manuscripta mathematica

A pseudo-algebra of observables for the dirac equation

Heinz Otto Cordes

Published Feb 1, 1983• 13 citations

DOI: 10.1007/bf01168582

Related papers

On the construction of the Feynman path integral for the Dirac equation (Introductory Workshop on Path Integrals and Pseudo-Differential Operators)

Wataru Ichinose

Jul 1, 20150 citations

A spin observable for a Dirac particle

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

Annals of PhysicsDec 11, 201217 citations

$(1+1)$ dimensional Dirac equation with non Hermitian interaction

Anjana Sinha, Pinaki Roy

Jan 1, 200533 citations

(1+1)-DIMENSIONAL DIRAC EQUATION WITH NON-HERMITIAN INTERACTION

A. SINHA, P. ROY

We study (1+1)-dimensional Dirac equation with non-Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo-supersymmetry.

arXiv:quant-ph/0511252Modern Physics Letters ASep 21, 200540 citations

On the Mathematical Basis of the Dirac Formulation of Quantum Mechanics

Manuel Gadella, F. Gómez-Cubillo

International Journal of Theoretical PhysicsOct 1, 200349 citations

On Dirac Observables

Heinz Otto Cordes

The Dirac equation admits a natural time-invariant algebra Q of unbounded operators of the Hilbert space H = L 2(ℝ3, ℂ4). Time-invariance means that $${{e}^{{iHt}}}Q{{e}^{ - }}^{{iHt}} = Q, $$ with the unitary $${e^{iHt}}:{\mathbf{H}} \to {\mathbf{H}}. $$ This is not a specific feature of the Dirac equation; any 1-st order strictly hyperbolic system (under mild additional assumptions) admits such an algebra. We propose to introduce Q as algebra of “really predictable observables” into v. Neumann’s theory of physical states and observables: Only the self-adjoint operators A ∈ Q can be really predicted. For other observables — especially for most dynamical observables — one must find an observable A0 ∈ Q “close” to A, perhaps only for a given physical state ψ. Energy H belongs to Q, but location (angular) momentum, spin,…, do not. This seems to explain at a glance the triumphs and difficulties Dirac’s theory encountered.

Birkhäuser Basel eBooksJan 1, 20003 citations

manuscripta mathematica

A pseudo-algebra of observables for the dirac equation

Heinz Otto Cordes

Published Feb 1, 1983• 13 citations

Publisher

DOI: 10.1007/bf01168582

Related papers

On the construction of the Feynman path integral for the Dirac equation (Introductory Workshop on Path Integrals and Pseudo-Differential Operators)

Wataru Ichinose

Jul 1, 20150 citations

A spin observable for a Dirac particle

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

Annals of PhysicsDec 11, 201217 citations

$(1+1)$ dimensional Dirac equation with non Hermitian interaction$(1+1)$ dimensional Dirac equation with non Hermitian interaction

Anjana Sinha, Pinaki Roy

We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.We study $(1+1)$ dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.

Jan 1, 200533 citations

(1+1)-DIMENSIONAL DIRAC EQUATION WITH NON-HERMITIAN INTERACTION

A. SINHA, P. ROY

arXiv:quant-ph/0511252Modern Physics Letters ASep 21, 200540 citations

On the Mathematical Basis of the Dirac Formulation of Quantum Mechanics

Manuel Gadella, F. Gómez-Cubillo

International Journal of Theoretical PhysicsOct 1, 200349 citations

On Dirac Observables

Heinz Otto Cordes

The Dirac equation admits a natural time-invariant algebra Q of unbounded operators of the Hilbert space H = L 2(ℝ3, ℂ4). Time-invariance means that ${{e}^{{iHt}}}Q{{e}^{ - }}^{{iHt}} = Q,$ with the unitary ${e^{iHt}}:{\mathbf{H}} \to {\mathbf{H}}.$ This is not a specific feature of the Dirac equation; any 1-st order strictly hyperbolic system (under mild additional assumptions) admits such an algebra. We propose to introduce Q as algebra of “really predictable observables” into v. Neumann’s theory of physical states and observables: Only the self-adjoint operators A ∈ Q can be really predicted. For other observables — especially for most dynamical observables — one must find an observable A0 ∈ Q “close” to A, perhaps only for a given physical state ψ. Energy H belongs to Q, but location (angular) momentum, spin,…, do not. This seems to explain at a glance the triumphs and difficulties Dirac’s theory encountered.The Dirac equation admits a natural time-invariant algebra Q of unbounded operators of the Hilbert space H = L 2(ℝ3, ℂ4). Time-invariance means that $${{e}^{{iHt}}}Q{{e}^{ - }}^{{iHt}} = Q, $$ with the unitary $${e^{iHt}}:{\mathbf{H}} \to {\mathbf{H}}. $$ This is not a specific feature of the Dirac equation; any 1-st order strictly hyperbolic system (under mild additional assumptions) admits such an algebra. We propose to introduce Q as algebra of “really predictable observables” into v. Neumann’s theory of physical states and observables: Only the self-adjoint operators A ∈ Q can be really predicted. For other observables — especially for most dynamical observables — one must find an observable A0 ∈ Q “close” to A, perhaps only for a given physical state ψ. Energy H belongs to Q, but location (angular) momentum, spin,…, do not. This seems to explain at a glance the triumphs and difficulties Dirac’s theory encountered.

Birkhäuser Basel eBooksJan 1, 20003 citations

(1+1)

dimensional Dirac equation with non Hermitian interaction

We study

(1+1)

dimensional Dirac equation with non Hermitian interactions, but real energies. In particular, we analyze the pseudoscalar and scalar interactions in detail, illustrating our observations with some examples. We also show that the relevant hidden symmetry of the Dirac equation with such an interaction is pseudo supersymmetry.

The Dirac equation admits a natural time-invariant algebra Q of unbounded operators of the Hilbert space H = L 2(ℝ3, ℂ4). Time-invariance means that

{{e}^{{iHt}}}Q{{e}^{ - }}^{{iHt}} = Q,

with the unitary

{e^{iHt}}:{\mathbf{H}} \to {\mathbf{H}}.

This is not a specific feature of the Dirac equation; any 1-st order strictly hyperbolic system (under mild additional assumptions) admits such an algebra. We propose to introduce Q as algebra of “really predictable observables” into v. Neumann’s theory of physical states and observables: Only the self-adjoint operators A ∈ Q can be really predicted. For other observables — especially for most dynamical observables — one must find an observable A0 ∈ Q “close” to A, perhaps only for a given physical state ψ. Energy H belongs to Q, but location (angular) momentum, spin,…, do not. This seems to explain at a glance the triumphs and difficulties Dirac’s theory encountered.