Information metric from Riemannian superspaces

DIEGO JULIO CIRILO; VICTOR AFONSO

PHYSICS LETTERS A

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2012 p. 3599 - 3603

0375-9601

The Fisher information metric is introduced in order to find the meaning of the probability distribution in classical and quantum systems described by Riemannian non-degenerated superspaces. In particular, the physical rôle played by the coefficients a and a∗ of the fermionic part of an emergent metric solution, obtained previously (Cirilo-Lombardo, 2012 [1]) is explored. We find that the metric solution of the superspace establishes a connexion between the Fisher metric and its quantum counterpart, corroborating early conjectures by Caianiello et al. This quantum mechanical extension of the Fisher metric is described by the C P1 structure of the Fubini?Study metric, with coordinates a and a∗.