# The Zeeman effect for the relativistic bound state

@article{Land1995TheZE, title={The Zeeman effect for the relativistic bound state}, author={Martin Land and Lawrence Paul Horwitz}, journal={Journal of Physics A}, year={1995}, volume={28}, pages={3289-3304} }

In the context of a relativistic quantum mechanics with invariant evolution parameter, solutions for the relativistic bound-state problem have been found, which yield a spectrum for the total mass coinciding with the non-relativistic Schrodinger energy spectrum. These spectra were obtained by choosing an arbitrary spacelike unit vector n, and restricting the support of the eigenfunctions in spacetime to the subspace of the Minkowski measure space, for which (Xperpendicular to )2=(x-(x.n)n)2>or…

## 19 Citations

### The unstable system in relativistic quantum mechanics

- Physics
- 1995

AbstractA soluble model for the relativistically covariant description of an unstable system is given in terms of relativistic quantum field theory, with a structure similar to Van Hove's…

### Spin, angular momentum and spin-statistics for a relativistic quantum many-body system

- Physics
- 2012

The adaptation of Wigner’s induced representation for a relativistic quantum theory making possible the construction of wave packets and admitting covariant expectation values for the coordinate…

### Off-Shell Quantum Electrodynamics

- Physics
- 1996

More than twenty years have passed since the threads of the `proper time formalism' in covariant classical and quantum mechanics were brought together to construct a canonical formalism for the…

### A chiral spin theory in the framework of an invariant evolution parameter formalism

- Physics
- 1997

We present a formulation for the construction of first-order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant…

### The Stueckelberg wave equation and the anomalous magnetic moment of the electron

- Physics
- 2012

The parametrized relativistic quantum mechanics of Stueckelberg (1942 Helv. Phys. Acta 15 23) represents time as an operator, and has been shown elsewhere to yield the recently observed phenomena of…

### Pre-Maxwell Electrodynamics

- Physics
- 1998

In the context of a covariant mechanics with Poincaré-invariant evolution parameter τ, Sa'ad, Horwitz, and Arshansky have argued that for the electromagnetic interaction to be well posed, the local…

### Particles and events in classical off-shell electrodynamics

- Physics
- 1997

Despite the many successes of the relativistic quantum theory developed by Horwitz et al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore…

### On Feynman's Approach to the Foundations of Gauge Theory

- Physics
- 1993

In 1948, Feynman showed Dyson how the Lorentz force law and homogeneous Maxwell equations could be derived from commutation relations among Euclidean coordinates and velocities, without reference to…

### Harmonic oscillator states with integer and non-integer orbital angular momentum

- Physics
- 2011

We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2),…

## References

SHOWING 1-10 OF 19 REFERENCES

### Selection rules for dipole radiation from a relativistic bound state

- Physics
- 1994

Recently, in the framework of a relativistic quantum theory with invariant evolution parameter, solutions have been found for the two-body bound state, whose mass spectrum agrees with the…

### The quantum relativistic two‐body bound state. I. The spectrum

- Physics
- 1989

In the framework of a manifestly covariant quantum theory on space‐time, it is shown that the ground state mass of a relativistic two‐body system with O(3,1) symmetric potential is lower when…

### On relativistic quantum theory for particles with spin 1/2

- Physics, Mathematics
- 1982

The authors study a family of Hilbert spaces with positive definite invariant scalar product for the quantum mechanical description of relativistic spin-1/2 particles. The Hermitian and…

### Solutions of the Relativistic Two-Body Problem. II. Quantum Mechanics

- Physics
- 1972

This paper discusses the formulation of a quantum mechanical equivalent of the relative time classical theory proposed in Part I. The relativistic wavefunction is derived and a covariant addition…

### Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction

- Physics
- 1950

The validity of the rules given in previous papers for the solution of problems in quantum electrodynamics is established. Starting with Fermi's formulation of the field as a set of harmonic…

### Space-Time Approach to Non-Relativistic Quantum Mechanics

- Physics
- 1948

Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which…

### The quantum relativistic two‐body bound state. II. The induced representation of SL(2,C)

- Mathematics, Physics
- 1989

It was shown in I [J. Math. Phys. 30, 66 (1989)] that the eigenfunctions for the reduced motion of the quantum relativistic bound state with O(3,1) symmetric potential have support in an O(2,1)…

### On gauge invariance and vacuum polarization

- Physics
- 1951

This paper is based on the elementary remark that the extraction of gauge invariant results from a formally gauge invariant theory is ensured if one employs methods of solution that involve only…

### 80 Years of Professor Wigner's Seminal Work "On Unitary Representations of the Inhomogeneous Lorentz Group"

- Physics
- 1939

It is perhaps the most fundamental principle of Quantum Mechanics that the system of states forms a linear manifold,1 in which a unitary scalar product is defined.2 The states are generally…

### Relativistic corrections to the Zeeman effect in hydrogenlike atoms and positronium.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1994

An approximately relativistic theory of bound states which ensures Poincare invariance of the atomic system to relative order and the Zeeman interaction Hamiltonian is derived for a two-body system.