Fields of Particles with Spin, Theory and Applications / Alina Ivashkevich.

Format:

Book

Author/Creator:

Ivashkevich, A. V. (Alina V.), author.

Series:

Physics research and technology.

Physics Research and Technology Series

Language:

English

Subjects (All):

Nuclear spin.

Particles (Nuclear physics)--Helicity.

Particles (Nuclear physics).

Physical Description:

1 online resource (454 pages)

Edition:

First edition.

Place of Publication:

New York : Nova Science Publishers, Inc., [2023]

Summary:

"The present book is devoted to the study the particles with spins in external fields and non- Euclidean space-time background. The key problems are: Coulomb task for a spin 1/2 particle and Heun equation; the hydrogen atom in de Sitter space; the fermion doublet in the non-Abelian monopole field and Pauli approximation; Pauli approximation for spin 1/2 and 1 particles in de Sitter space; the Dirac and Majorana particles in Schwarzschild space; the Dirac - Maxwell fields and spinor space structure; particles with spin 3/2, solutions with different symmetries and eliminating the gauge degrees of freedom in massless case; the matrix 30-component equation for a spin 2 field in Riemannian space-time; Finslerian geometzization of physical problems. The book may be of interest to researchers; it may serve as a pedagogical tool for either self study or in courses at both the undergraduate and graduate level"-- Provided by publisher.

Contents:

Intro

Fields of Particles with Spin,Theory and Applications

Contents

Preface

Introduction

Chapter 1Confluent Heun Functions and theCoulomb Problem for Spin 1/2 Particle

1.1 The Coulomb Problem: Solutions Constructed byHypergeometricand Partially by Heun Functions

1.2 Standard Treatment of the Coulomb Problem

1.3 Solutions Constructed Completely in Terms ofHeun Functions

Chapter 2Spin 1/2 Particle in 2D Spaces ofConstant Curvature, inPresence of Magnetic Field

2.1 Cylindric and Conformal Coordinates in Lobachevsky PlaneH2

2.2 Landau Problem for a Scalar Particle in the Plane H2

2.3 Dirac Particle in (x, y) Coordinates, Model H2

2.4 Landau Problem in the Spherical Model S2, Coordinates(r,˚)

2.5 Complex Poincar´e Half-Plane for Spherical 2-Space

Chapter 3Hydrogen Atom in Static de SitterSpaces

3.1 Separation of the Variables in dS Space

3.2 Qualitative Discussion

3.3 Reducing Radial Equation to the General Heun Equation

3.4 Semi-Classical Study

3.5 The Hydrogen Atom in AdS Space

3.6 Qualitative Study of the Problem in AdS Space

3.7 Semi-Classical Study for AdS Space

3.8 Spin 1/2 Particle in dS and AdS Spaces

Chapter 4Scalar Particle in Non-Static de SitterSpaces

4.1 Nonrelativistic Approximation, and Riemann Geometry

4.2 Schr¨odinger Equation in de Sitter Non-Static Models

4.3 Solving Equations

4.4 Klein-Gordon-Fock Equation in Curved Space-Time

4.5 Solving Equation in Expanding de Sitter Metric

4.6 Solving Equation in Oscillating de Sitter Metric

Chapter 5Spin 1/2 Particle in Nonstatic de SitterSpaces, Spherical Coordinates

5.1 Particle in Expanding de Sitter Model

5.2 Neutrino in Expanding de Sitter Space

5.3 Pauli Equation in Expanding de Sitter Space

5.4 Spin 1/2 Particle in Oscillating de Sitter Model.

5.5 Pauli Equation in Oscillating de Sitter Space

Chapter 6Spin 1/2 Particle in Non-static de SitterModels, Quasi-Cartesian Coordinates

6.1 Separation of the Variables in the Dirac Equation

6.2 Solving Equations in the Time Variable t

6.3 Behavior of Solutions in the Variable t Nearthe Points cos(t) = 0

6.4 Constructing Solutions in the Variable z

6.5 Majorana Spinor Field

6.6 Independent Majorana Components

Chapter 7The Fermion Doublet in Non-AbelianMonopole Field, Pauli Approximation,Geometry

7.1 Pauli Equation for Fermion Doublet, GeneralAnalysis

7.2 Non-Abelian Monopole in Schwinger Gauge

7.3 Separating the Variables

7.4 Nonrelativistic Approximation, the Case j = 0

7.5 Nonrelativistic Approximation, the Case j &gt

0

7.6 The Doublet in the Spaces of Constant Curvature

7.7 Geometrization of the Monopole Problem, KCC-Invariants

7.8 The Euclidean Space

7.9 Riemannian Space

7.10 Lobachevsky Space

7.11 Pure Monopole BPZ-Solution, Euclidean Space

7.12 Geometrizing the Doublet Problem, the Case j = 0

7.13 Non-Relativistic Approximation, the Case j &gt

Chapter 8To Analysis of the Dirac and MajoranaParticle in Schwarzschild Field

8.1 Dirac and Weyl Equations in External Gravitational Field

8.2 Majorana Spinor Fields

8.3 Spin 1/2 Particle in Schwarzschild Field

8.4 Separation of the Variables

8.5 The Case of Majorana Particle

8.6 Qualitative Study

8.7 Analytical Treatment

8.8 Structure of the Power Series

8.9 General Study of the Tunneling Effect

8.10 Geometrization of the Maxwell and Dirac Theories inSchwarzschield Space-Time

Chapter 9Dirac Particle in Cylindric ParabolicCoordinates and SpinorSpace Structure

9.1 Spinor Structure and Solutions of the Klein-Gordon-FockEquation

9.2 Solutions of the Klein-Gordon-Fock Equation and Spinors.

9.3 The Dirac Particle and the Space with Spinor Structure

Chapter 10Maxwell Equations in Space withSpinor Structure

10.1 Spinor Form of Maxwell Equations

10.2 Cylindrical Parabolic Coordinates

10.3 Continuity and Spinor Space Structure

10.4 Helicity Operator

Chapter 11Geometrization of MaxwellElectrodynamics

11.1 Optics and Lagrange Formalism

11.2 The Euler-Lagrange Equations

Chapter 12Finslerian Geometrization for theProblemof a Vector Particle in ExternalCoulomb Field

12.1 Setting the Problem

12.2 KCC-Invariants

12.3 Second KCC-Invariant

12.4 Natural Splitting 4+4

12.5 Natural Splitting, Real-Valued Representation

12.6 Projections of 8 Equations on Different Planes

Chapter 13The Study of a Spin 1 Particle withAnomalous MagneticMoment in the Coulomb Field

13.1 Separation of the Variables

13.2 The Case of Minimal j = 0

13.3 The Non-Relativistic Approximation at j = 0

13.4 Non-Relativistic Equations, j = 1,2,3, ...

13.5 KCC-Geometrical Approach to the Problem

Chapter 14Vector Particle with Electric QuadrupleMoment in the Coulomb Field

14.1 Initial Equation

14.2 Separating the Variables in the Relativistic Equation

14.3 States with Parity P = (−1) j+1

14.4 The Case of Minimal j = 0

14.5 Non-Relativistic Approximation, P =(−1) j+1, j =1,2,3, ...

14.6 Non-Relativistic Radial Equations, the Case of j=1,2,3, ...

14.7 KCC-Geometrical Approach

Chapter 15Massive and Massless Fields with Spin3/2, Solutions andHelicity Operator

15.1 Massive and Massless Spin 3/2 Fields

15.2 Separating the Variables

15.3 Helicity Operator

15.4 Helicity Operator and Solutions of the Wave Equation

15.5 The Plane Wave Solutions in Massless Case

15.6 Relation to Initial Basis

15.7 Helicity Operator.

Chapter 16Solutions with Spherical Symmetry fora Massive Spin 3/2 Particle

16.1 System of Equations and Spherical Symmetry

16.2 Separating the Variables

16.3 Separating the Variables and Additional Constraints

16.4 Solving Equations for Functions f0,g0

16.5 The Matrix Form of the Main System

16.6 The Case of Minimal Value j = 1/2

16.7 Studying General Case j = 3/2,5/2, ...

16.8 Further Study of the Solutions

16.9 Accounting for Algebraic and Differential Constraints

Chapter 17Massless Spin 3/2 Field, SphericalSolutions, Exclusion of theGauge Degrees of Freedom

17.1 Massless Spin 3/2 Particle, General Theory

17.2 Separation of the Variables

17.3 Gradient Type Solutions

17.4 Solving the System of Radial Equations

17.5 Solving the Homogeneous Equations

Chapter 18Spin 3/2 Massless Field, CylindricSymmetry, Eliminating theGauge Degrees of Freedom

18.1 Separating the Variables

18.2 Massless Field

18.3 Gauge Solutions

18.4 Solving the Second Order Equations, the First Order Constraints

Chapter 19On the Matrix Equation for a Spin 2Particle in Riemannian Space-Time,Tetrad Method

19.1 The Spin 2 Particle in Minkowski Space

19.2 Structure of the Matrices of the First Order System for aSpin 2 Field

19.3 Extension to Riemannian Space-Time Geometry

19.4 The Spin 2 Field in Cylindrical Coordinates

19.5 The Equation in Spherical Coordinates

19.6 The Structure of the Lorentzian Generators

19.7 Relativistic Invariance, Additional Checking

19.8 Matrix Blocks in the Theory of Spin 2 Particle

Conclusion

Bibliography

Index

Blank Page.

Notes:

Description based on print version record.

Includes bibliographical references and index.

Other Format:

Print version: Ivashkevich, Alina Fields of Particles with Spin, Theory and Applications

ISBN:

979-88-911-3113-2