Operator-valued Feynman integral via conditional Feynman integrals on a function space

• Autorzy: Dong Cho
• Języki publikacji: EN

Abstrakty

EN

Let C 0r [0; t] denote the analogue of the r-dimensional Wiener space, define X t: C r[0; t] → ℝ2r by X t (x) = (x(0); x(t)). In this paper, we introduce a simple formula for the conditional expectations with the conditioning function X t. Using this formula, we evaluate the conditional analytic Feynman integral for the functional $$ \Gamma _t \left( x \right) = exp \left\{ {\int_0^t {\theta \left( {s,x\left( s \right)} \right)d\eta \left( s \right)} } \right\}\varphi \left( {x\left( t \right)} \right) x \in C^r \left[ {0,t} \right] $$, where η is a complex Borel measure on [0, t], and θ(s, ·) and φ are the Fourier-Stieltjes transforms of the complex Borel measures on ℝr. We then introduce an integral transform as an analytic operator-valued Feynman integral over C r [0, t], and evaluate the integral transform for the function Γt via the conditional analytic Feynman integral as a kernel.

Słowa kluczowe

EN

Analogue of Wiener measure; Conditional analytic Feynman integral; Conditional analytic Wiener integral; Operator-valued Feynman integral; Simple formula for conditional expectation; Wiener space

Kategorie tematyczne

• 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 5
• Strony: 908-927

Daty

wydano

2010-10-01

online

2010-09-28

Twórcy

autor

Dong Cho

• Kyonggi University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0059-7