diffeomorphism

(redirected from Diffeomorphism group)

diffeomorphism

[‚dif·ē·ə′mȯr·fiz·əm]
(mathematics)
A bijective function, with domain and range in the same or different Euclidean spaces, such that both the function and its inverse have continuous mixed partial derivatives of all orders in neighborhoods of each point of their respective domains.
References in periodicals archive ?
Beyond its importance in mathematical physics, it appears also as a geodesic equation on diffeomorphism group of a circle with right invariant [L.sup.2] metric (see [15] and references therein).
It is believed that LQG can unify all presently known interactions by implementing their common symmetry group, the four-dimensional diffeomorphism group, which is almost completely broken in perturbative approaches.
But there is a globally defined symmetry group, which is an invariance group of GR, namely the diffeomorphism group, diff, which, from the local point of view, is the active version of local coordinate transformations.
Physics extensively uses "infinite" groups: the gauge groups in Particle Physics; the diffeomorphism group, the Bondi-Metzner-Sachs group, and so on in general relativity; the Kac-Moody and loop groups in string theories; and so on are all infinite dimensional.
The monograph explores Fredholm properties and index theory, uniform structures of Clifford bundles, ILH diffeomorphism groups, Lie groups of Fourier integral operators, Teichmuller theory, functional algebraic topology, and relative zeta functions.