanics