In this paper,we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds.As an example of application,we study the dependence of the four-dimensional quantum Yang–Mills effective ac...In this paper,we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds.As an example of application,we study the dependence of the four-dimensional quantum Yang–Mills effective action on the special gauge transformation with respect to the background field.Also,we formulate some open questions about a structure of divergences for a special type of regularization in the presence of the background field formalism.展开更多
By adopting in-line lensless Fourier setup and phase-shifting technique, we recorded the phase-shifting digital hologram at short distance. As the Fresnel diffraction condition is no longer valid, the convolution appr...By adopting in-line lensless Fourier setup and phase-shifting technique, we recorded the phase-shifting digital hologram at short distance. As the Fresnel diffraction condition is no longer valid, the convolution approach is chosen for the reconstruction. However, the simulated reference wave for the reconstruction would suffer from severe undersampling due to the comparatively large pixel size. To solve this problem, sine-interpolation is introduced to get the pixel-size of the hologram reduced prior to the reconstruction. The experimental results show that an object image of high fidelity is obtained with this method.展开更多
基金supported by the Ministry of Science and Higher Education of the Russian Federation,agreement 07515-2022-289supported in parts by the Foundation for the Advancement of Theoretical Physics and Mathematics‘BASIS’,grant‘Young Russian Mathematics’。
文摘In this paper,we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds.As an example of application,we study the dependence of the four-dimensional quantum Yang–Mills effective action on the special gauge transformation with respect to the background field.Also,we formulate some open questions about a structure of divergences for a special type of regularization in the presence of the background field formalism.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60747001 and 60467003)
文摘By adopting in-line lensless Fourier setup and phase-shifting technique, we recorded the phase-shifting digital hologram at short distance. As the Fresnel diffraction condition is no longer valid, the convolution approach is chosen for the reconstruction. However, the simulated reference wave for the reconstruction would suffer from severe undersampling due to the comparatively large pixel size. To solve this problem, sine-interpolation is introduced to get the pixel-size of the hologram reduced prior to the reconstruction. The experimental results show that an object image of high fidelity is obtained with this method.
