Results 11 to 20 of about 32,626 (182)
Mathematics, 2020 We prove that the Wiener integral, the analytic Wiener integral and the analytic Feynman integral of the first variation of F(x)=exp{∫0Tθ(t,x(t))dt} successfully exist under the certain condition, where θ(t,u)=∫Rexp{iuv}dσt(v) is a Fourier–Stieltjes ...
Young Sik Kim
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Bulletin of the Korean Mathematical Society, 2004 The authors define the conditional generalized Fourier-Feynman transform and conditional generalized convolution product for functionals on a function space which is rather general than the Wiener space and was introduced by \textit{S. J. Chang} and \textit{D. Skoug} [Integral Transforms Spec. Funct. 14, No. 5, 375--393 (2003; Zbl 1043.28014)].
Chang, Seung Jun, Choi, Jae Gil
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CONDITIONAL GENERALIZED FOURIER-FEYNMAN TRANSFORM OF FUNCTIONALS IN A FRESNEL TYPE CLASS [PDF]
Communications of the Korean Mathematical Society, 2011 In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space [0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform.
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FOURIER-FEYNMAN TRANSFORM AND CONVOLUTION OF FOURIER-TYPE FUNCTIONALS ON WIENER SPACE [PDF]
East Asian mathematical journal, 2013 Abstract. We develop a Fourier-Feynman theory for Fourier-type func-tionals k F and [F on Wiener space. We show that Fourier-Feynmantransform and convolution of Fourier-type functionals exist. We alsoshow that the Fourier-Feynman transform of the convolution product ofFourier-type functionals is a product of Fourier-Feynman transforms ofeach ...
Byoung Soo Kim
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Feynman diagrams in four-dimensional holomorphic theories and the Operatope
Journal of High Energy Physics, 2023 We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”).
Kasia Budzik +4 more
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Wightman-Function Approach to the Relativistic Complex-Ghost Field Theory [PDF]
, 2006 The relativistic complex-ghost field theory is covariantly formulated in terms of Wightman functions. The Fourier transform of the 2-point Wightman function of a complex-ghost pair is explicitly calculated, and its spontaneous breakdown of Lorentz ...
Nakanishi, Noboru
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Translation Theorems for Fourier-Feynman Transforms and Conditional Fourier-Feynman Transforms
Rocky Mountain Journal of Mathematics, 2000 In this paper, the authors establish translation theorems for generalized Fourier-Feynman transforms of very general functionals defined on a Wiener space. They also obtain general translation theorems for generalized conditional Fourier-Feynman transforms and show that these general translation theorems apply to two well-known classes of functionals ...
Change, Seung Jun +2 more
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Convolution and Fourier-Feynman Transforms
Rocky Mountain Journal of Mathematics, 1997 For a class of functionals on the Wiener space of the form \[ F(x)= \exp\Biggl\{\int^T_0 f(t,x(t))dt\Biggr\}, \] a new definition of the convolution product is proposed. This convolution product is commutative. The \(L_p\) analytic Fourier-Feynman transform, introduced by \textit{G. W. Johnson} and \textit{D. L. Skoug} [Mich. Math. J. 26, 103-127 (1979;
Huffman, Timothy +2 more
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A Partial Derivative Approach to the Change of Scale Formula for the Function Space Integral
Entropy, 2020 We investigate the partial derivative approach to the change of scale formula for the functon space integral and we investigate the vector calculus approach to the directional derivative on the function space and prove relationships among the Wiener ...
Young Sik Kim
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Waves on Noncommutative Spacetime and Gamma-Ray Bursts [PDF]
, 1999 Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime $[x^i,t]=\imath\lambda x^i$. A natural wave equation is derived and the associated phenomena of {\it in vacuo} dispersion are discussed ...
Amelino-Camelia G. +9 more
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