Giardino, S.
2017.
``Four-dimensional conformal field theory using quaternions''. Advances in Applied Clifford Algebras. 27(3):2457–2471.
AbstractWe 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.
Giardino, S.
2017.
``Möbius transformation for left-derivative quaternion holomorphic functions''. Adv. Appl. Clifford Algebras (aceito para publica\c cão). 27(2):1161–1173.
AbstractHolomorphic 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.
Giardino, S.
2017.
``Quaternionic Ahraronov-Bohm effect''. Adv. Appl. Clifford Algebras. 27(3):2445–2456.
AbstractA 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.
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