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E-raamat: Quantum Field Theory: An Introduction For Chemical Physicists

(Stony Brook Univ, Usa)
  • Formaat: 284 pages
  • Ilmumisaeg: 26-Oct-2021
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811239908
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Quantum Field Theory: An Introduction For Chemical PhysicistsSuurem pilt
  • Formaat: 284 pages
  • Ilmumisaeg: 26-Oct-2021
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789811239908
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This introduction to quantum field theory (QFT) is written by a physical chemist for physical chemists, chemical physicists, and other non-physicists with knowledge of quantum theory but who want to explore ways in which they might use the power of QFT in their investigations. This book starts where many graduate courses in quantum theory that are offered to chemistry students leave off and first develops some of the necessary tools, such as Fock algebra, which is applied to solving the quantum oscillator problem. Then it is used to develop the theory of coherent states, time-dependent perturbation theory, and the treatment of bosons and fermions. With this background, the QFT of a perfect gas is derived and a connection to thermodynamics is demonstrated. Application to imperfect gases provides a new approach to modelling gas-liquid phase transitions. The book concludes with photons and their interaction with molecular ensembles, and brings us to full circle by deriving the blackbody radiation law, which started it all. The power of the QFT methodology and the breadth of its applications should fascinate the reader as it has the author.

Preface v
About the Author vii
1 Introduction 1(8)
1.1 Why this Book?
1(1)
1.2 What is Required of the Reader?
1(1)
1.3 What is the Subject Matter of this Book?
2(7)
1.3.1
Chapter 2: The Harmonic Oscillator
2(1)
1.3.2
Chapter 3: Time-dependent Perturbation Expansions
2(1)
1.3.3
Chapter 4: Spinless Particles
3(1)
1.3.4
Chapter 5: Charge and Spin
3(1)
1.3.5
Chapter 6: The Perfect Molecular Gas
4(1)
1.3.6
Chapter 7: Real Gases; Phase Transitions
5(1)
1.3.7
Chapter 8: Photons
6(1)
1.3.8
Chapter 9: Light-molecule Interactions
7(1)
1.3.9
Chapter 10: Conclusions, Acknowledgments, and Notes
8(1)
2 The Harmonic Oscillator: A Treatment by Fock Operators 9(38)
2.1 Introduction
9(1)
2.2 The Schrodinger Equation
10(1)
2.3 Fock Operators
11(2)
2.4 Solution of the Harmonic Oscillator Problem with Fock Algebra
13(4)
2.5 Some Properties of the Hermite Polynomials
17(2)
2.6 Evaluation of the Normalization Constant
19(2)
2.7 Bra and Ket Notation
21(2)
2.8 Matrix Elements of the Operators x and p
23(2)
2.9 The Uncertainty Product
25(1)
2.10 Superposition of States; Completeness
26(1)
2.11 Minimal Wave Packet; the Translation Operator
27(8)
2.12 Time Evolution: The Schrodinger Picture
35(4)
2.13 Time Evolution: The Heisenberg Picture
39(3)
2.14 Summary for
Chapter 2
42(5)
3 Time-Dependent Perturbation Expansions 47(45)
3.1 Introduction
47(1)
3.2 The Dirac or Interaction Picture
48(4)
3.3 Normal Ordering of Strings of Fock Operators: Wick's Theorem
52(6)
3.4 Application of Normal Ordering by Wick's Theorem: Glauber States
58(8)
3.5 Perturbation Treatment of the Time Evolution of a Wave Packet
66(23)
3.5.1 Summation to Infinite Order; Connected Graphs
76(13)
3.6 Summary for
Chapter 3
89(3)
4 Spinless Particles 92(24)
4.1 Introduction
92(1)
4.2 Mechanics of the Harmonic Oscillator
93(5)
4.2.1 Lagrangian Mechanics
93(2)
4.2.2 Constants of Motion: Momentum and the Hamiltonian
95(1)
4.2.3 Quantization of the Harmonic Oscillator
96(2)
4.3 Classical Klein-Gordon Field Theory
98(8)
4.3.1 Vectors and Derivatives in Space-time
98(1)
4.3.2 The Klein-Gordon Lagrangian
99(1)
4.3.3 The Klein-Gordon Equation
99(2)
4.3.4 Canonical Momentum and Hamiltonian
101(2)
4.3.5 Constants of Motion
103(3)
4.4 The Quantized Klein-Gordon Field
106(5)
4.4.1 Quantization of the Fields
106(1)
4.4.2 Commutation Relations in Quantum Field Theory
106(3)
4.4.3 Excitation States of the Quantized Klein-Gordon Field
109(2)
4.5 Time Dependence: The Schrodinger and Heisenberg Pictures
111(2)
4.5.1 The Schrodinger Picture
111(1)
4.5.2 The Heisenberg Picture
112(1)
4.6 A Note on Relativistic Invariance
113(2)
4.7 Summary for
Chapter 4
115(1)
5 Charge and Spin 116(34)
5.1 Introduction
116(1)
5.2 Charged Particles
116(12)
5.2.1 Complex Classical Scalar Fields
117(2)
5.2.2 Quantum Field Theory of Charged Particles
119(7)
5.2.3 Coupling to a Classical Electromagnetic Field
126(2)
5.3 Particles with Spin
128(19)
5.3.1 The Pauli Equation
129(1)
5.3.2 The Dirac Equation
130(18)
5.3.2.1 The Dirac Lagrangian
132(1)
5.3.2.2 The Dirac Field Momentum
133(1)
5.3.2.3 Constants of the Motion
134(2)
5.3.2.4 Coupling to the Electromagnetic Field
136(2)
5.3.2.5 Solutions for Free Dirac Particles
138(3)
5.3.2.6 Quantization of the Dirac Field
141(3)
5.3.2.7 The Quantized Dirac Hamiltonian
144(2)
5.3.2.8 The Quantized Charge Density
146(1)
5.4 Summary for
Chapter 5
147(1)
5.5 Appendix A: Schwinger's Harmonic-Oscillator Model for Spin
148(2)
5.5.1 Spin Eigenvalues and Eigenvectors
149(1)
5.5.2 Rotation of the Spin Axes
149(1)
6 The Perfect Molecular Gas 150(31)
6.1 Introduction
150(1)
6.2 Molecular Fock Operators
151(3)
6.3 Wick's Theorem
154(6)
6.4 Coherent Ensembles of Independent Molecules
160(3)
6.5 The Isodasic Molecular Ensemble
163(4)
6.6 Trace of the Isodasic Operator
167(5)
6.7 Molecular Statistics for Coherent and Isodasic Ensembles
172(8)
6.8 Summary for
Chapter 6
180(1)
7 Real Gases and Phase Transitions 181(11)
7.1 Introduction
181(1)
7.2 Ensembles of Interacting Molecules
182(6)
7.2.1 Short-range Correlations
183(2)
7.2.2 Long-range Correlations
185(2)
7.2.3 Long-range Coulomb Correlations
187(1)
7.2.4 Self-consistent Iterative Methods
188(1)
7.3 The Pair-correlation Function for Interacting Molecules
188(1)
7.4 Caveat
189(1)
7.5 Summary for
Chapter 7
190(2)
7.5.1 What has been Accomplished so Far
190(1)
7.5.2 What Needs to be Done
190(2)
8 Photons 192(48)
8.1 Introduction
192(1)
8.2 Quantum Electrodynamics
193(18)
8.2.1 The Classical Theory
193(8)
8.2.1.1 The Electromagnetic 4-Vector Potential
194(1)
8.2.1.2 Maxwell's Equations in Terms of the Potentials
194(1)
8.2.1.3 Gauge Invariance
195(1)
8.2.1.4 The Electromagnetic Tensor
196(1)
8.2.1.5 Maxwell's Equations in Terms of the Electromagnetic Tensor
197(1)
8.2.1.6 The Lagrangian Density for Electromagnetic Fields
197(2)
8.2.1.7 The Canonical Momentum and Hamiltonian
199(2)
8.2.2 Quantization of the Fields
201(8)
8.2.2.1 The Vector Potential
201(1)
8.2.2.2 The Electric Field
201(1)
8.2.2.3 The Magnetic Field
201(1)
8.2.2.4 The Hamiltonian
202(3)
8.2.2.5 Photon States
205(4)
8.2.3 Wick's Theorem
209(7)
8.2.3.1 Normal Order
209(1)
8.2.3.2 Illustrations of the use of Wick's Theorem
209(2)
8.3 Coherent Photons
211(5)
8.4 Ensemble Operator and Fields for a Coherent Laser Pulse
216(12)
8.4.1 Generalization to Continuous Values of k
217(2)
8.4.2 Poisson Distribution for Photons in a Continuum of Wave Vectors
219(3)
8.4.3 Average Fields for a Coherent Source
222(3)
8.4.4 The k-Distribution for a Coherent Laser Pulse
225(2)
8.4.5 Focused Laser Pulse
227(1)
8.5 Ensemble Operator and Fields for Incoherent Light
228(10)
8.5.1 Randomization of the Phases
228(3)
8.5.2 Properties of the Random-Phase Ensemble Operator
231(2)
8.5.3 Homogeneous Light Beams and Black Body Radiation
233(1)
8.5.4 An Incoherent Inhomogeneous Light Pulse
234(4)
8.6 Summary and Discussion for
Chapter 8
238(2)
9 Light-Molecule Interaction 240(26)
9.1 Introduction
240(1)
9.2 Quantization of the Interaction
241(7)
9.2.1 The Charge Current
241(2)
9.2.2 The Electric Dipole Interaction
243(5)
9.3 Homogeneous Grand Canonical Ensemble Operators
248(1)
9.3.1 The Molecular Ensemble
248(1)
9.3.2 The Photon Ensemble
249(1)
9.4 Dynamics
249(8)
9.5 The Einstein Coefficients and Planck's Black Body Formula
257(2)
9.6 Multiphoton Absorption
259(1)
9.7 Appendix A: Derivation of Equation (9.73)
260(2)
9.8 Appendix B: A Thermodynamic Derivation of the Planck Distribution
262(4)
9.8.1 The Empirical Observations
262(1)
9.8.2 Thermodynamic Temperature
262(2)
9.8.3 Planck's Empirical Formula
264(1)
9.8.4 Interpretation of Equation (9B.16)
265(1)
10. Conclusions, Acknowledgements, and References 266
10.1 Conclusions
266(1)
10.2 Acknowledgements
266(1)
10.3 Notes
267
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