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arXiv · 1410.3446

Quantizing the Homogeneous Linear Perturbations about Taub using the Jacobi Method of Second Variation

Joseph H. Bae
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Abstract

Applying the Jacobi method of second variation to the Bianchi IX system in Misner variables $(\alpha, \beta_+, \beta_-)$, we specialize to the Taub space background $(\beta_- = 0)$ and obtain the governing equations for linearized homogeneous perturbations $(\alpha', \beta_+', \beta_-')$ thereabout. Employing a canonical transformation, we isolate two decoupled gauge-invariant linearized variables ($\beta_-'$ and $Q_+' = p_+ \alpha' + p_\alpha \beta_+'$), together with their conjugate momenta and linearized Hamiltonians. These two linearized Hamiltonians are of time-dependent harmonic oscillator form, and we quantize them to get time-dependent Schr\"{o}dinger equations. For the case of $Q_+'$, we are able to solve for the discrete solutions and the exact quantum squeezed states.

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Joseph H. Bae. 2014-10-13. Quantizing the Homogeneous Linear Perturbations about Taub using the Jacobi Method of Second Variation. https://doi.org/10.1088/0264-9381/32/14/145002

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