We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane) fI CP 1 . We also extend this picture to the N = 2k superconformal mechanics described in terms of Lobache...

Over the past years, invisibility cloaks have been extensively discussed since transformation optics emerges. Generally, the electromagnetic parameters of invisibility cloaks are complicated tensors, yet difficult to realize. As a special method of transformation optics, conformal mapping helps us design invisibility cloak with isotropic materials of a refractive index distribution. However, fo...

The theorem of conformal equivalence points out conditions under which the Einstein Lagrangian plus scalar eld can be transformed con-formally into a Lagrangian of higher order. Here the conformal equivalence is investigated for the Friedman model if both theories are quantized. Therefore we introduce an intrinsic formalism to quantize the higher order theory in the framework of the Hamiltonian...

We apply the theory of transformation electromagnetics to source arrays and show that a complex conformal antenna array can be made to behave like a geometrically different array when surrounded with a properly designed transformation electromagnetics medium. Numerical simulations are presented to show how a nonuniform circular array can be made to radiate and receive as a uniformly spaced line...

In recent years, the use of conformal transformation techniques has become widespread in the literature on gravitational theories alternative to general relativity, on cosmology, and on nonminimally coupled scalar fields. Tipically, the transformation to the Einstein frame is generated by a fundamental scalar field already present in the theory. In this context, the problem of which conformal f...