Elementary Particles with Internal Structure in External Fields. Volume II. Physical Problems

Vasiliy Vasilievich Kisel

Elena Mikhaylovna Ovsiyuk
Mozyr State Pedagogical University, Belarus

Olga Vladimirovna Beko
Institute of Physics National Academy of Sciences of Belarus

Yana Aleksandrovna Voynova
Institute of Physics National Academy of Sciences of Belarus

Series: Computational Mathematics and Analysis
BISAC: SCI040000




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The book represents a systematical development of several rarely used or new mathematical techniques to construct new wave equations for elementary particles. On this ground, it develops the quantum mechanics of the particles with additional electromagnetic structures in presence of external electromagnetic fields, and, on the curved space-time background, it details many new exactly solvable problems in the field. In Volume II, the wave equations for particles of spin 0, 1/2, 1 with additional intrinsic structure (such as polarizability, anomalous magnetic moment, quadrupole electric moment, Darwin–Cox structure) are solved for several special types of external electric and magnetic fields, in Minkowski flat space and in spaces with simple non-Euclidean geometry: hyperbolic Lobachevsky and spherical Riemann models.

The main attention is focused on new and additional effects which are due to the more general structure of the wave equations in presence of external fields. The following problems are considered: reflection of spin 0 and spin 1 particles by an effective (geometrical) medium; Schrodinger and Dirac particles in electric field on the background of Lobachevsky and Riemann models (LR-models); Dirac-K¨ahler boson in LR-models; spinless particle with polarizability in Coulomb and magnetic fields; spin 1/2 particle with anomalous magnetic moment in homogeneous magnetic and electric fields, and in Coulomb field; spin 1 particle (ordinary and with polarizability) in external magnetic field; spin 1 particle with anomalous magnetic and quadrupole moment in magnetic and electric fields; spinless Darwin–Cox particle with intrinsic structure in external electric and magnetic fields in Euclid, Lobachevsky and Riemann models; fermion with two masses in presence of magnetic field.


Chapter 1. Fermions in Riemannian Space-Time

Chapter 2. Majorana Fermion and Pauli Approximation

Chapter 3. Boson Fields of Spin 1 and 0 in Curved Space-Time

Chapter 4. On Reflection of Fermions by Effective Medium

Chapter 5. Particles in Electric Field, Curved Space Models

Chapter 6. The Dirac–K¨ahler Particle in Curved Space

Chapter 7. Particle with Polarizability in Coulomb Field

Chapter 8. Scalar Particle with Polarizability in Magnetic Field

Chapter 9. Spin 1/2 Particle with Anomalous Magnetic Moment

Chapter 10. Spin 1/2 Particle in the Uniform Electric Field

Chapter 11. Particle of Spin 1/2 with anomalous magnetic moment in the Coulomb Field

Chapter 12. Spin 1 Particle in External Magnetic field

Chapter 13. Spin 1 Particle with Polarizability in Magnetic Field

Chapter 14. Spin 1 Particle, Anomalous Moment and Magnetic Field

Chapter 15. Spin 1 Particle in Electric field

Chapter 16. Scalar Cox’s Particle with Intrinsic Structure

Chapter 17. Spin 1/2 Particle with Two Masses in Magnetic Field


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