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Waves, Particles and Fields: Introducing Quantum Field Theory [Pehme köide]

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(Fischer-Cripps Laboratories Pty Ltd, Sydney, Australia)
  • Formaat: Paperback / softback, 338 pages, kõrgus x laius: 254x178 mm, kaal: 676 g, 6 Tables, black and white; 103 Illustrations, black and white
  • Ilmumisaeg: 06-Jul-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367198762
  • ISBN-13: 9780367198763
Teised raamatud teemal:
Waves, Particles and Fields: Introducing Quantum Field TheorySuurem pilt
  • Formaat: Paperback / softback, 338 pages, kõrgus x laius: 254x178 mm, kaal: 676 g, 6 Tables, black and white; 103 Illustrations, black and white
  • Ilmumisaeg: 06-Jul-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367198762
  • ISBN-13: 9780367198763
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367198763.html
Märksõnad:
This book fills a gap in the middle ground between the transition from the quantum mechanics of a single electron, to the concept of a quantum field. In doing so, the book is divided into two parts; the first provides the necessary background to quantum theory extending from Planck’s formulation of black body radiation to Schrodinger’s equation; and the second part explores Dirac’s relativistic electron to quantum fields, finishing with an description of Feynman diagrams and their meaning. Much more than a popular account, yet not too heavy so as to be inaccessible, this book assumes no prior knowledge of quantum physics or field theory and provides the necessary foundations for readers to then progress to more advanced texts on quantum field theory. It will be of interest to undergraduate students in physics and mathematics, in addition to an interested, general audience.Features:Provides an extensive yet accessible background to the conceptsContains numerous, illustrative diagramsPresents in-depth explanations of difficult subjects

Arvustused

"Formal initiation into 20th-century physics occurs when one begins a systematic study of relativity and quantum mechanics. There are any number of standard texts and lecture notes on these two foundations of todays physics. Unlike the classic texts of Leonard Schiff, David Bohm, David Griffiths, and Albert Messiah, this volume offers a sturdy steppingstone to the grand edifice: it is well organized and clearly presented, with only brief introductory notes to the topics.

Fischer-Cripps (formerly, Univ. of Technology, Sydney) presents the student with all the required mathematics in a succinct way. A brief discussion of vector space would have been a worthwhile addition. Those who have not previously seen scalars, vectors, and complex numbers need to do some serious work before venturing into this text, which only reviews these concepts. Readers with some acquaintance with the basics will learn the concepts, structure, and bases of the physics that is essential for an understanding of quantum field theory, leading to Feynman diagrams. This book can serve as an excellent text not only for students who plan to specialize eventually in high-powered theoretical physics, but also for those whose goal may be to work in nuclear physics, astrophysics, solid-state physics, and the like. All college libraries should own this work.

Summing Up: Highly recommended. Upper-division undergraduates. Students enrolled in two-year technical programs."

V. V. Raman, emeritus, Rochester Institute of Technology in CHOICE, September 2020

Acknowledgements xi
1 Mathematics 1(18)
1.1 Introduction
1(1)
1.2 Complex Numbers
1(5)
1.2.1 Complex Numbers
1(3)
1.2.2 Complex Quantities
4(1)
1.2.3 Complex Functions
5(1)
1.3 Scalars and Vectors
6(5)
1.3.1 Scalars
6(1)
1.3.2 Vectors
6(3)
1.3.3 Dot and Cross Product
9(1)
1.3.4 Vector Differentiation
10(1)
1.4 Differential Equations
11(3)
1.4.1 Differential Equations
11(1)
1.4.2 Solutions to Differential Equations
12(1)
1.4.3 Differential Operators
12(2)
1.5 Partial Derivatives
14(1)
1.6 Matrices
14(5)
2 Waves 19(16)
2.1 Introduction
19(1)
2.2 Periodic Motion
19(1)
2.3 Simple Harmonic Motion
20(2)
2.4 Wave Function
22(2)
2.5 Wave Equation
24(2)
2.6 Complex Representation of a Wave
26(2)
2.7 Energy Carried by a Wave
28(2)
2.8 Superposition
30(1)
2.9 Standing Waves
31(2)
2.10 Beats
33(1)
2.11 Superposition in Complex Form
34(1)
3 Electromagnetic Waves 35(10)
3.1 Electromagnetism
35(5)
3.2 Energy in Electromagnetic Waves
40(5)
4 Kinetic Theory of Gases 45(26)
4.1 Introduction
45(1)
4.2 Pressure and Temperature
46(5)
4.2.1 Pressure
46(2)
4.2.2 Temperature
48(1)
4.2.3 Degrees of Freedom
49(1)
4.2.4 Equipartition of Energy
49(1)
4.2.5 Internal Energy
50(1)
4.3 Statistical Mechanics
51(20)
4.3.1 Statistical Weight
51(2)
4.3.2 Boltzmann Distribution
53(1)
4.3.3 Velocity Distribution
54(3)
4.3.4 Partition Function
57(2)
4.3.5 Properties of the Partition Function
59(3)
4.3.6 Energy Density of States
62(1)
4.3.7 Energy in a Harmonic Oscillator System
63(3)
4.3.8 Average Energy in a Harmonic Oscillator System
66(5)
5 Quantum Theory 71(18)
5.1 Introduction
71(1)
5.2 Black Body Radiation
71(2)
5.3 Cavity Radiation
73(1)
5.4 Frequency Density of States
74(6)
5.4.1 Density of States - 1D
74(1)
5.4.2 Density of States - 1D Revisited
75(1)
5.4.3 Density of States - 2D
76(2)
5.4.4 Density of States - 3D
78(2)
5.5 Rayleigh-Jeans Radiation Law
80(2)
5.6 The Birth of Quantum Physics
82(7)
5.6.1 Introduction
82(1)
5.6.2 Boltzmann Statistics
83(1)
5.6.3 Rayleigh-Jeans Radiation Law
83(1)
5.6.4 Planck's Radiation Law
84(1)
5.6.5 Forms of the Radiation Laws
85(1)
5.6.6 Stefan-Boltzmann Radiation Law
86(1)
5.6.7 Wien Displacement Law
87(2)
6 The Bohr Atom 89(12)
6.1 Introduction
89(1)
6.2 The Photoelectric Effect
89(1)
6.3 Line Spectra
90(1)
6.4 The Bohr Atom
91(3)
6.5 The Rydberg Constant
94(2)
6.6 Matter Waves
96(3)
6.7 The Photon
99(2)
7 The New Quantum Theory 101(30)
7.1 Introduction
101(1)
7.2 The Schrodinger Equation
101(3)
7.3 Solutions to the Schrodinger Equation
104(15)
7.3.1 Separation of Variables
104(2)
7.3.2 Solution to the Time-Dependent Schrodinger Equation
106(1)
7.3.3 The Wave Function
107(1)
7.3.4 Normalisation
108(1)
7.3.5 Solutions to the Time-Independent Schrodinger Equation
109(10)
7.3.5.1 The Zero-Potential
109(5)
7.3.5.2 The Infinite Square Well Potential
114(5)
7.4 Significance of the Boundaries
119(3)
7.4.1 Free Electron
119(1)
7.4.2 Bound Electron
120(2)
7.5 Wave Functions and Photons
122(3)
7.6 Spin
125(3)
7.6.1 Spin Angular Momentum
125(1)
7.6.2 Quantum Numbers
126(2)
7.7 Significance of the Schrodinger Equation
128(3)
8 Relativity 131(38)
8.1 Introduction
131(1)
8.2 Special Relativity
131(30)
8.2.1 The Michelson-Morley Experiment
131(4)
8.2.2 The Principle of Relativity
135(1)
8.2.3 Frames of Reference
136(1)
8.2.3.1 Distance
136(1)
8.2.3.2 Velocity and Acceleration
137(1)
8.2.4 Postulates of Special Relativity
137(1)
8.2.5 Time Dilation
138(2)
8.2.6 Length Contraction
140(2)
8.2.7 Lorentz Transformations
142(12)
8.2.7.1 Lorentz Distance Transformation
142(1)
8.2.7.2 Lorentz Time Transformation
143(2)
8.2.7.3 Lorentz Velocity Transformation
145(2)
8.2.7.4 Momentum and Mass Transformations
147(3)
8.2.7.5 Mass and Energy Transformations
150(4)
8.2.8 Consequences of Special Relativity
154(4)
8.2.8.1 Energy and Momentum
154(2)
8.2.8.2 Kinetic Energy
156(1)
8.2.8.3 Photons
157(1)
8.2.9 Summary of Special Relativity
158(3)
8.2.9.1 Length
158(1)
8.2.9.2 Time
158(1)
8.2.9.3 Velocity
159(1)
8.2.9.4 Mass
159(1)
8.2.9.5 Momentum
160(1)
8.2.9.6 Energy
160(1)
8.3 General Relativity
161(5)
8.3.1 Introduction
161(1)
8.3.2 Space-Time
162(4)
8.4 Conclusion
166(3)
9 Advanced Mathematics 169(30)
9.1 Vector Calculus
169(11)
9.1.1 Vector Differential Operator
169(1)
9.1.2 Line Integral
170(4)
9.1.3 Multiple Integrals
174(1)
9.1.4 Surface and Volume Integrals
175(4)
9.1.5 Stokes' Theorem
179(1)
9.2 Gauss' Law
180(2)
9.3 Continuity Equation
182(1)
9.4 Four-Vectors
183(6)
9.4.1 Four-Position
183(2)
9.4.2 Four-Velocity
185(1)
9.4.3 Four-Momentum
186(1)
9.4.4 Dot Product of Four-Vectors
187(1)
9.4.5 Four-Differential Operator, and the d'Alembertian
188(1)
9.5 The Hamiltonian
189(2)
9.6 The Lagrangian
191(8)
9.6.1 Action
191(1)
9.6.2 Variational Calculus
192(2)
9.6.3 Equations of Motion
194(5)
10 Relativistic Quantum Mechanics 199(16)
10.1 The Dirac Equation
199(4)
10.2 Solutions to the Dirac Equation
203(7)
10.2.1 At Rest
203(3)
10.2.2 Constant Velocity
206(4)
10.3 Antimatter
210(1)
10.4 Natural Units
210(2)
10.5 Single Particle Dirac Equation
212(3)
11 Probability Flow 215(10)
11.1 Introduction
215(1)
11.2 Probability Current
215(3)
11.3 The Adjoint Dirac Equation
218(7)
12 Wave Functions and Spinors 225(8)
12.1 Particles
225(2)
12.2 Dirac Spinors
227(2)
12.3 Antiparticles
229(4)
13 Classical Field Theory 233(14)
13.1 Classical Field Theory
233(1)
13.2 Action
233(2)
13.3 The Lagrangian
235(3)
13.4 The Euler-Lagrange Equation
238(4)
13.5 Lagrangian for a Free Particle
242(3)
13.6 Lagrangian for a Free Particle in a Scalar Field
245(1)
13.7 Lagrangian for the Dirac Field
245(2)
14 Lorentz Invariance 247(12)
14.1 Introduction
247(1)
14.2 Transformations
248(1)
14.3 Contravariant and Covariant Notation
249(6)
14.4 Transformation Matrix
255(4)
15 The Electromagnetic Field 259(30)
15.1 Introduction
259(1)
15.2 The Scalar Potential
260(2)
15.3 The Vector Potential
262(1)
15.4 Maxwell's Equations in Potential Form
263(4)
15.4.1 Maxwell's Equations and the Vector Potential
263(2)
15.4.2 The Four-Potential
265(2)
15.5 Transformations of the Four-Potential
267(1)
15.6 Lagrangian for the Electromagnetic Field
268(3)
15.6.1 The Lagrangian for a Field
268(1)
15.6.2 The Lagrangian for the Electromagnetic Field
269(2)
15.7 The Electromagnetic Field Tensor
271(8)
15.7.1 The Electromagnetic Field Tensor
271(4)
15.7.2 The Lagrangian for the Electromagnetic Field Tensor
275(4)
15.8 Charged Particle in an Electromagnetic Field
279(4)
15.9 Transformations of the Electromagnetic Field
283(2)
15.10 The Electromagnetic Wave
285(4)
16 The Quantum Field 289(20)
16.1 Introduction
289(1)
16.2 Classical Fields
290(2)
16.2.1 Scalar Field (Spin 0)
290(1)
16.2.2 Dirac Field (Spin 1/2)
291(1)
16.2.3 Vector Field (Spin 1)
291(1)
16.3 The Harmonic Oscillator
292(14)
16.3.1 Commutator
292(2)
16.3.2 Energy Levels
294(5)
16.3.2.1 Energy Levels
294(1)
16.3.2.2 Power Series Method
294(2)
16.3.2.3 Operator Method
296(3)
16.3.3 The Harmonic Oscillator Field
299(2)
16.3.4 Particles
301(3)
16.3.5 The Quantum Field
304(2)
16.4 Propagators
306(2)
16.5 Interactions
308(1)
17 Feynman Diagrams 309(20)
17.1 Introduction
309(1)
17.2 Quantum Electrodynamics
309(5)
17.2.1 Path Taken by a Photon
309(1)
17.2.2 Alternate Paths
310(2)
17.2.3 Successive Steps
312(2)
17.3 The Behaviour of Light
314(3)
17.3.1 Straight-Line Path
314(1)
17.3.2 Single Slit Diffraction
315(1)
17.3.3 Double Slit Interference
316(1)
17.4 Action
317(1)
17.5 Feynman Diagrams
318(6)
17.5.1 Feynman Diagrams
318(2)
17.5.2 External Particles
320(1)
17.5.2.1 Particles
320(1)
17.5.2.2 Antiparticles
321(1)
17.5.2.3 Photons
321(1)
17.5.3 Interactions
321(2)
17.5.3.1 Vertex Factor
321(1)
17.5.3.2 Photon Propagator
322(1)
17.5.4 Electron-Photon Interactions
323(1)
17.6 Components of a Feynman Diagram
324(1)
17.7 A Feynman Diagram
325(1)
17.8 Renormalisation
326(1)
17.9 Connection to Experimental Results
327(2)
18 Conclusion 329(2)
Appendix 331(6)
Index 337
Anthony Fischer-Cripps is an experienced lecturer in physics and a former senior scientist at CSIRO, Australians national scientific research institution. Dr. Cripps has published several student books over the years as well as undertaking fundamental research in applied physics in the field of nanoindentation.