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

(Fischer-Cripps Laboratories Pty Ltd, Sydney, Australia)
  • Formaat: Hardback, 338 pages, kõrgus x laius: 254x178 mm, kaal: 775 g, 6 Tables, black and white; 103 Illustrations, black and white
  • Ilmumisaeg: 25-Jun-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367198789
  • ISBN-13: 9780367198787
Teised raamatud teemal:
Waves, Particles and Fields: Introducing Quantum Field TheorySuurem pilt
  • Formaat: Hardback, 338 pages, kõrgus x laius: 254x178 mm, kaal: 775 g, 6 Tables, black and white; 103 Illustrations, black and white
  • Ilmumisaeg: 25-Jun-2019
  • Kirjastus: CRC Press
  • ISBN-10: 0367198789
  • ISBN-13: 9780367198787
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367198787.html
Märksõnad:

This book fills a gap in the middle ground between 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 concepts

  • Contains numerous, illustrative diagrams

    • Presents 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(1)
    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(1)
    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(1)
    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(1)
    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(1)
    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(1)
    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.