arXiv subjects
Publications and source records attributed to Hartmut Pilkuhn.
For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The operator's time dependence is generalized to a Klein-Gordon equation. It ensures relativistic kinematics in radiative decays. The new operator is not hermitian.
For the S-states of muonium and positronium, the hyperfine shifts to the order $α^6$ of a recently derived two-fermion equation with explicit $\cal CPT$-invariance are checked against the results of a nonrelativistic reduction, and the leading $α^8$ shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for $r\to 0$ of the Dirac hyperfine operator, such that the resulting extended operator can be used nonperturbatively. The binding correction to magnetic moments is mentioned.
For the S-states of positronium and muonium, the terms of an expansion of energy levels in powers of the fine structure constant $α$ are also members of a "recoil series". The first two terms of that series are calculated to all orders in $α$.
An eight-component formalism is proposed for the relativistic two-fermion problem. In QED, it extends the applicability of the Dirac equation with hyperfine interaction to the positronium case. The use of exact relativistic two-body kinematics entails a CP-invariant spectrum which is symmetric in the total cms energy. It allows the extension of recent α^6 recoil corrections to the positronium case, and implies new recoil corrections to the fine and hyperfine structures and to the Bethe logarithm.