# Hidden symmetries of relativistic hydrogen atom

@article{Simulik2019HiddenSO, title={Hidden symmetries of relativistic hydrogen atom}, author={Volodimir Simulik}, journal={Journal of Physics: Conference Series}, year={2019} }

The Dirac equation in the external Coulomb field is proved to possess the symmetry determined by the 31 operators, which form the 31-dimensional algebra. Two different fermionic realizations of the SO(1,3) algebra of the Lorentz group are found. Two different bosonic realizations of this algebra are found as well. All generators of the above mentioned algebras commute with the operator of the Dirac equation in the external Coulomb field, and, therefore, determine the algebras of invariance of…

## One Citation

O ct 2 02 1 On the 256-dimensional gamma matrix representation of the Clifford algebra

- 2021

## References

SHOWING 1-10 OF 35 REFERENCES

Dirac equation and spin 1 representations, a connection with symmetries of the Maxwell equations

- Mathematics
- 1992

A unitary operator on the space of spinors that makes it possible to associate each transformation in this space with a transformation in the space of electromagnetic field strengths is found. A…

On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit

- Physics
- 1950

By a canonical transformation on the Dirac Hamiltonian for a free particle, a representation of the Dirac theory is obtained in which positive and negative energy states are separately represented by…

APPLICATION OF THE GENERALIZED CLIFFORD-DIRAC ALGEBRA TO THE PROOF OF THE DIRAC EQUATION FERMI-BOSE DUALITY

- Physics
- 2013

The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the…

The quantum theory of the electron

- Physics
- 1928

The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of…

The virial theorem and the Dirac H atom

- Physics
- 1982

The relativistic quantum‐mechanical analog of the virial theorem is formulated and used to solve the Dirac hydrogen atom in a simple way. In this manner the solutions are automatically classified…

SO(4) symmetry in the relativistic hydrogen atom

- Physics
- 2008

We show that the relativistic hydrogen atom possesses an SO(4) symmetry by introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is still preserved in the relativistic quantum…

Relation of charge independence and baryon conservation to Pauli’s transformation

- Physics
- 1958

(ricevuto il 5 Novcmbre 1957) FAULI (1) has recently introduced a 4-parameter group, isomorphic to the group of unitary 2 • 2 matrices, which leaves the neutrino equation invariant. These generalized…

On the Gamma Matrix Representations of SO(8) and Clifford Algebras

- MathematicsAdvances in Applied Clifford Algebras
- 2018

The gamma matrix representation of 28-dimensional SO(8) algebra, which contains the standard and additional spin operators, is under consideration. The 64-dimensional representations of the Clifford…

On the relativistic hydrogen atom

- Physics
- 1996

In the present article we revisit the problem of a relativistic Dirac electron. Using a second order formalism which reduces the problem of finding the energy spectrum to solving the Whittaker…