Namespaces
Variants
Actions

Fedosov trace formula

From Encyclopedia of Mathematics
Revision as of 17:17, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

An asymptotic formula as for the "localized" trace of the exponential of a Hamiltonian . The leading terms of this expansion can be calculated in terms of the fixed points of the classical Hamiltonian flow associated to (provided that it has only isolated fixed points, see below). Explicitly,

Here, the meaning of , and is the following. First, is a pseudo-differential operator with compactly supported Weyl symbol (cf. also Symbol of an operator). Let and be the homogeneous components of , and denote by the Hamiltonian flow associated to (cf. also Hamiltonian system). The formula above is proved under the assumption that, on the support of , the flow has only isolated fixed points, denoted by . Then and . See [a1].

References

[a1] B. Fedosov, "Trace formula for Schrödinger operator" Russian J. Math. Phys. , 1 (1993) pp. 447–463
How to Cite This Entry:
Fedosov trace formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fedosov_trace_formula&oldid=50490
This article was adapted from an original article by Victor Nistor (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article