IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Optimal Paths for Symmetric Actions in the Unitary Group
Autor/es:
JORGE ANTEZANA; GABRIEL LAROTONDA; ALEJANDRO VARELA
Revista:
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Editorial:
SPRINGER
Referencias:
Lugar: Berlin; Año: 2014 vol. 328 p. 481 - 481
ISSN:
0010-3616
Resumen:
Given a positive and unitarily invariant Lagrangian L defined in the space of Hermitian matrices, and a fixed interval [a,b] in R, we study the action defined in the Lie group of n x n unitary matrices U(n) by$$S(c)=int_a^b L(dot{c})$$where c:[a,b] --> U(n) is a rectifiable curve. We prove that the one-parameter subgroups of U(n) are the optimal paths, provided the spectrum of the exponent is bounded by $pi$.  Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in U(n) as well as angular metrics in the Grassmann manifold.