Deformation quantization of the Pais-Uhlenbeck fourth order oscillator

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• 作者：Jasel Berra-Montiel^a ; ^{jberra@fc.uaslp.mx" class="auth_mail" title="E-mail the corresponding author} ; Alberto Molgado^a ; ^b ; ^{molgado@fc.uaslp.mx" class="auth_mail" title="E-mail the corresponding author} ; Efraí ; n Rojas^c ; ^{efrojas@uv.mx" class="auth_mail" title="E-mail the corresponding author}
• 关键词：81S30 ; 70H50 ; 53D55 ; 46L65
• 刊名：Annals of Physics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：362
• 期：Complete
• 页码：298-310
• 全文大小：411 K

文摘

We analyze the quantization of the Pais–Uhlenbeck fourth order oscillator within the framework of deformation quantization. Our approach exploits the Noether symmetries of the system by proposing integrals of motion as the variables to obtain a solution to the ⋆$\star$-genvalue equation, namely the Wigner function. We also obtain, by means of a quantum canonical transformation the wave function associated to the Schrödinger equation of the system. We show that unitary evolution of the system is guaranteed by means of the quantum canonical transformation and via the properties of the constructed Wigner function, even in the so called equal frequency limit of the model, in agreement with recent results.