Quantum Oscillations: A simple principle underlying important aspects of physics

✍ Scribed by Fumihiko Suekane

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 177
• Series: Lecture Notes in Physics, 985; 985
• Edition: 1st ed. 2021
• Category: Library

✦ Synopsis

This book addresses various aspects of physics, using Quantum oscillation (QO) as a common denominator. QO plays an important role in many aspects of physics, such as the Weinberg angle, Caribbo angle, neutrino oscillation, K⁰ oscillation and CP violation, mass generation by the Higgs field, hadron mass pattern, lepton anomalous magnetic moment, spin precession, hydrogen HI line, etc.

Usually, these subjects are taught separately. As such, this book allows readers to learn about a wide range of physics subjects in a unified manner and to gain farther-reaching perspectives. The readers may be surprised at the fact that different looking physics are actually closely related with each other. They will also find essential information on quantum mechanics at the heart from many concrete examples. Though the book is mainly intended for graduate students of particle, nuclear and astrophysics, undergraduate students and researchers will also benefit from the content.

✦ Table of Contents

Preface
Acknowledgements
Contents
1 Basics of the Quantum Oscillation
1.1 Introduction
1.2 State Mixing and Quantum Oscillation
1.2.1 Transition
1.2.2 Mass Eigenstate
1.2.3 Quantum Oscillation
Part IElectromagnetic Interactions
2 Motion of Electron Spin in Magnetic Fields
2.1 Introduction
2.2 Spin-1/2 and Magnetic Field
2.3 The Pauli Equation
2.3.1 Empirical Derivation of the Pauli Equation
2.3.2 Derivation of the Pauli Equation from the Dirac Equation
2.3.3 Physical Meaning of the Pauli Equation
2.4 Spin Motion in the Magnetic Field "0245B=(0,0,B); The Simplest Case
2.4.1 Energy Eigenstate
2.4.2 Spin Precession
2.5 Spin Motion in Magnetic Field "0245B=(B,0,0)
2.5.1 Energy Eigenstates
2.5.2 Oscillation and Precession
2.6 Spin Motion in Magnetic Field "0245B=(0,B,0)
2.6.1 Energy Eigenstates
2.6.2 Oscillation and Precession
2.7 Spin Motion in an Arbitrary Magnetic Field: "0245B=(Bx,By,Bz)
2.7.1 Energy Eigenstate
2.7.2 Oscillation and Precession
2.8 If Electron Mass is Included
3 Hydrogen Hyperfine Splitting and HI Line
3.1 Introduction
3.2 Spin Structure of the Hydrogen Atom
3.2.1 Oscillation Between |"322A37E "322B37F rangle and |"322B37F "322A37E rangle States
3.3 Hydrogen Magnetic Moment Under External Magnetic Field
3.4 Hydrogen 21cm Line
4 Anomalous Magnetic Moment
4.1 Introduction
4.2 Helicity Conservation
4.2.1 Anomalous Magnetic Moment
4.2.2 Measurements
5 Positronium
5.1 Introduction
5.2 HK: e+-e- Binding State by Electrostatic Potential
5.2.1 HM: MM-MM Interactions
5.2.2 HA: Pair Annihilation and Creation
5.2.3 HM+HA: Both Effects
Part IIHiggs Field
6 Weinberg Angle
6.1 Introduction
6.2 General Formula of Electromagnetic and Weak Interactions
6.2.1 Correspondence to Photon and Z0
6.3 The Origin of the Vector Boson Transitions; Higgs Field
6.4 Chirality Dependence of the Weak Interactions
6.5 Test of the Electroweak Theory
6.5.1 Measurements of sin2 θW
6.5.2 Test of the Electroweak Theory
7 Fermion Mass and Chirality Oscillation
7.1 Introduction
7.2 Chirality
7.3 Dirac Equation as Chirality Transition Equation
7.4 Decay Effect
8 Quark Mass, Cabibbo Angle and CKM Mixing Matrix
8.1 Introduction
8.2 Four-Quark System and Cabibbo Angle, θC
8.2.1 Quark Flavor Oscillation
8.2.2 Uncertainty Principle
8.3 Six-Quark System
8.3.1 Measurement of the CKM Matrix Elements
8.3.2 Transition Amplitude Gαβ
8.3.3 Quark Flavor Oscillation
Part IIIWeak Interactions
9 K0-overlineK0 Oscillation and CP Violation
9.1 Introduction
9.2 K0-overlineK0 Oscillation and Prediction of the Charm Quark Mass
9.3 Six-Quark System and CP Violation
9.3.1 K0-overlineK0 Oscillation of Six-Quark System
9.3.2 Oscillation of K0 CP Eigenstate
9.4 Discovery of CP Violation and Measurement of α
Part IVStrong Interactions
10 Quark Structure of Mesons
10.1 Introduction
10.2 u, d, s-Quark Masses
10.3 π+-ρ+ Mass Difference
10.4 Structure of ρ0,ω and φ
10.4.1 Mixing Between |uoverlineurangle and |doverlinedrangle
10.4.2 Mixing Between |soverlinesrangle and |uoverlineurangle, |doverlinedrangle Systems
10.4.3 Experimental Confirmation of the Vector Meson Structure
10.5 Structure of π0, η and η'
10.6 Color Structure of Meson
11 Quark Structure of Baryons
11.1 Introduction
11.2 Totally Antisymmetric State
11.3 Δ++ Baryon
11.3.1 Δ+ Baryon
11.4 Spin-1/2 Baryon
11.4.1 Why Spin-1/2 (uuu) Baryon Does Not Exist?
11.4.2 Quark Structure of Proton
11.4.3 Λ, Σ0 and Σ0*
11.5 Isospin
Part VUnknown Origin
12 Neutrino Oscillation: Relativistic Oscillation of Three-Flavor System
12.1 Introduction
12.2 Two-Flavor Oscillation
12.2.1 Neutrino Transition Amplitudes
12.2.2 Oscillation
12.2.3 Relativistic Oscillation Probability
12.2.4 Another Way to Derive Relativistic Neutrino Oscillation
12.2.5 A Relation Between Transition Amplitudes and Neutrino Flavor Mass
12.3 Three-Flavor Neutrino Oscillation
12.4 Measurements of Oscillation Parameters
12.4.1 θ23 and Δm232
12.4.2 θ12 and Δm122
12.4.3 θ13
12.4.4 δ
12.4.5 Summary of the Measurements
A Appendix A: Summary of Parameters and Formulas
A.1 Physics Parameters
A.2 Spinors
A.3 Pauli Matrix
A.4 Dirac Matrix
A.5 Dirac Equation
A.6 Two Spin Interaction
B Appendix B
B.1 Summary of Two Body Oscillation Formula
B.2 How to Solve the Generalized Pauli Equation
B.3 Wave Functions That Satisfy the Pauli Equation
B.3.1 Energy Eigenstate
B.3.2 Oscillation
C Appendix C
C.1 Summary of Oscillations and Mixings
Index
Index