Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important pr...Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1], non-renormalizable scalar fields, such as (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [2] and (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [3], as well as the quantum theory of Einstein’s general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of non-renormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity that are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for non-renormalizable covariant scalar fields and Einstein’s gravity.展开更多
By employing an adiabatic invariant and implementing the Bohr- Sommerfield quantization rule, I study the quantization of a regular black hole in- spired by noncommutative geometry in AdS3 spacetime. The entropy spect...By employing an adiabatic invariant and implementing the Bohr- Sommerfield quantization rule, I study the quantization of a regular black hole in- spired by noncommutative geometry in AdS3 spacetime. The entropy spectrum as well as the horizon area spectrum of the black hole is obtained. It is shown that the spectra are discrete, and the spacing of the entropy spectrum is equidistant; in the limit rh2/4θ ≥1, the area spectrum depends on the noncommutative parameter and the cos- mological constant, but the spacing of the area spectrum is equidistant up to leading order √θe- 2Ml2/θ in θ, and is independent of the noncommutative parameter and the cosmological constant.展开更多
Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one o...Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein’s gravity.展开更多
文摘Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1], non-renormalizable scalar fields, such as (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [2] and (<i>ϕ</i><sup>12</sup>)<sub>3</sub> [3], as well as the quantum theory of Einstein’s general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of non-renormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity that are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for non-renormalizable covariant scalar fields and Einstein’s gravity.
基金supported by the Natural Science Foundation of Education Department of Shannxi Provincial Government(Grant No.12JK0954)the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology(Grant No.BJ12-02)
文摘By employing an adiabatic invariant and implementing the Bohr- Sommerfield quantization rule, I study the quantization of a regular black hole in- spired by noncommutative geometry in AdS3 spacetime. The entropy spectrum as well as the horizon area spectrum of the black hole is obtained. It is shown that the spectra are discrete, and the spacing of the entropy spectrum is equidistant; in the limit rh2/4θ ≥1, the area spectrum depends on the noncommutative parameter and the cos- mological constant, but the spacing of the area spectrum is equidistant up to leading order √θe- 2Ml2/θ in θ, and is independent of the noncommutative parameter and the cosmological constant.
文摘Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented and bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein’s gravity.
