Scale symmetry in classical and quantum mechanics

Scale symmetry in classical and quantum mechanics

In this paper we address again the issue of the scale anomaly in quantum mechanical models with inverse square potential. In particular we examine the interplay between the classical and quantum aspects of the system using in both cases an operatorial approach.

PT symmetry in classical and quantum statistical mechanics.

PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. PT-symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The...

Classical Mechanics and Κ-symmetry

In this letter we analyze two local extensions of a model introduced some time ago to obtain a path integral formalism for Classical Mechanics. In particular, we show that these extensions exhibit a nonrelativistic local symmetry which is very similar to the well known κ-symmetry introduced in the literature almost 20 years ago. Differently from the latter, this nonrelativistic local symmetry g...

Symmetry in quantum mechanics

Symmetry in quantum mechanics