physics/9809032 1 Quantum theory of magnetic quadrupole lenses for spin- 2 particles∗ Sameen Ahmed KHAN Dipartimento di Fisica Galileo Galilei Universit`adiPadova Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Padova Via Marzolo 8 Padova 35131 ITALY E-mail:
[email protected], http://www.pd.infn.it/∼khan/welcome.html Abstract General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, 1 appropriate to the situation under study. In the context of spin-2 particles, these guidelines are used starting with the Dirac equation. The spinor the- ory just constructed is used to obtain the transfer maps for normal and skew magnetic quadrupoles respectively. As expected the traditional transfer maps get modified by the quantum contributions. The classical limit of the quan- tum formalism presented, reproduces the well-known Lie algebraic formalism of charged-particle beam optics. 1 Keywords: Beam physics, Beam optics, Accelerator optics, Spin- 2 particle, Anoma- lous magnetic moment, Quantum mechanics, Dirac equation, Foldy-Wouthuysen transformation, Polarization, Thomas-Bargmann-Michel-Telegdi equation, Magnetic quadrupole lenses, Stern-Gerlach kicks, Quantum corrections to the classical theory. PACS: 29.20.-c (Cyclic accelerators and storage rings), 29.27.-a (Beams in particle accelerators), 29.27.Hj (Polarized beams), 41.75.-i (Charged-particle beams), 41.75.Ht (Relativistic electron and positron beams), 41.85.-p (Beam optics), 41.85.Ja (Beam transport), 41.85.Lc (Beam focusing and bending magnets). ∗Presented at the Workshop on “Quantum Aspects of Beam Physics”, 15th ICFA (International Committee for Future Accelerators) Advanced Beam Dynamics Workshop, January 4–9, 1998, Mon- terey, California, U.S.A.