Pais–Uhlenbeck oscillator
E471861
The Pais–Uhlenbeck oscillator is a higher-derivative harmonic oscillator model in theoretical physics that serves as a key example in the study of stability and quantization issues in higher-order field theories.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
higher-derivative harmonic oscillator
ⓘ
theoretical physics model ⓘ toy model in quantum field theory ⓘ |
| appearsIn |
analyses of non-Hermitian but PT-symmetric Hamiltonians
ⓘ
discussions of renormalizable higher-derivative models ⓘ studies of classical stability of higher-order systems ⓘ |
| field |
classical mechanics
ⓘ
quantum field theory ⓘ quantum mechanics ⓘ theoretical physics ⓘ |
| hasEquationOfMotion | fourth-order linear differential equation in time ⓘ |
| hasHamiltonianFormulation | can be written as a system of coupled oscillators with opposite signs of energy ⓘ |
| hasLagrangianForm | L contains terms quadratic in acceleration ⓘ |
| hasParameter | set of characteristic frequencies ⓘ |
| hasProperty |
can exhibit Ostrogradsky instability in standard formulation
ⓘ
can exhibit ghost degrees of freedom ⓘ fourth-order equation of motion in the simplest version ⓘ higher-order time derivatives in the Lagrangian ⓘ non-degenerate frequency spectrum in generic case ⓘ serves as a prototype for higher-derivative field theories ⓘ |
| hasQuantizationIssue |
potential violation of unitarity
ⓘ
presence of negative norm states in naive quantization ⓘ |
| hasResolutionApproach |
PT-symmetric quantization to avoid ghosts
ⓘ
constrained Hamiltonian formulations ⓘ modified inner product in Hilbert space ⓘ |
| hasVariant |
PT-symmetric Pais–Uhlenbeck oscillator
NERFINISHED
ⓘ
degenerate Pais–Uhlenbeck oscillator ⓘ non-degenerate Pais–Uhlenbeck oscillator ⓘ |
| introducedIn | 20th century theoretical physics literature ⓘ |
| mathematicallyDescribedBy | linear differential operators of fourth order in time ⓘ |
| namedAfter |
Abraham Pais
NERFINISHED
ⓘ
George Uhlenbeck NERFINISHED ⓘ |
| relatedTo |
Lee–Wick theories
NERFINISHED
ⓘ
Ostrogradsky instability NERFINISHED ⓘ ghost fields ⓘ higher-derivative gravity ⓘ nonlocal field theories ⓘ |
| studiedFor |
Ostrogradsky theorem implications
ⓘ
PT-symmetric quantization ⓘ ghost problem in quantum field theory ⓘ non-Hermitian Hamiltonian formulations ⓘ quantization of higher-derivative systems ⓘ stability issues in higher-order theories ⓘ |
| usedAs |
example in canonical quantization of higher-order systems
ⓘ
example in path-integral quantization with higher derivatives ⓘ example in studies of unitarity in higher-derivative models ⓘ testbed for alternative quantization schemes ⓘ |
Referenced by (1)
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