The conceptual framework of quantum field theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2013
|
| Edition: | Reprinted with corrections |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverzeichnis Seite [765] - 776 |
| Physical Description: | x, 782 Seiten Illustrationen, Diagramme |
| ISBN: | 9780199573264 |
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MARC
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Record in the Search Index
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| adam_text | Contents
1
Origins I: From the arrow of time to the first quantum field
1
1.1
Quantum prehistory: crises in classical physics
1
1.2
Early work on cavity radiation
3
1.3
Planck s route to the quantization of energy
8
1.4
First inklings of field quantization: Einstein and energy fluctuations
14
1.5
The first true quantum field: Jordan and energy fluctuations
18
2
Origins II: Gestation and birth of interacting field theory:
from Dirac to Shelter Island
30
2.1
Introducing interactions: Dirac and the beginnings of quantum
electrodynamics
31
2.2
Completing the formalism for free fields: Jordan, Klein, Wigner,
Pauli,
and
Heisenberg 40
2.3
Problems with interacting fields: infinite seas, divergent integrals,
and renormalization
46
3
Dynamics I: The physical ingredients of quantum field theory:
dynamics, symmetries, scales
57
4
Dynamics II: Quantum mechanical preliminaries
69
4.1
The canonical (operator) framework
70
4.2
The functional (path-integral) framework
86
4.3
Scattering theory
96
4.4
Problems
106
5
Dynamics III:
Relat
ivistic quantum mechanics
108
5.1
The
Lorentz
and
Poincaré
groups
108
5.2
Relativistic multi-particle states (without spin) 111
5.3
Relativistic multi-particle states (general spin)
114
5.4
How not to construct a relativistic quantum theory
121
5.5
A simple condition for Lorentz-invariant scattering
125
5.6
Problems
130
6
Dynamics IV: Aspects of locality: clustering, microcausality,
and analyticity
132
6.1
Clustering and the smoothness of scattering amplitudes
133
6.2
Hamiltonians leading to clustering theories
138
6.3
Constructing clustering Hamiltonians: second quantization
144
6.4
Constructing a relativistic. clustering theory
149
6.5
Local fields, non-Iocalizable particles!
159
viii Contents
6.6
From microcausality to analyticity
164
6.7
Problems
169
7
Dynamics V: Construction of local covariant fields
171
7.1
Constructing local, Lorentz-invariant Hamiltomans
171
7.2
Finite-dimensional representations of the homogeneous
Lorentz
group
173
7.3
Local covariant fields for massive particles of any spin:
the Spin-Statistics theorem
177
7.4
Local covariant fields for spin-^ (spinor fields)
184
7.5
Local covariant fields for spin-1 (vector fields)
198
7.6
Some simple theories and processes
202
7.7
Problems
215
8
Dynamics VI: The classical limit of quantum fields
219
8.1
Complementarity issues for quantum fields
219
8.2
When is a quantum field classical ?
223
8.3
Coherent states of a quantum field
228
8.4
Signs, stability, symmetry-breaking
234
8.5
Problems
238
9
Dynamics
VII:
Interacting fields: general aspects
240
9.1
Field theory in
Heisenberg
representation: heuristics
241
9.2
Field theory in
Heisenberg
representation: axiomatics
253
9.3
Asymptotic formalism I: the Haag-Ruelle scattering theory
268
9.4
Asymptotic formalism II: the Lehmann-Symanzik-Zimmermann
(LSZ) theory
281
9.5
Spectral properties of field theory
289
9.6
General aspects of the particle—field connection
297
9.7
Problems
304
10
Dynamics
VIII:
Interacting fields: perturbative aspects
307
10.1
Perturbation theory in interaction picture and Wick s
theorem
309
10.2
Feynman graphs and Feynman rules
314
10.3
Path-integral formulation of field theory
325
10.4
Graphical concepts: iV-particle irreducibility
341
10.5
How to stop worrying about Haag s theorem
359
10.6
Problems
371
11
Dynamics IX: Interacting fields: non-perturbative aspects
374
11.1
On the (non-)convergence of perturbation theory
376
11.2
Perturbatively non-perturbative processes: threshhokl bound
states
386
11.3
Essentially non-perturbative processes: non-Borel-summability
in field theory
400
11.4
Problems
411
Contents
¡χ
12
Symmetries I: Continuous spacetime symmetry: why we need
Lagrangians in field theory
414
12.1
The problem with derivatively coupled theories: seagulls,
Schwinger
terms, and T* products
414
12.2
Canonical formalism in quantum field theory
416
12.3
General condition for Lorentz-invariant field theory
421
12.4
Noether s theorem, the stress-energy tensor, and all that stuff
426
12.5
Applications of Noether s theorem
431
12.6
Beyond
Poincaré: supersymmetry
and superfields
443
12.7
Problems
464
13
Symmetries II: Discrete spacetime symmetries
469
13.1
Parity properties of a general local covariant field
470
13.2
Charge-conjugation properties of a general local covariant field
474
13.3
Time-reversal properties of a general local covariant field
477
13.4
The TCP and Spin-Statistics
theorema
478
13.5
Problems
485
14
Symmetries III: Global symmetries in field theory
487
14.1
Exact global symmetries are rare.
489
14.2
Spontaneous breaking of global symmetries: the
Goldstone
theorem
492
14.3
Spontaneous breaking of global symmetries: dynamical aspects
495
14.4
Problems
507
15
Symmetries IV: Local symmetries in field theory
509
15.1
Gauge symmetry: an example in particle mechanics
509
15.2
Constrained Hamiltonian systems
512
15.3
Abelian gauge theory as a constrained Hamiltonian system
519
15.4
Non-
abelian gauge theory: construction and functional integral
formulation
529
15.5
Explicit quantum-breaking of global symmetries: anomalies
544
15.6
Spontaneous symmetry-breaking in theories with a local
gauge symmetry
552
15.7
Problems
565
16
Scales I: Scale sensitivity of field theory amplitudes and
effective field theories
569
16.1
Scale separation as a precondition for theoretical science
570
16.2
General structure of local effective Lagrangians
571
16.3
Scaling properties of effective Lagrangians: relevant, marginal,
and irrelevant operators
574
16.4
The renormalization group
581
16.5
Regularization methods in field theory
588
16.6
Effective field theories: a compendium
595
16.7
Problems
608
x
Contents
17
Scales II: Perturbatively renormalizable field theories
610
17.1 Weinberges
power-counting theorem and the divergence structure
of Feynman integrals
613
17.2
Counterterms. subtractions, and perturbative renormalizability
629
17.3
Renormalizatioii and symmetry
645
17.4
Renormalization group approach to renormalizability
652
17.5
Problems
660
18
Scales III: Short-distance structure of quantum field theory
662
18.1
Local composite operators in field theory
664
18.2
Factorizable structure of field theory amplitudes: the operator
product expansion
679
18.3
Renormalization group equations for renormalized amplitudes
698
18.4
Problems
708
19
Scales IV: Long-distance structure of quantum field theory
712
19.1
The infrared catastrophe in unbroken abelian gauge theory
713
19.2
The Bloch-Nordsieck resolution
724
19.3
Unbroken non-abelian gauge theory: confinement
728
19.4
How confinement works: three-dimensional gauge theory
744
19.5
Problems
752
Appendix A The functional calculus
754
Appendix
В
Rates and cross-sections
756
Appendix
C Majorana
spinor
algebra
761
References
765
Index
777
The book attempts to provide an introduction to quantum field theory emphasizing
conceptual issues frequently neglected in more utilitarian treatments of the sublet.
The book is divided into four
parís,
entitled respectively Origins , Dynamics ,
Symmetries , and Scales The emphasis is conceptual— the aim is to build the
theory up systematically from some clearly stated foundational concepts —and
therefore to a large extent anti-historical, but two historical chapters ( Origins ) are
included to situate quanfum field theory in the larger conies of modern physical
theories. The three remaining sections of the book
foliový o
step-by-step reconstruc¬
tion of this framework beginning with just a few basic assumptions:
relativista
invariance,
the basic principles of quantum mechanics, and the prohibition of
physical action at a distance embodied in the clustering principle. The Dynamics
section of the book lays out the basic structure of quantum field theory arising from
the sequential insertion of quantum-mechanical, relativistic, and locality constraints.
The central rofe of symmetries in relativistic quantum field theories is explored in the
third section of the book, while in the final section, entitled Scales , we explore in
derail the feature of quantum field theories most critical for their enormous phenom-
enological success —the scale separation property embodied by the renormalization
group properties of a theory defined by an effective local Lagrangian.
Anthony Duncan is a Professor of Physics at the University of Pittsburgh.
|
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| era_facet | Geschichte |
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| spelling | Duncan, Anthony H. Verfasser (DE-588)1025836685 aut The conceptual framework of quantum field theory Anthony Duncan Reprinted with corrections Oxford Oxford University Press 2013 © 2012 x, 782 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite [765] - 776 Geschichte gnd rswk-swf Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenfeldtheorie (DE-588)4047984-5 s Geschichte z DE-604 Erscheint auch als Online-Ausgabe 978-0-19-164220-3 DE-601 pdf/application http://zbmath.org/?q=an:1252.81001 Zentralblatt MATH Inhaltstext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027392654&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027392654&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Duncan, Anthony H. The conceptual framework of quantum field theory Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4123623-3 |
| title | The conceptual framework of quantum field theory |
| title_auth | The conceptual framework of quantum field theory |
| title_exact_search | The conceptual framework of quantum field theory |
| title_full | The conceptual framework of quantum field theory Anthony Duncan |
| title_fullStr | The conceptual framework of quantum field theory Anthony Duncan |
| title_full_unstemmed | The conceptual framework of quantum field theory Anthony Duncan |
| title_short | The conceptual framework of quantum field theory |
| title_sort | the conceptual framework of quantum field theory |
| topic | Quantum field theory Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Quantum field theory Quantenfeldtheorie Lehrbuch |
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