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Quantum Field Theory for the Gifted Amateur [Kietas viršelis]

4.35/5 (273 ratings by Goodreads)
(Professor of Physics, Department of Physics, University of Oxford), (Lecturer in Physics, Department of Physics, University of Durham)
  • Formatas: Hardback, 504 pages, aukštis x plotis x storis: 248x195x30 mm, weight: 1002 g, 242 b/w illustrations
  • Išleidimo metai: 17-Apr-2014
  • Leidėjas: Oxford University Press
  • ISBN-10: 0199699321
  • ISBN-13: 9780199699322
Kitos knygos pagal šią temą:
Quantum Field Theory for the Gifted AmateurDidesnis paveikslėlis
  • Formatas: Hardback, 504 pages, aukštis x plotis x storis: 248x195x30 mm, weight: 1002 g, 242 b/w illustrations
  • Išleidimo metai: 17-Apr-2014
  • Leidėjas: Oxford University Press
  • ISBN-10: 0199699321
  • ISBN-13: 9780199699322
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780199699322.html
Raktažodžiai:
Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in detail. Using numerous worked examples, diagrams, and careful physically motivated explanations, this book will smooth the path towards understanding the radically different and revolutionary view of the physical world that quantum field theory provides, and which all physicists should have the opportunity to experience.

To request a copy of the Solutions Manual, visit http://global.oup.com/uk/academic/physics/admin/solutions.

Recenzijos

A refreshing hands-on approach ... [ and] a tremendous resource to have to hand or perhaps to use as a textbook for a first course on QFT to a mixed audience. * Clifford V. Johnson, Physics Today * A treasury of contemporary material presented concisely and lucidly in a format that I can recommend for independent study ... I believe that this volume offers an attractive, new "rock and roll" approach, filling a large void in the spectrum of QFT books. * Johann Rafelski, CERN Courier * The authors succeed remarkably in opening up the concepts of Quantum Field Theory to a broad, physically and mathematically trained readership. [ ...] The book is a valuable addition to the wide range of QFT books already available, and is suitable as self-study for the novice, as accompaniment for courses, and also as a valuable reference for those already familiar with the subject. * Physik Journal * This is a wonderful, and much needed book ... Why have the authors been so successful? It is the way the book has been structured. Each of the 50 chapters is short. Every chapter starts with a readable plan of what is to be explained and why; and finishes with a compact summary of the key ideas that have been covered. Moreover, the language is kept as simple as possible. The aim is always to be clear and difficult ideas are approached gently. The text is interspersed with a large number of detailed worked examples which are central to the story and which are arranged so as not to intimidate the reader ... They have produced an accessible book that gives us a wonderful opportunity to understand QFT and its numerous applications * Alan D. Martin, Contemporary Physics * There is a need for a book on Quantum Field Theory that is not directed at specialists but, rather, sets out the concepts underlying this subject for a broader scientific audience and conveys joy in their beauty. Lancaster and Blundell have written with this goal in mind, and they have succeeded admirably. * Michael Peskin, SLAC Naitonal Accelerator Laboratory, Stanford University * This wonderful and exciting book is optimal for physics graduate students. The authors are brilliant educators who use worked examples, diagrams and mathematical hints placed in the margins to perfect their pedagogy and explain quantum field theory. * Barry R. Masters, Optics & Photonics News *

0 Overture
1(8)
0.1 What is quantum field theory?
1(1)
0.2 What is a field?
2(1)
0.3 Who is this book for?
2(1)
0.4 Special relativity
3(3)
0.5 Fourier transforms
6(1)
0.6 Electromagnetism
7(2)
I The Universe as a set of harmonic oscillators
9(40)
1 Lagrangians
10(9)
1.1 Fermat's principle
10(1)
1.2 Newton's laws
10(1)
1.3 Functional
11(3)
1.4 Lagrangians and least action
14(2)
1.5 Why does it work?
16(3)
Exercises
17(2)
2 Simple harmonic oscillators
19(9)
2.1 Introduction
19(1)
2.2 Mass on a spring
19(4)
2.3 A trivial generalization
23(2)
2.4 Phonons
25(3)
Exercises
27(1)
3 Occupation number representation
28(9)
3.1 A particle in a box
28(1)
3.2 Changing-the notation
29(2)
3.3 Replace state labels with operators
31(1)
3.4 Indistinguishability and symmetry
31(4)
3.5 The continuum limit
35(2)
Exercises
36(1)
4 Making second quantization work
37(12)
4.1 Field operators
37(2)
4.2 How to second quantize an operator
39(4)
4.3 The kinetic energy and the tight-binding Hamiltonian
43(1)
4.4 Two particles
44(2)
4.5 The Hubbard model
46(3)
Exercises
48(1)
II Writing down Lagrangians
49(22)
5 Continuous systems
50(9)
5.1 Lagrangians and Hamiltonians
50(2)
5.2 A charged particle in an electromagnetic field
52(2)
5.3 Classical fields
54(1)
5.4 Lagrangian and Hamiltonian density
55(4)
Exercises
58(1)
6 A first stab at relativistic quantum mechanics
59(5)
6.1 The Klein-Gordon equation
59(2)
6.2 Probability currents and densities
61(1)
6.3 Feynman's interpretation of the negative energy states
61(2)
6.4 No conclusions
63(1)
Exercises
63(1)
7 Examples of Lagrangians, or how to write down a theory
64(7)
7.1 A massless scalar field
64(1)
7.2 A massive scalar field
65(1)
7.3 An external source
66(1)
7.4 The φ4 theory
67(1)
7.5 Two scalar fields
67(1)
7.6 The complex scalar field
68(3)
Exercises
69(2)
III The need for quantum fields
71(72)
8 The passage of time
72(7)
8.1 Schrodinger's picture and the time-evolution operator
72(2)
8.2 The Heisenberg picture
74(1)
8.3 The death of single-particle quantum mechanics
75(1)
8.4 Old quantum theory is dead; long live fields!
76(3)
Exercises
78(1)
9 Quantum mechanical transformations
79(11)
9.1 Translations in spacetime
79(3)
9.2 Rotations
82(1)
9.3 Representations of transformations
83(2)
9.4 Transformations of quantum fields
85(1)
9.5 Lorentz transformations
86(4)
Exercises
88(2)
10 Symmetry
90(8)
10.1 Invariance and conservation
90(2)
10.2 Noether's theorem
92(2)
10.3 Spacetime translation
94(2)
10.4 Other symmetries
96(2)
Exercises
97(1)
11 Canonical quantization of fields
98(11)
11.1 The canonical quantization machine
98(3)
11.2 Normalizing factors
101(1)
11.3 What becomes of the Hamiltonian?
102(2)
11.4 Normal ordering
104(2)
11.5 The meaning of the mode expansion
106(3)
Exercises
108(1)
12 Examples of canonical quantization
109(8)
12.1 Complex scalar field theory
109(2)
12.2 Noether's current for complex scalar field theory
111(1)
12.3 Complex scalar field theory in the non-relativistic limit
112(5)
Exercises
116(1)
13 Fields with many components and massive electromagnetism
117(9)
13.1 Internal symmetries
117(3)
13.2 Massive electromagnetism
120(3)
13.3 Polarizations and projections
123(3)
Exercises
125(1)
14 Gauge fields and gauge theory
126(9)
14.1 What is a gauge field?
126(3)
14.2 Electromagnetism is the simplest gauge theory
129(2)
14.3 Canonical quantization of the electromagnetic field
131(4)
Exercises
134(1)
15 Discrete transformations
135(8)
15.1 Charge conjugation
135(1)
15.2 Parity
136(1)
15.3 Time reversal
137(2)
15.4 Combinations of discrete and continuous transformations
139(4)
Exercises
142(1)
IV Propagators and perturbations
143(52)
16 Propagators and Green's functions
144(10)
16.1 What is a Green's function?
144(2)
16.2 Propagators in quantum mechanics
146(3)
16.3 Turning it around: quantum mechanics from the propagator and a first look at perturbation theory
149(2)
16.4 The many faces of the propagator
151(3)
Exercises
152(2)
17 Propagators and fields
154(11)
17.1 The field propagator in outline
155(1)
17.2 The Feynman propagator
156(2)
17.3 Finding the free propagator for scalar field theory
158(1)
17.4 Yukawa's force-carrying particles
159(3)
17.5 Anatomy of the propagator
162(3)
Exercises
163(2)
18 The 5-matrix
165(10)
18.1 The 5-matrix: a hero for our times
166(1)
18.2 Some new machinery: the interaction representation
167(1)
18.3 The interaction picture applied to scattering
168(1)
18.4 Perturbation expansion of the 5-matrix
169(2)
18.5 Wick's theorem
171(4)
Exercises
174(1)
19 Expanding the 5-matrix: Feynman diagrams
175(13)
19.1 Meet some interactions
176(1)
19.2 The example of φ4 theory
177(4)
19.3 Anatomy of a diagram
181(1)
19.4 Symmetry factors
182(1)
19.5 Calculations in p-space
183(3)
19.6 A first look at scattering
186(2)
Exercises
187(1)
20 Scattering theory
188(7)
20.1 Another theory: Yukawa's ψ† ψφ interactions
188(2)
20.2 Scattering in the ψ† ψφ theory
190(2)
20.3 The transition matrix and the invariant amplitude
192(1)
20.4 The scattering cross-section
193(2)
Exercises
194(1)
V Interlude: wisdom from statistical physics
195(14)
21 Statistical physics: a crash course
196(5)
21.1 Statistical mechanics in a nutshell
196(1)
21.2 Sources in statistical physics
197(1)
21.3 A look ahead
198(3)
Exercises
199(2)
22 The generating functional for fields
201(8)
22.1 How to find Green's functions
201(2)
22.2 Linking things up with the Gell-Mann-Low theorem
203(1)
22.3 How to calculate Green's functions with diagrams
204(2)
22.4 More facts about diagrams
206(3)
Exercises
208(1)
VI Path integrals
209(50)
23 Path integrals: I said to him, `You're crazy'
210(11)
23.1 How to do quantum mechanics using path integrals
210(3)
23.2 The Gaussian integral
213(4)
23.3 The propagator for the simple harmonic oscillator
217(4)
Exercises
220(1)
24 Field integrals
221(7)
24.1 The functional integral for fields
221(1)
24.2 Which field integrals should you do?
222(1)
24.3 The generating functional for scalar fields
223(5)
Exercises
226(2)
25 Statistical field theory
228(9)
25.1 Wick rotation and Euclidean space
229(2)
25.2 The partition function
231(2)
25.3 Perturbation theory and Feynman rules
233(4)
Exercises
236(1)
26 Broken symmetry
237(10)
26.1 Landau theory
237(2)
26.2 Breaking symmetry with a Lagrangian
239(1)
26.3 Breaking a continuous symmetry: Goldstone modes
240(2)
26.4 Breaking a symmetry in a gauge theory
242(2)
26.5 Order in reduced dimensions
244(3)
Exercises
245(2)
27 Coherent states
247(8)
27.1 Coherent states of the harmonic oscillator
247(2)
27.2 What do coherent states look like?
249(1)
27.3 Number, phase and the phase operator
250(2)
27.4 Examples of coherent States
252(3)
Exercises
253(2)
28 Grassmann numbers: coherent states and the path integral for fermions
255(4)
28.1 Grassmann numbers
255(2)
28.2 Coherentstates for fermions
257(1)
28.3 The path integral for fermions
257(2)
Exercises
258(1)
VII Topological ideas
259(14)
29 Topological objects
260(7)
29.1 What is topology?
260(2)
29.2 Kinks
262(2)
29.3 Vortices
264(3)
Exercises
266(1)
30 Topological field theory
267(6)
30.1 Fractional statistics a la Wilczek: the strange case of anyons
267(2)
30.2 Chern-Simons theory
269(2)
30.3 Fractional statistics from Chern-Simons theory
271(2)
Exercises
272(1)
VIII Renormalization: taming the infinite
273(48)
31 Renormalization, quasiparticles and the Fermi surface
274(11)
31.1 Recap: interacting and non-interacting theories
274(2)
31.2 Quasiparticles
276(1)
31.3 The propagator for a dressed particle
277(2)
31.4 Elementary quasiparticles in a metal
279(1)
31.5 The Landau Fermi liquid
280(5)
Exercises
284(1)
32 Renormalization: the problem and its solution
285(10)
32.1 The problem is divergences
285(2)
32.2 The solution is counterterms
287(1)
32.3 How to tame an integral
288(2)
32.4 What counterterms mean
290(2)
32.5 Making renormalization even simpler
292(1)
32.6 Which theories are renormalizable?
293(2)
Exercises
294(1)
33 Renormalization in action: propagators and Feynman diagrams
295(7)
33.1 How interactions change the propagator in perturbation theory
295(2)
33.2 The role of counterterms: renormalization conditions
297(1)
33.3 The vertex function
298(4)
Exercises
300(2)
34 The renormalization group
302(11)
34.1 The problem
302(2)
34.2 Flows in parameter space
304(1)
34.3 The renormalization group method
305(2)
34.4 Application 1: asymptotic freedom
307(1)
34.5 Application 2: Anderson localization
308(1)
34.6 Application 3: the Kosterlitz-Thouless transition
309(4)
Exercises
312(1)
35 Ferromagnetism: a renormalization group tutorial
313(8)
35.1 Background: critical phenomena and scaling
313(2)
35.2 The ferromagnetic transition and critical phenomena
315(6)
Exercises
320(1)
IX Putting a spin on QFT
321(48)
36 The Dirac equation
322(14)
36.1 The Dirac equation
322(1)
36.2 Massless particles: left- and right-handed wave functions
323(4)
36.3 Dirac and Weyl spinors
327(3)
36.4 Basis states for superpositions
330(2)
36.5 The non-relativistic limit of the Dirac equation
332(4)
Exercises
334(2)
37 How to transform a spinor
336(5)
37.1 Spinors aren't vectors
336(1)
37.2 Rotating spinors
337(1)
37.3 Boosting spinors
337(2)
37.4 Why are there four components in the Dirac equation?
339(2)
Exercises
340(1)
38 The quantum Dirac field
341(7)
38.1 Canonical quantization and Noether current
341(2)
38.2 The fermion propagator
343(2)
38.3 Feynman rules and scattering
345(1)
38.4 Local symmetry and a gauge theory for fermions
346(2)
Exercises
347(1)
39 A rough guide to quantum electrodynamics
348(7)
39.1 Quantum light and the photon propagator
348(1)
39.2 Feynman rules and a first QED process
349(2)
39.3 Gauge invariance in QED
351(4)
Exercises
353(2)
40 QED scattering: three famous cross-sections
355(5)
40.1 Example 1: Rutherford scattering
355(1)
40.2 Example 2: Spin sums and the Mott formula
356(1)
40.3 Example 3: Compton scattering
357(1)
40.4 Crossing symmetry
358(2)
Exercises
359(1)
41 The renormalization of QED and two great results
360(9)
41.1 Renormalizing the photon propagator: dielectric vacuum
361(3)
41.2 The renormalization group and the electric charge
364(1)
41.3 Vertex corrections and the electron g-factor
365(4)
Exercises
368(1)
X Some applications from the world of condensed matter
369(54)
42 Superfluids
370(10)
42.1 Bogoliubov's hunting license
370(2)
42.2 Bogoliubov's transformation
372(2)
42.3 Superfluids and fields
374(3)
42.4 The current in a superfluid
377(3)
Exercises
379(1)
43 The many-body problem and the metal
380(20)
43.1 Mean-field theory
380(3)
43.2 The Hartree-Fock ground state energy of a metal
383(3)
43.3 Excitations in the mean-field approximation
386(2)
43.4 Electrons and holes
388(1)
43.5 Finding the excitations with propagators
389(1)
43.6 Ground states and excitations
390(3)
43.7 The random phase approximation
393(7)
Exercises
398(2)
44 Superconductors
400(11)
44.1 A model of a superconductor
400(2)
44.2 The ground state is made of Cooper pairs
402(1)
44.3 Ground state energy
403(2)
44.4 The quasiparticles are bogolons
405(1)
44.5 Broken symmetry
406(1)
44.6 Field theory of a charged superfluid
407(4)
Exercises
409(2)
45 The fractional quantum Hall fluid
411(12)
45.1 Magnetic translations
411(2)
45.2 Landau Levels
413(2)
45.3 The integer quantum Hall effect
415(2)
45.4 The fractional quantum Hall effect
417(6)
Exercises
421(2)
XI Some applications from the world of particle physics
423(44)
46 Non-abelian gauge theory
424(9)
46.1 Abelian gauge theory revisited
424(1)
46.2 Yang-Mills theory
425(3)
46.3 Interactions and dynamics of Wμ
428(2)
46.4 Breaking symmetry with a non-abelian gauge theory
430(3)
Exercises
432(1)
47 The Weinberg-Salam model
433(11)
47.1 The symmetries of Nature before symmetry breaking
434(3)
47.2 Introducing the. Higgs field
437(1)
47.3 Symmetry breaking the Higgs field
438(1)
47.4 The origin of electron mass
439(1)
47.5 The photon and the gauge bosons
440(4)
Exercises
443(1)
48 Majorana fermions
444(7)
48.1 The Majorana solution
444(2)
48.2 Field operators
446(1)
48.3 Majorana mass and charge
447(4)
Exercises
450(1)
49 Magnetic monopoles
451(6)
49.1 Dirac's monopole and the Dirac string
451(2)
49.2 The 't Hooft-Polyakov monopole
453(4)
Exercises
456(1)
50 Instantons, tunnelling and the end of the world
457(10)
50.1 Instantons in quantum particle mechanics
458(1)
50.2 A particle in a potential well
459(1)
50.3 A particle in a double well
460(3)
50.4 The fate of the false vacuum
463(4)
Exercises
466(1)
A Further reading
467(6)
B Useful complex analysis
473(7)
B.1 What is an analytic function?
473(1)
B.2 What is a pole?
474(1)
B.3 How to find a residue
474(1)
B.4 Three rules of contour integrals
475(2)
B.5 What is a branch cut?
477(1)
B.6 The principal value of an integral
478(2)
Index 480
Tom Lancaster was a Research Fellow in Physics at the University of Oxford, before becoming a Lecturer at the University of Durham in 2012.



Stephen J. Blundell is a Professor of Physics at the University of Oxford and a Fellow of Mansfield College, Oxford.