Approaches To Path Integrals
Functional integrals where the space of integration are paths (ν = 1) can be defined in many different ways. The definitions fall in two different classes: the constructions derived from Wiener's theory yield an integral based on a measure; whereas the constructions following Feynman's path integral do not. Even within these two broad divisions, the integrals are not identical, that is, they are defined for different classes of functions.
Read more about this topic: Functional Integration
Famous quotes containing the words approaches to, approaches and/or path:
“Someone approaches to say his life is ruined
and to fall down at your feet
and pound his head upon the sidewalk.”
—David Ignatow (b. 1914)
“I should say that the most prominent scientific men of our country, and perhaps of this age, are either serving the arts and not pure science, or are performing faithful but quite subordinate labors in particular departments. They make no steady and systematic approaches to the central fact.... There is wanting constant and accurate observation with enough of theory to direct and discipline it. But, above all, there is wanting genius.”
—Henry David Thoreau (1817–1862)
“Childhood is an adventure both for children and for their parents. There should be freedom to explore and joy in discovery. The important discoveries for both parents and children seldom come at the points where the path is smooth and straight. It is the curves in that path to adventure that make the trip interesting and worthwhile.”
—Lawrence Kutner (20th century)