The Feynman integrand as a white noise distribution beyond perturbation theory

2008 ◽  
Author(s):  
Martin Grothaus ◽  
Anna Vogel ◽  
Christopher C. Bernido ◽  
M. Victoria Carpio-Bernido
Keyword(s):  
Perturbation Theory ◽  
White Noise ◽  
Noise Distribution ◽  
White Noise Distribution

scholarly journals Transformations on white noise functions associated with second order differential operators of diagonal type

1998 ◽  
Vol 149 ◽  
pp. 173-192 ◽  
Author(s):  
Dong Myung Chung ◽  
Un Cig Ji ◽  
Nobuaki Obata
Keyword(s):  
White Noise ◽  
Differential Operators ◽  
Transformation Groups ◽  
Cauchy Problems ◽  
Noise Distribution ◽  
Number Operator ◽  
Parameter Transformation ◽  
Infinite Dimensional ◽  
White Noise Distribution Theory ◽  
White Noise Distribution

Abstract.A generalized number operator and a generalized Gross Laplacian are introduced on the basis of white noise distribution theory. The equicontinuity is examined and associated one-parameter transformation groups are constructed. An infinite dimensional analogue of ax + b group and Cauchy problems on white noise space are discussed.

WHITE NOISE ANALYSIS ON A NEW SPACE OF HIDA DISTRIBUTIONS

1999 ◽  
Vol 02 (03) ◽  
pp. 315-335 ◽  
Author(s):  
I. KUBO ◽  
H.-H. KUO ◽  
A. SENGUPTA
Keyword(s):  
White Noise ◽  
Noise Analysis ◽  
Distribution Theory ◽  
Noise Distribution ◽  
White Noise Analysis ◽  
Bell Numbers ◽  
New Space ◽  
White Noise Distribution Theory ◽  
White Noise Distribution ◽  
White Noise Space

Let {α(n); n≥0} be a sequence of positive numbers satisfying certain conditions. A Gel'fand triple [Formula: see text] associated with the sequence {α (n); n ≥ 0} has been introduced on a white noise space (ℰ′,μ) by Cochran, Kuo and Sengupta. In this paper we obtain additional conditions on the sequence {α(n); n≥0} in order to carry out white noise distribution theory on the space (ℰ′,μ). Moreover, we show that the Bell numbers satisfy these additional conditions.

White noise delta functions and infinite-dimensional Laplacians

2020 ◽  
pp. 2050028
Author(s):  
Luigi Accardi ◽  
Ai Hasegawa ◽  
Un Cig Ji ◽  
Kimiaki Saitô
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Time Derivative ◽  
Delta Function ◽  
Itô Formula ◽  
Ito Formula ◽  
Infinite Dimensional ◽  
Delta Functions ◽  
Definition Of ◽  
White Noise Distribution

In this paper, we introduce a new white noise delta function based on the Kubo–Yokoi delta function and an infinite-dimensional Brownian motion. We also give a white noise differential equation induced by the delta function through the Itô formula introducing a differential operator directed by the time derivative of the infinite-dimensional Brownian motion and an extension of the definition of the Volterra Laplacian. Moreover, we give an extension of the Itô formula for the white noise distribution of the infinite-dimensional Brownian motion.

scholarly journals The Hamiltonian path integrand for the charged particle in a constant magnetic field as white noise distribution

2015 ◽  
Vol 18 (02) ◽  
pp. 1550010 ◽  
Author(s):  
Wolfgang Bock ◽  
Martin Grothaus
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
White Noise ◽  
Constant Magnetic Field ◽  
Noise Analysis ◽  
Hamiltonian Path ◽  
Coordinate Space ◽  
Gauss Kernel ◽  
Dependent Potential ◽  
White Noise Distribution

The concepts of Hamiltonian Feynman integrals in white noise analysis are used to realize as the first velocity-dependent potential of the Hamiltonian Feynman integrand for a charged particle in a constant magnetic field in coordinate space as a Hida distribution. For this purpose the velocity-dependent potential gives rise to a generalized Gauss kernel. Besides the propagators, the generating functionals are obtained.

scholarly journals ON IRREDUCIBILITY OF THE ENERGY REPRESENTATION OF THE GAUGE GROUP AND THE WHITE NOISE DISTRIBUTION THEORY

2005 ◽  
Vol 08 (02) ◽  
pp. 153-177 ◽  
Author(s):  
YOSHIHITO SHIMADA
Keyword(s):  
Riemannian Manifold ◽  
Gauge Group ◽  
Lie Group ◽  
Compact Riemannian Manifold ◽  
Integral Kernel ◽  
Compact Lie Group ◽  
Noise Distribution ◽  
Kernel Operators ◽  
White Noise Distribution Theory ◽  
White Noise Distribution

We consider the energy representation for the gauge group. The gauge group is the set of C∞-mappings from a compact Riemannian manifold to a semi-simple compact Lie group. In this paper, we obtain irreducibility of the energy representation of the gauge group for any dimension of M. To prove irreducibility for the energy representation, we use the fact that each operator from a space of test functionals to a space of generalized functionals is realized as a series of integral kernel operators, called the Fock expansion.

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