Canonical formalism and quantization of perturbative sector of higher-derivative theories

Exact Paraxial Quantization

A non-perturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. The theoretical formalism yields a seamless transition between the paraxial- and the Maxwell-equation solutions. This obviates the need to introduce either "ad hoc" or perturbatively-defined field operators. In the limit of narrow beam-like fields, the theory is in agreement with approximated quantization schemes provided by other authors.

带有高阶导数微扰的Pais-Uhlenbeck振子的正则量子化：一种协变相空间方法

Canonical quantization of the Pais-Uhlenbeck oscillator with a higher-derivative perturbation: a covariant phase space approach

本文采用协变相空间方法，对带平方加速度微扰的Pais-Uhlenbeck振子进行正则量子化，得到与精确低能理论一致的结果，消除了Ostrogradsky鬼，扩展了微扰量子化方案至高阶导数理论。

On quantization of systems with second class constraints

It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and on a surface is considered. The results coincide with those of the "thin layer method". Influence of the non-physical variables on the physical sector is demonstrated.

Perturbative approach to Dynamical Casimir effect in an interface of dielectric mediums

Electromagnetic field quantization in the presence of two semi-infinite dielectrics with moving interface is investigated in $1+1$-dimensional space-time. The moving interface is modeled for small displacements and the field equation is solved perturbatively. Input-output relations and spectral distribution of emitted photons are obtained and the effect of small transitions trough the interface discussed.

Half Quantization

A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical systems will be named half quantum. The aim of this paper is to derive the dynamical evolution of a general half quantum system from its full quantum formulation. The standard approach would be to use quantum mechanics to make predictions for the time evolution of the half quantum initial data. The main problem is how can quantum mechanics be applied to a dy…

Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation

The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report a closed-form formula that exactly resums the perturbative WKB series to all-orders for two turning point problem. The formula is elegantly interpreted as the action evaluated using the product of spatially-varying wavenumber and a coefficient related to the wave transmissivity; unit transmissivity yields the Bohr-Sommerfeld quantization.