Dirac string
E569023
gauge artifact
line singularity
theoretical construct in quantum field theory
topological defect (idealized)
A Dirac string is a theoretical, unobservable line-like singularity in the electromagnetic potential that allows a magnetic monopole to exist consistently in quantum theory.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
gauge artifact
ⓘ
line singularity ⓘ theoretical construct in quantum field theory ⓘ topological defect (idealized) ⓘ |
| appearsInEquation | A_φ potential of Dirac monopole in spherical coordinates ⓘ |
| appearsInTheory |
Dirac monopole theory
ⓘ
U(1) gauge theory with magnetic charge ⓘ quantum electrodynamics NERFINISHED ⓘ |
| category |
concept in gauge theory
ⓘ
concept in mathematical physics ⓘ concept in theoretical physics ⓘ |
| conditionForUnobservability | Dirac quantization condition e g = 2π n (in natural units) ⓘ |
| describedAs |
semi-infinite line attached to a magnetic monopole
ⓘ
string of singular gauge potential extending from monopole ⓘ |
| existsOnlyIn | potential description, not in field strength ⓘ |
| fieldStrengthProperty | electromagnetic field tensor is regular away from monopole ⓘ |
| gaugeChoiceProperty |
can be hidden by using multiple gauge patches
ⓘ
location can be moved by gauge transformation ⓘ |
| hasProperty |
carries no observable magnetic field except at monopole
ⓘ
gauge-dependent ⓘ line-like singularity in vector potential ⓘ mathematical artifact required for monopole description ⓘ unobservable in physical measurements ⓘ |
| introducedBy | Paul Dirac NERFINISHED ⓘ |
| introducedInContext | quantization of magnetic charge ⓘ |
| introducedInYear | 1931 (Dirac monopole paper) ⓘ |
| mathematicalRole |
allows definition of monopole magnetic field from a vector potential
ⓘ
represents singular gauge transformation line ⓘ |
| namedAfter | Paul Dirac NERFINISHED ⓘ |
| observabilityCondition | phase change around string must be integer multiple of 2π ⓘ |
| physicalInterpretation |
no direct observable consequences if charge quantization holds
ⓘ
unphysical artifact removable by gauge choice ⓘ |
| quantumMechanicalRole | affects phase of charged particle wavefunction around string ⓘ |
| relatedToConcept |
Aharonov–Bohm phase (formal analogy)
ⓘ
Dirac quantization condition NERFINISHED ⓘ Wu–Yang monopole NERFINISHED ⓘ fiber bundle description of monopoles ⓘ gauge potential ⓘ magnetic monopole ⓘ vector potential singularity ⓘ |
| singularityLocationExample |
θ = 0 (positive z-axis) in alternative gauge
ⓘ
θ = π (negative z-axis) in standard Dirac monopole gauge ⓘ |
| topologicalRole | represents nontrivial first Chern class of U(1) bundle ⓘ |
| usedFor |
constructing monopole vector potentials
ⓘ
deriving charge quantization from single-valued wavefunctions ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.