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51.
We derive the basic canonical brackets amongst the creation and annihilation operators for a two (1 + 1)- dimensional (2D) gauge field theoretic model of an interacting Hodge theory where a U(1) gauge field (Aμ) is coupled with the fermionic Dirac fields (ψ and ψ). In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries (and the concept of their generators) that are present in the theory. We do not use the definition of the canonical conjugate momenta (corresponding to the basic fields of the theory) anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries (and corresponding generators) provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level. 相似文献
52.
53.
In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension in , and later this result has been extended to more general non-tangentially accessible domains and beyond.In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph Γ of dimension d in , , with a small Lipschitz constant. We construct a linear degenerate elliptic operator L such that the corresponding harmonic measure is absolutely continuous with respect to the Hausdorff measure on Γ. More generally, we provide sufficient conditions on the matrix of coefficients of L which guarantee the mutual absolute continuity of and the Hausdorff measure. 相似文献
54.
Joachim Toft 《Applied and Computational Harmonic Analysis》2019,46(1):154-176
We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator is a Schatten-q operator from to and r-nuclear operator from to when for suitable p, q and r in . 相似文献
55.
Natasha Samko 《Mathematical Methods in the Applied Sciences》2020,43(16):9416-9434
We find conditions for the boundedness of integral operators commuting with dilations and rotations in a local generalized Morrey space. We also show that under the same conditions, these operators preserve the subspace of such Morrey space, known as vanishing Morrey space. We also give necessary conditions for the boundedness when the kernel is non-negative. In the case of classical Morrey spaces, the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case, we also obtain similar results for global Morrey spaces. In the case of radial kernels, we also obtain stronger estimates of via spherical means of . We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multidimensional versions, and others. 相似文献
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57.
本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论. 相似文献
58.
Fabrizio Colombo Samuele Mongodi Marco Peloso Stefano Pinton 《Mathematical Methods in the Applied Sciences》2019,42(5):1662-1686
Let e?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory. 相似文献
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60.
O.M. Lyulin V.I. Perevalov H. Tran J.-Y. Mandin V. Dana L. Rgalia-Jarlot X. Thomas D. Dcatoire 《Journal of Quantitative Spectroscopy & Radiative Transfer》2009,110(17):1815-1824
Using the Fourier transform spectra of the acetylene molecule recorded near 1.5-μm, the intensities of 111 lines belonging to seven hot bands of the main isotopologue 12C2H2 have been retrieved by means of a multispectrum fitting procedure. Considering the density of lines in the spectra, and the fact that the measured bands are the weakest observed, the accuracy of the measurements is around 10%. At first stage, an empirical treatment of these data has been performed, leading to the vibrational transition dipole moment squared and some Herman–Wallis coefficients. Then the measured line intensities of this work and collected ones from the literature have been treated simultaneously within the framework of the effective operator approach. 相似文献