Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-08-12
Phys.Rev. A71 (2005) 042110
Physics
High Energy Physics
High Energy Physics - Theory
RevTeX4, 20 pages. Final version, to appear in Phys. Rev. A
Scientific paper
10.1103/PhysRevA.71.042110
As a model, the Pais-Uhlenbeck fourth order oscillator with equation of motion $d^4q/dt^4+(\omega_1^2+\omega_2^2)d^2q/dt^2 +\omega_1^2\omega_2^2 q=0$ is a quantum-mechanical prototype of a field theory containing both second and fourth order derivative terms. With its dynamical degrees of freedom obeying constraints due to the presence of higher order time derivatives, the model cannot be quantized canonically. We thus quantize it using the method of Dirac constraints to construct the correct quantum-mechanical Hamiltonian for the system, and find that the Hamiltonian diagonalizes in the positive and negative norm states that are characteristic of higher derivative field theories. However, we also find that the oscillator commutation relations become singular in the $\omega_1 \to \omega_2$ limit, a limit which corresponds to a prototype of a pure fourth order theory. Thus the particle content of the $\omega_1 =\omega_2$ theory cannot be inferred from that of the $\omega_1 \neq \omega_2$ theory; and in fact in the $\omega_1 \to \omega_2$ limit we find that all of the $\omega_1 \neq \omega_2$ negative norm states move off shell, with the spectrum of asymptotic in and out states of the equal frequency theory being found to be completely devoid of states with either negative energy or negative norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero energy theorem of Boulware, Horowitz and Strominger, and show how in the equal frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive energy theorem instead.
Davidson Aharon
Mannheim Philip D.
No associations
LandOfFree
Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-575229