No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model

A. Pais and G. E. Uhlenbeck, Phys. Rev. 79

1950

Earlier work this paper cites.

T. D. Lee, Phys. Rev. 95

1954

Earlier work this paper cites.

G. Källén and W. Pauli, Dan. Mat.-Fys. Medd. 30

1955

Earlier work this paper cites.

W. Heisenberg, Nucl. Phys. 4

1957

Earlier work this paper cites.

C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80

1999

Earlier work this paper cites.

A. Mostafazadeh, J. Math. Phys. 43

2002

Cited alongside, same era.

A. Mostafazadeh, J. Math. Phys. 43

2003

Cited alongside, same era.

P. Dorey, C. Dunning and R. Tateo, J. Phys. A 34

2004

Cited alongside, same era.

C. M. Bender, D. C. Brody, and H. F. Jones, Phys. Rev. Lett. 89

2004

Cited alongside, same era.

C. M. Bender, S. F. Brandt, J.-H. Chen, and Q. Wang, Phys. Rev. D 71

2005

Cited alongside, same era.

E. A. Ivanov and A. V. Smilga, arXiv: hep-th/0703038; T. Curtright, L. Mezincescu, and D. Schuster, J. Math. Phys. (to appear), arXiv: quant-ph/0603170; T. Curtright, E. Ivanov, L. Mezincescu, and P. K. Townsend, arXiv: hep-th/0612300

Cited in the paper.

With the identifications ω 1 2 + ω 2 2 = 2 ​ k 2 + M 2 \omega_{1}^{2}+\omega_{2}^{2}=2k^{2}+M^{2} , ω 1 2 ​ ω 2 2 = k 4 + k 2 ​ M 2 \omega_{1}^{2}\omega_{2}^{2}=k^{4}+k^{2}M^{2} , this equation of motion is the quantum-mechanical limit of the field-theoretic second-plus-fourth order ( − ∂ t 2 + ∇ 2 ) ( − ∂ t 2 + ∇ 2 − M 2 ) ϕ ( x ¯ , t ) = 0 (-\partial_{t}^{2}+\nabla^{2})(-\partial_{t}^{2}+\nabla^{2}-M^{2})\phi(\bar{x},t)=0 in field configurations of the form ϕ ⁡ ( x ¯ , t ) = z ⁡ ( t ) ​ e i ​ k ¯ ⋅ x ¯ \phi(\bar{x},t)=z(t)e^{i\bar{k}\cdot\bar{x}} . The M = 0 M=0 pure fourth order theory corresponds to ω 1 = ω 2 = k \omega_{1}=\omega_{2}=k

Cited in the paper.

P. D. Mannheim and A. Davidson, arXiv: hep-th/0001115

Cited in the paper.

Despite the introduction of y = − i ​ z y=-iz and q = i ​ p z q=ip_{z} , since y y and q q are Hermitian operators, their c-number eigenvalue coordinates and momenta are strictly real

Cited in the paper.

Although quantum mechanics is usually formulated in terms of Hermitian operators, Hermiticity is only sufficient to give real eigenvalues but not necessary. Specifically, while a Hermitian operator has real eigenvalues, there is no converse theorem that says that the eigenvalues of a non-Hermitian operator are not real. The Hamiltonian ( 11

Cited in the paper.

With ( 3

Cited in the paper.

In [ 14 , 15 , 16 ] it was shown that even if one uses the Dirac inner product for the Pais-Uhlenbeck theory, in the equal frequency limit (the case relevant to conformal gravity) the states of negative norm decouple from the Hamiltonian. With the Hamiltonian of ( 17

Cited in the paper.

P. D. Mannheim and A. Davidson, Phys. Rev. A 71

2005

Later among the works it cites.

In the context of quantum gravitational fluctuations higher-order terms are encountered in the standard Einstein theory of gravity, where their emergence as renormalization counterterms threatens the viability of the theory. This point is stressed in S. W. Hawking and T. Hertog, Phys. Rev. D 65

2006

Later among the works it cites.

C. M. Bender, P. N. Meisinger, and Q. Wang, J. Phys. A: Math. Gen. 36

2006

Later among the works it cites.

C. M. Bender, Contemp. Phys. 46

2007

Closest in time.

P. D. Mannheim, Found. Phys. 37

2007

Closest in time.