A method of Foldy-Wouthuysen transformation for relativistic spin-1/2 particles in external fields is proposed. It permits determination of the Hamilton operator in the Foldy-Wouthuysen representation with any accuracy. Interactions between a particle having an anomalous magnetic moment and nonstationary electromagnetic and electroweak fields are investigated.

The behavior of spin−1/2 particle in a weak static gravitational field is considered. The Dirac Hamiltonian is diagonalized by the Foldy-Wouthuysen transformation providing also the simple form for the momentum and spin polarization operators. The operator equations of momentum and spin motion are derived for a first time. Their semiclassical limit is analyzed. The dipole spin-gravity coupling in the previously found (another) Hamiltonian does not lead to any observable effects. The general agreement between the quantum and classical analysis is established, contrary to several recent claims. The expression for gravitational Stern-Gerlach force is derived. The helicity evolution in the gravitational field and corresponding accelerated frame coincides, being the manifestation of the equivalence principle.

A new highly sensitive method of looking for electric dipole moments of charged particles in storage rings is described. The major systematic errors inherent in the method are addressed and ways to minimize them are suggested. It seems possible to measure the muon EDM to levels that test speculative theories beyond the standard model. PACS numbers: 13.40. Em, 12.60.Jv, 14.60.Ef, 29.20.Dh The existence of a permanent electric dipole moment (EDM) for an elementary particle would violate parity (P) and time reversal symmetry (T) [1]. Therefore under the assumption of CPT invariance, a non-zero EDM would signal CP violation. In the standard model, the electron EDM is < 10 −38 e · cm [2] with the muon EDM scaled up by the mass ratio m µ /m e , a factor of 207, but some new theories predict much larger values [3,4]. For example, ref.[4] predicts the muon EDM could be as large as 5 × 10 −23 e · cm, while the electron EDM is predicted to be ∼ 10 −28 e · cm, an order of magnitude below the present limit [5]. The current 95% confidence limit for the muon EDM is 10 −18 e·cm [6]. This paper discusses a new way of using a magnetic storage ring to measure the EDM of the muon, which also can be applied to other charged particles.To measure the EDM experimentally, the particle should be in an electric field which exerts a torque on the dipole and induces an observable precession of its spin. If the particle is charged this electric field inevitably accelerates the particle; it will move to a region where the field is zero or leave the scene. An example is the nucleus at the center of an atom in equilibrium; the net force and therefore the net electric field at the nucleus must average to zero according to Schiff's theorem [7]. Any applied external electric field will be shielded from the nucleus by the electrons in the atom. The overall effect is to suppress the EDM signal, making it more difficult to measure. The suppression would be total but for the many known exceptions to Schiff's theorem when weak and strong forces, weak electron-nucleon forces, finite particle sizes, and relativistic effects are included. Suppression of the EDM signal by Schiff's theorem is completely avoided in a magnetic storage ring [8,9] such as proposed here, because the particle is not in equilibrium; there is a net centripetal force, and this force is entirely supplied by a net electric field as seen in the muon rest frame.In particular, when a muon of velocity β = v/c and relativistic mass factor γ = (1 − β 2 ) − 1 2 is circulating in a horizontal plane due to a vertical magnetic field B, it will according to a Lorentz transformation experience both an electric and a magnetic field, E * and B * , in its own rest frame. The so-called motional electric field, E * = γc β × B, can be much larger than any practical applied electric field. Its action on the particle supplies the radial centripetal force, Thomas spin precession, and spin precession due to any non-vanishing EDM. B * produces precession due to the muon magnetic moment. The combined spi...

A general method of the Foldy-Wouthyusen ͑FW͒ transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite commutation relations between even and odd operators. The final FW Hamiltonian can be expanded into a power series in the Planck constant which characterizes the order of magnitude of quantum corrections. Exact expressions for low-order terms in the Planck constant can be derived. Finding these expressions allows one to perform a simple transition to the semiclassical approximation which defines a classical limit of the relativistic quantum mechanics. As an example, interactions of spin-1/2 and scalar particles with a strong electromagnetic field have been considered. Quantum and semiclassical equations of motion of particles and their spins have been deduced. Full agreement between quantum and classical theories has been established.

The cryogenic storage ring CSR Review of Scientific Instruments 87, 063115 (2016); https://doi