Sergio Giardino

We have built a constrained four-dimensional quaternion-parametrized conformal field theory using quaternion holomorphic functions as the generators of quaternionic conformal transformations. With the two-dimensional complex-parametrized conformal field theory as our model, we study the stress tensor, the conserved charge, the symmetry generators, the quantization conditions and several operator product expansions. Future applications are also addressed.

Holomorphic quaternion functions only admit affine functions; thus, the Möbius transformation for these functions, which we call quaternionic holomorphic transformation (QHT), only comprises similarity transformations. We determine a general group X which has the group G of QHT as a particular case. Furthermore, we observe that the Möbius group and the Heisenberg group may be obtained by making X more symmetric. We provide matrix representations for the group X and for its algebra x. The Lie algebra is neither simple nor semi-simple, and so it is not classified among the classical Lie algebras. We prove that the group G comprises SU(2,C) rotations, dilations and translations. The only fixed point of the QHT is located at infinity, and the QHT does not admit a cross-ratio. Physical applications are addressed at the conclusion.

A quaternionic analog of the Aharonov–Bohm effect is developed without the usual anti-hermitian operators in quaternionic quantum mechanics. A quaternionic phase links the solutions obtained to ordinary complex wave functions, and new theoretical studies and experimental tests are possible for them.

This study examines quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be understood as a correction to complex quantum mechanics, but it may also be a structure that can be used to study phenomena that cannot be described through the framework of complex quantum mechanics.

Using the WKB approximation we analyse the tunnelling of a pulsating string in deformed Minkowski spacetime.

The scattering of a Dirac particle has been studied for a quaternionic potential step. In the potential region an additional diffusion solution is obtained. The quaternionic solution which generalizes the complex one presents an amplification of the reflection and transmission rates. A detailed analysis of the quaternionic spinorial velocities shed new light on the additional solution. For pure quaternionic potentials, the interesting and surprising result of total transmission is found. This suggests that the presence of pure quaternionic potentials cannot be seen by analyzing the reflection or transmission rates. It has been observed by measuring the mean value of some operator.