## 20 Citations

### Quaternionic wave function

- PhysicsInternational Journal of Modern Physics A
- 2019

We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence…

### n-Regular functions in quaternionic analysis

- MathematicsInternational Journal of Mathematics
- 2021

In this paper, we study left and right [Formula: see text]-regular functions that originally were introduced in [I. Frenkel and M. Libine, Quaternionic analysis, representation theory and physics II,…

### Quaternionic scalar field in the real hilbert space

- MathematicsInternational Journal of Modern Physics A
- 2022

Using the complex Klein-Gordon ﬁeld as a model, we quantize the quaternionic scalar ﬁeld in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the…

### Perturbative 4D conformal field theories and representation theory of diagram algebras

- Mathematics
- 2020

The correlators of free four dimensional conformal field theories (CFT4) have been shown to be given by amplitudes in two-dimensional so (4 , 2) equivariant topological field theories (TFT2), by…

### The Poisson Integral Formula and Representations of SU(1,1)

- Mathematics
- 2011

We present a new proof of the Poisson integral formula for harmonic functions using the methods of representation theory. In doing so, we exhibit the irreducible subspaces and unitary structure of a…

### Magic identities for the conformal four-point integrals; the Minkowski metric case

- MathematicsJournal of Functional Analysis
- 2020

### Low-dimensional dynamics in non-Abelian Kuramoto model on the 3-sphere.

- MathematicsChaos
- 2018

This paper states that these generalized oscillators evolve by the action of the group GH of (quaternionic) Möbius transformations that preserve S3 that satisfy a certain system of quaternion-valued ordinary differential equations, that is an extension of the Watanabe-Strogatz system.

### A corresponding Cullen-regularity for split-quaternionic-valued functions

- Mathematics
- 2017

*Correspondence: jeunkim@pusan.ac.kr Department of Mathematics, Dongguk University, Gyeongju-si, 38066, Republic of Korea Abstract We give a representation of the class of Cullen-regular functions in…

### Stability Analysis of Quaternion-Valued Neural Networks: Decomposition and Direct Approaches

- Mathematics, EngineeringIEEE Transactions on Neural Networks and Learning Systems
- 2018

The global stability of quaternion-valued neural networks (QVNNs) with time-varying delays is investigated directly by the techniques of the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) whereQuaternion self-conjugate matrices and quaternions positive definite matrices are used.

### A corresponding Cullen-regularity for split-quaternionic-valued functions

- Mathematics
- 2017

We give a representation of the class of Cullen-regular functions in split-quaternions. We consider each Cullen’s form of split-quaternions, which provides corresponding Cauchy-Riemann equations for…

## References

SHOWING 1-10 OF 58 REFERENCES

### Quaternionic analysis

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1979

The richness of the theory of functions over the complex field makes it natural to look for a similar theory for the only other non-trivial real associative division algebra, namely the quaternions.…

### Analytic continuation of the holomorphic discrete series of a semi-simple Lie group

- Mathematics
- 1976

O. Introduction In this paper, we are mainly interested in the construction of certain Hilbert spaces of holomorphic functions on an irreducible hermitian symmatric space D = G/K on which G acts by a…

### Analysis on the minimal representation of O(p;q) { I. Realization via conformal geometry

- Mathematics
- 2001

### Analysis on the minimal representation of

- Mathematics
- 2002

For the group O(p;q) we give a new construction of its minimal unitary represen- tation via Euclidean Fourier analysis. This is an extension of the q = 2 case, where the representation is the mass…

### On the Role of Division, Jordan and Related Algebras in Particle Physics

- Mathematics
- 1996

Part 1 Quaternions: algebraic structures Jordan formulation, H-Hilbert spaces and groups vector products, parallelisms and quaternionic manifolds quaternionic function theory arithmetics of…

### Special Functions and the Theory of Group Representations

- Mathematics
- 1968

A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible…

### The Two-Loop Ladder Diagram and Representations of U(2,2)

- Physics
- 2013

Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to…