共查询到20条相似文献,搜索用时 15 毫秒
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We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics. 相似文献
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Arttu K. Rajantie 《Nuclear Physics B》1996,480(3):451-752
The two-point integrals contributing to the self-energy of a particle in a three-dimensional quantum field theory are calculated to two-loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to three-loop order. For almost every integral an expression in terms of elementary and dilogarithm functions is obtained. For two integrals, the master integral and the Mercedes integral, a one-dimensional integral representation is obtained with an integrand consisting only of elementary functions. The results are applied to a scalar λφ4 theory. 相似文献
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Jerry Tessendorf 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(4):751-760
The propagation kernel for time dependent radiative transfer is represented by a Feynman path integral (FPI). The FPI is approximately evaluated in the spatial-Fourier domain. Spatial diffusion is exhibited in the kernel when the approximations lead to a Gaussian dependence on the Fourier domain wave vector. The approximations provide an explicit expression for the diffusion matrix. They also provide an asymptotic criterion for the self-consistency of the diffusion approximation. The criterion is weakly violated in the limit of large numbers of scattering lengths. Additional expansion of higher-order terms may resolve whether this weak violation is significant. 相似文献
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M. AsoreyP. Facchi G. Florio V.I. Man'ko G. Marmo S. Pascazio E.C.G. Sudarshan 《Physics letters. A》2011,375(5):861-866
We scrutinize the effects of non-ideal data acquisition on the tomograms of quantum states. The presence of a weight function, schematizing the effects of a finite window or equivalently noise, only affects the state reconstruction procedure by a normalization constant. The results are extended to a discrete mesh and show that quantum tomography is robust under incomplete and approximate knowledge of tomograms. 相似文献
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The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe
and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike
particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some
inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as
a lower bound for the entropy is clarified. 相似文献
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In the path-integral formulation of quantum mechanics, the phase factor e
iS(x〈t〉) is associated with every path x〈t〉. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the complex
phase was a mathematical device invoked to extract wave behaviour in a particle framework. In this paper we show that the
continuous phase itself can have a discrete origin in time reversal and that the propagator can be drawn by a single deterministic
path.
1On leave from Department of Mathematics, Ryerson University, Toronto,
Ontario Canada. 相似文献
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基于Green函数的相空间生成泛函,导出了广义正则Ward恒等式.指出无须作出相空间生成泛函中对正则动量的路径积分,即可求得树图近似下的Feynman规则.对场的拉氏量添加一个四维散度项后,场的传播子发生了改变. 相似文献
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Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein--Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the “potential noise” of the apparatus or environment and “inner correlation” of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem. 相似文献
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There is a fruitful analogy between mechanics and optics. To describe the transition from quantum mechanics to classical mechanics, Feynman introduced the concept of an “integral over all paths”. The Feynman integral is used here to describe the transition from wave optics to geometrical optics. We suggest simple mathematical tools that allow use the Feynman integral and its approximation to calculate the radiation transport through an optically inhomogeneous layer and through an aperture in an infinite opaque screen. 相似文献
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Thomas Garm Pedersen 《Physics letters. A》2018,382(28):1837-1841
Bessel functions play an important role for quantum states in spherical and cylindrical geometries. In cases of perfect confinement, the energy of Schrödinger and massless Dirac fermions is determined by the zeros and intersections of Bessel functions, respectively. In an external electric field, standard perturbation theory therefore expresses the polarizability as a sum over these zeros or intersections. Both non-relativistic and relativistic polarizabilities can be calculated analytically, however. Hence, by equating analytical expressions to perturbation expansions, several sum rules for the zeros and intersections of Bessel functions emerge. 相似文献
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The optimized perturbation expansions, Grunberg's fastest apparent convergence and Stevenson's principle of minimal sensitivity, are applied to some low-energy QED quantities. The optimization does not disturb the experimentally established values, and, at higher orders, its effects are in the direction of reducing small differences between theoretical and experimental values. 相似文献
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William T.Rhodes 《声学学报:英文版》1993,(3)
A Feynman diagram theory for acousto—optic(AO)interactions is es-tablished,which provides a general method to calculate the scatteringamplitudes and intensities for both single-frequency and multifrequency AOinteractions.The method is based on counting the number of allowableFeynman diagrams.Some important assertions have been proved rigorously inthis paper. 相似文献