Feynman checkerboard model
E3528
discrete-time path integral
lattice model
model in quantum field theory
model in theoretical physics
path integral formulation
quantum mechanical model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
Aliases (2)
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
discrete-time path integral
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lattice model → model in quantum field theory → model in theoretical physics → path integral formulation → quantum mechanical model → |
| aimsToExplain |
connection between relativistic motion and spinor structure
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emergence of the Dirac equation from discrete paths → |
| alsoKnownAs |
Feynman chessboard model
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Feynman path integral on a lattice → |
| appliesTo |
Dirac particle in one spatial dimension
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|
| assumes |
discrete spacetime lattice with lightlike links
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particle moves only left or right at each time step → |
| basedOn |
path integral formulation of quantum mechanics
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|
| category |
Feynman diagrams and path integrals
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lattice quantum field theory models → |
| coreMechanism |
assigning amplitudes to corners where direction changes
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|
| creator |
Richard Feynman
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|
| describes |
relativistic quantum particle in 1+1 dimensions
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|
| dimension |
1+1
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|
| field |
lattice field theory
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mathematical physics → quantum field theory → quantum mechanics → relativistic quantum mechanics → |
| historicalContext |
introduced in the context of path integrals for relativistic particles
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|
| illustrates |
how spin-1/2 behavior can emerge from path sums
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relativistic propagation at the speed of light with direction reversals → |
| influenced |
discrete models of relativistic quantum mechanics
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later work on quantum walks → |
| limitBehavior |
continuum limit reproduces the Dirac propagator in 1+1 dimensions
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|
| mathematicalRepresentation |
sum over lattice paths with complex weights
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|
| pedagogicalUse |
teaching path integrals
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teaching the Dirac equation in low dimensions → |
| relatedTo |
Dirac equation
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Feynman path integral → Weyl equation in 1+1 dimensions → discrete-time quantum walk → lattice Dirac fermions → sum-over-paths approach → |
| spatialDimension |
1
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|
| temporalDimension |
1
→
|
| usedFor |
derivation of the 1+1 dimensional Dirac equation
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|
| usesConcept |
amplitudes associated with corners in paths
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lattice discretization of spacetime → lightlike lattice paths → sum over histories → zigzag paths at speed of light → |
Referenced by (3)
| Subject (surface form when different) | Predicate |
|---|---|
|
Feynman checkerboard model
("Feynman chessboard model")
→
Feynman checkerboard model ("Feynman path integral on a lattice") → |
alsoKnownAs |
|
Richard Feynman
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|
knownFor |