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El. knyga: New Perspectives On Einstein's E = Mc2

(Univ Of Maryland, Usa), (New York Univ, Usa)
  • Formatas: 200 pages
  • Išleidimo metai: 18-Sep-2018
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789813237728
Kitos knygos pagal šią temą:
New Perspectives On Einstein's E = Mc2Didesnis paveikslėlis
  • Formatas: 200 pages
  • Išleidimo metai: 18-Sep-2018
  • Leidėjas: World Scientific Publishing Co Pte Ltd
  • Kalba: eng
  • ISBN-13: 9789813237728
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Einstein's energy–momentum relation is applicable to particles of all speeds, including the particle at rest and the massless particle moving with the speed of light. If one formula or formalism is applicable to all speeds, we say it is "Lorentz-covariant." As for the internal space-time symmetries, there does not appear to be a clear way to approach this problem. For a particle at rest, there are three spin degrees of freedom. For a massless particle, there are helicity and gauge degrees of freedom. The aim of this book is to present one Lorentz-covariant picture of these two different space-time symmetries. Using the same mathematical tool, it is possible to give a Lorentz-covariant picture of Gell-Mann's quark model for the proton at rest and Feynman's parton model for the fast-moving proton. The mathematical formalism for these aspects of the Lorentz covariance is based on two-by-two matrices and harmonic oscillators which serve as two basic scientific languages for many different branches of physics. It is pointed out that the formalism presented in this book is applicable to various aspects of optical sciences of current interest.

Preface v
1 Introduction
1(8)
1.1 Dirac's Approach
2(1)
1.2 Feynman's Approach
3(2)
1.3 Wigner's Little Groups
5(1)
1.4 Scope of This Book
6(3)
2 Einstein's Philosophical Base
9(12)
2.1 Introduction
10(1)
2.2 Geographic Origin of Kantianism and Taoism
11(2)
2.3 Kantian Influence on Einstein
13(3)
2.4 Hegelian Approach to the History of Physics
16(1)
2.5 Einstein between Kant and Hegel
17(1)
2.6 Born's Reciprocity Principle
18(1)
2.7 Einstein and Yukawa
18(3)
3 More about Einstein
21(12)
3.1 Einstein's Bern, the Birth Place of E = mc2
22(3)
3.2 Einstein's Contribution to Quantum World
25(3)
3.3 Experimental Verification of Einstein's Special Relativity
28(5)
4 Einstein in the United States
33(20)
4.1 Einstein in Princeton
34(2)
4.2 Einstein's House
36(4)
4.3 Einstein in Washington
40(3)
4.4 Einstein and the First Nuclear Bomb
43(5)
4.5 Heisenberg on Einstein
48(5)
5 Introduction to the Lorentz Group
53(12)
5.1 Lie Algebra of the Lorentz Group
54(2)
5.2 2×2 Representation of the Lorentz Group
56(3)
5.3 Four-vectors in the 2×2 Representation
59(2)
5.4 Subgroups of the Lorentz Group
61(1)
5.5 Transformation Properties in the 2×2 Representation
62(1)
5.6 Decompositions of the SL(2, c) Matrices
63(2)
6 Wigner's Little Groups
65(20)
6.1 Introduction
67(3)
6.2 Wigner's Little Groups
70(3)
6.3 Massless Particles
73(2)
6.4 Spin-1/2 Particles
75(3)
6.5 Massless Particle as a Limiting Case of a Massive Particle
78(4)
6.6 Continuity Problem
82(3)
7 Lorentz Completion of the Little Groups
85(20)
7.1 Introduction
86(1)
7.2 Loop Representation of Wigner's Little Groups
87(3)
7.3 Parity, Time Reversal, and Charge Conjugation
90(2)
7.4 Dirac Matrices as a Representation of the Little Group
92(3)
7.5 Polarization of Massless Neutrinos
95(1)
7.6 Scalars, Vectors, and Tensors
96(9)
7.6.1 Four-vectors
98(2)
7.6.2 Second-rank Tensor
100(2)
7.6.3 Higher Spins
102(3)
8 Lorentz-covariant Harmonic Oscillators
105(22)
8.1 Introduction
105(2)
8.2 Dirac's Approach to Lorentz-covariant Wave Functions
107(2)
8.3 Running Waves and Standing Waves
109(4)
8.4 Little Groups for Relativistic Extended Particles
113(2)
8.5 Transformation Properties of the Covariant Oscillator Wave Functions
115(2)
8.6 Lorentz Contraction of Harmonic Oscillators
117(2)
8.7 Physical Principles in Quantum Field Theory and in Covariant Oscillator Formalism
119(5)
8.7.1 Physical Principles in Quantum Field Theory
122(1)
8.7.2 Physical Principles in the Covariant Oscillator Formalism
123(1)
8.8 Further Field Theoretic Concepts in the Covariant Oscillator Formalism
124(3)
9 Quarks and Partons
127(20)
9.1 Introduction
127(1)
9.2 Evolution of the Hydrogen Atom
128(2)
9.3 Lorentz-covariant Quark Model
130(1)
9.4 Feynman's Parton Picture
131(5)
9.5 Proton Structure Function
136(3)
9.6 Proton Form Factor and Lorentz Coherence
139(4)
9.7 Coherence in Momentum-Energy Space
143(4)
10 Feynman's Rest of the Universe
147(20)
10.1 Introduction
148(3)
10.2 Coupled Oscillators and Covariant Oscillators
151(2)
10.3 Entangled Oscillators
153(2)
10.4 Density Matrix and Entropy
155(1)
10.5 Entropy and Lorentz Transformation
156(3)
10.6 Hadronic Temperature
159(2)
10.7 Quark-Parton Phase Transitions
161(1)
10.8 Wigner Functions and Uncertainty Relations
162(3)
10.9 Lorentz-invariant Uncertainty Relation
165(2)
11 Further Applications of the Lorentz Group
167(8)
11.1 Ray Optics
168(1)
11.2 Polarization Optics
169(2)
11.3 Coherent States and Squeezed States
171(2)
11.4 Entanglement Problems
173(2)
Bibliography 175
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