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Evaluation formulas for a conditional Feynman integral over Wiener paths in abstract Wiener space

Kun Soo Chang, Dong Hyun Cho, Il Yoo (2004)

Czechoslovak Mathematical Journal

In this paper, we introduce a simple formula for conditional Wiener integrals over C 0 ( 𝔹 ) , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on C 0 ( 𝔹 ) in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral...

Existence of skyrmions

Schmitt, Andreas (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Summary: We give an introduction to the Skyrme model from a mathematical point of view. Hereby, we show that it is difficult to solve the field equation even by means of the classical ansatz, the so-called hedgehog ansatz. Our main result is an extended existence proof for solutions of the field equation in the hedgehog ansatz.

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