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1.
We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and
first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
In this paper, we evaluate various analytic Feynman integrals of first variation, conditional first variation, Fourier-Feynman
transform and conditional Fourier-Feynman transform of cylinder type functions defined over Wiener paths in abstract Wiener
space. We also derive the analytic Feynman integral of the conditional Fourier-Feynman transform for the product of the cylinder
type functions which define the functions in a Banach algebra introduced by Yoo, with n linear factors. 相似文献
3.
We consider an extension of the Feynman path integral to the quantum mechanics of noncommuting spatial coordinates and formulate the corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians). The basis of our approach is that a quantum mechanical system with a noncommutative configuration space can be regarded as another effective system with commuting spatial coordinates. Because the path integral for quadratic Lagrangians is exactly solvable and a general formula for the probability amplitude exists, we restrict our research to this class of Lagrangians. We find a general relation between quadratic Lagrangians in their commutative and noncommutative regimes and present the corresponding noncommutative path integral. This method is illustrated with two quantum mechanical systems in the noncommutative plane: a particle in a constant field and a harmonic oscillator. 相似文献
4.
In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED. 相似文献
5.
6.
阮永红 《浙江大学学报(理学版)》2002,29(2):144-148
利用Feynman路径积分变分方法,推导了整个电声子耦合区域的量子阱中束缚极化子的基态能。对其数值结果研究表明:当量子阱的约束势达到一定值,极化子的基态能修正-△E随电声子耦合常数α的增加激剧增大,约束势导致有效电声子耦合从无约束势时的弱耦合向居间耦合或强耦合渡越。更重要的是,我们发现存在一个量子阱的临界有效宽度lz0,当lZ小于临界值时,-△E随lz变小很快增大;当lz大于临界值时,随lz变大,-△E几乎不变。 相似文献
7.
We present a rigorous and functorial quantization scheme for affine field theories, i.e., field theories where local spaces of solutions are affine spaces. The target framework for the quantization is the general boundary formulation, allowing to implement manifest locality without the necessity for metric or causal background structures. The quantization combines the holomorphic version of geometric quantization for state spaces with the Feynman path integral quantization for amplitudes. We also develop an adapted notion of coherent states, discuss vacuum states, and consider observables and their Berezin–Toeplitz quantization. Moreover, we derive a factorization identity for the amplitude in the special case of a linear field theory modified by a source-like term and comment on its use as a generating functional for a generalized S-matrix. 相似文献
8.
Planning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other. 相似文献
9.
We use the higher covariant derivative regularization to investigate a new identity for Green’s functions. It relates certain
coefficients of the matter superfield vertex function for which one of the external matter legs is not chiral. Calculations
in the first nontrivial order (for the two-loop vertex function) demonstrate that the new identity also holds in the non-Abelian
Yang-Mills theory with matter fields. We demonstrate that the new identity follows because the three-loop integrals determining
the Gell-Mann-Low function are integrals of total derivatives.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 270–281, August, 2008. 相似文献
10.
We calculate the two-loop Gell-Mann-Low function for the N=1 supersymmetric Yang-Mills theory regularized by higher covariant
derivatives. We show that the integrals determining this function reduce to total derivatives and can be easily calculated
analytically.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 398–414, June, 2008. 相似文献