Feynman measure
From Encyclopedia of Mathematics
A complex pre-measure defined on cylindrical sets in the space of functions ,
,
, with values in
,
by the formula
![]() | (1) |
![]() |
Here is a parameter,
, and
![]() |
![]() |
![]() |
where is some Borel subset in
. Sometimes one also considers the so-called conditional Feynman measure
obtained from the measure (1) by restricting it to the set of trajectories with "end" at the point
:
. The measure
, and also
, was introduced by R.P. Feynman in connection with representing the semi-group
, where
is a Sturm–Liouville operator, in the form of a path integral — a Feynman integral.
References
[1] | R.P. Feynman, "Space-time approach to non-relativistic quantum mechanics" Rev. Modern Phys. , 20 (1948) pp. 367–387 |
[2] | Yu.L. Daletskii, "Integration in function spaces" Progress in Mathematics , 4 (1969) pp. 87–132 Itogi Nauk. Mat. Anal. 1966 (1967) pp. 83–124 |
[3] | S.A. Albeverio, R.J. Høegh-Krohn, "Mathematical theory of Feynman path integrals" , Springer (1976) |
How to Cite This Entry:
Feynman measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Feynman_measure&oldid=46916
Feynman measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Feynman_measure&oldid=46916
This article was adapted from an original article by R.A. Minlos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article