Gauge theory of elementary particle physics, problems and solutions: problems and solutions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Clarendon Press [u.a.]
2007
|
| Ausgabe: | reprint. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 306 S. graph. Darst. |
| ISBN: | 9780198506218 |
Internformat
MARC
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| 100 | 1 | |a Cheng, Ta-Pei |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Gauge theory of elementary particle physics, problems and solutions |b problems and solutions |c Ta-Pei Cheng and Ling-Fong Li |
| 250 | |a reprint. | ||
| 264 | 1 | |a Oxford [u.a.] |b Clarendon Press [u.a.] |c 2007 | |
| 300 | |a X, 306 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 689 | 1 | 0 | |a Eichtheorie |0 (DE-588)4122125-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Li, Ling-Fong |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016369994&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804137451910856704 |
|---|---|
| adam_text | Contents
1
Field quantization
1.1
Simple exercises in
λφ4
theory
1
1.2
Auxiliary field
6
1.3
Disconnected diagrams
8
1.4
Simple external field problem
9
1.5
Path integral for a free particle
11
1.6
Path integral for a general quadratic action
13
1.7
Spreading of a wave packet
16
1.8
Path integral for a harmonic oscillator
17
1.9
Path integral for a partition function
21
1.10
Partition function for an SHO system
23
1.11
Non-standard path-integral representation
25
1.12
Weyl ordering of operators
26
1.13
Generating functional for a scalar field
32
1.14
Poles in Green s function
35
2
Renormalization
2.1
Counterterms in
λφ4
theory and in QED
37
2.2
Divergences in non-linear chiral theory
39
2.3
Divergences in lower-dimensional field theories
41
2.4
n-Dimensional
spherical coordinates
43
2.5
Some integrals in dimensional regularization
46
2.6
Vacuum polarization and subtraction schemes
49
2.7
Renormalization of
λφ3
theory in
η
dimensions
53
2.8
Renormalization of composite operators
57
2.9
Cutkosky rules
59
3
Renormalization group
3.1
Homogeneous renormalization-group equation
63
3.2
Renormalization constants
64
3.3
/S-functionforQED
67
3.4
Behaviour of
g
near a simple fixed point
69
3.5
Running coupling near a general fixed point
70
3.6
One-loop renormalization-group equation in massless
λφ4
theory
7
1
3.7
/S-function for the Yukawa coupling
72
3.8
Solving the renormalization-group equation by Coleman s method
75
3.9
Anomalous dimensions for composite operators
77
viu
Contents
4
Group
theory and the quark model
4.1
Unitary and hermitian matrices
78
4.2
SUCn) matrices
79
4.3
Reality of
811(2)
representations
79
4.4
An identity for unitary matrices
81
4.5
An identity for SU(2) matrices
82
4.6
SU(3)
algebra in terms of quark fields
83
4.7
Combining two spin- states
85
4.8
The SU(2) adjoint representation
87
4.9
Couplings of SU(2) vector representations
89
4.10
Isospin breaking effects
90
4.11
Spin wave function of three quarks
93
4.12
Permutation symmetry in the spin-isospin space
96
4.13
Combining two fundamental representations
97
4.14
SU(3) invariant octet baryon-meson couplings
100
4.15
Isospin wave functions of two
pions
105
4.16 Isospins
in non-leptonic weak processes
107
5
Chiral symmetry
5.1
Another derivation of Noether
s
current
110
5.2
Lagrangian with second derivatives 111
5.3
Conservation laws in a non-relativistic theory
113
5.4
Symmetries of the linear
σ
-model
115
5.5
Spontaneous symmetry breaking in the
σ
-model
122
5.6
PCAC in the
σ
-model
123
5.7
Non-linear
σ
-model
I
126
5.8
Non-linear
σ
-model
II
128
5.9
Non-linear
σ
-model
III
130
5.10
SSB by two scalars in the vector representation
133
6
Renormalization and symmetry
6.1
Path-integral derivation of axial anomaly
136
6.2
Axial anomaly and
η
—>
γγ
140
6.3
Soft symmetry breaking and renormalizability
142
6.4
Calculation of the one-loop effective potential
143
7
The
Parton
model and scaling
7.1
The Gottfried sum rule
146
7.2
Calculation of OPE Wilson coefficients
147
7.3
atot(e+e~
—>·
hadrons) and short-distance physics
151
7.4
OPE of two charged weak currents
155
7.5
The total decay rate of the W-boson
156
8
Gauge symmetries
8.1
The gauge field in tensor notation
158
8.2
Gauge field and geometry
161
8.3
General relativity as a gauge theory
163
Contents ix
8.4
0(и)
gauge theory
165
8.5
Broken generators and
Goldstone
bosons
167
8.6
Symmetry breaking by an adjoint scalar
169
8.7
Symmetry breaking and the coset space
171
8.8
Scalar potential and first-order phase transition
172
8.9
Superconductivity as a Higgs phenomenon
173
9
Quantum gauge theories
9.1
Propagator in the covariant
Щ
gauge
175
9.2
The propagator for a massive vector field
176
9.3
Gauge boson propagator in the axial gauge
177
9.4
Gauge boson propagator in the Coulomb gauge
178
9.5
Gauge
invariance
of a scattering amplitude
180
9.6
Ward identities in QED
180
9.7 Nilpotent BRST
charges
184
9.8
BRST
charges and physical states
186
10
Quantum chromodynamics
10.1
Colour factors in QCD loops
188
10.2
Running gauge coupling in two-loop
191
10.3
Cross-section for three-jet events
193
10.4
Operator-product expansion of two currents
198
10.5
Calculating Wilson coefficients
201
11
Electroweak theory
11.1
Crural spinors and
helicity
states
205
11.2
The polarization vector for a fermion
206
11.3
The
pion
decay rate and
/π
208
11.4
Uniqueness of the standard model scalar potential
212
11.5
Electromagnetic and gauge couplings
213
11.6
Fermion mass-matrix diagonalization
214
11.7
An example of calculable mixing angles
215
11.8
Conservation of the
В
—
L
quantum number
216
12
Electroweak phenomenology
12.1
Atomic parity violation
218
12.2
Polarization asymmetry of
Z
-» ƒ ƒ 221
12.3
Simple
т
-lepton
decays
222
12.4
Electron neutrino scatterings
223
12.5
CP properties of kaon non-leptonic decays
225
12.6
Z
-*
H H
is forbidden
226
12.7
AI = ì
enhancement by short-distance QCD
227
12.8
Scalar interactions and the equivalence theorem
230
12.9
Two-body decays of a heavy Higgs boson
234
x
Contents
13
Topics
in f
lavourdynamics
13.1
Anomaly-free condition in a technicolour theory
238
13.2
Pseudo-Goldstone bosons in a technicolour model
239
13.3
Properties of
Majorana
fermions
239
13.4
μ
—*■
е у
and heavy neutrinos
244
13.5
Leptonic mixings in a vector-like theory
250
13.6
Muomum-antimuonium transition
252
14
Grand unification
14.1
Content of
SU(5)
representations
255
14.2
Higgs potential for
SU(5)
adjoint scalars
256
14.3
Massive gauge bosons in
80(5) 258
14.4 Baryon
number non-conserving operators
260
14.5
ЅО(и)
group algebra
260
14.6
Spinor representations of
ЅО(и)
263
14.7
Relation between
ЅО(2и)
and SU(n) groups
267
14.8
Construction of SO(2n) spinors
269
15
Magnetic
monopoles
15.1
The Sine-Gordon equation
275
15.2
Planar vortex field
280
15.3
Stability of soliton
282
15.4
Monopole
and angular momentum
283
16
Instantons
16.1
The saddle-point method
289
16.2
An application of the saddle-point method
292
16.3
A Euclidean double-well problem
295
References
301
Index
303
|
| adam_txt |
Contents
1
Field quantization
1.1
Simple exercises in
λφ4
theory
1
1.2
Auxiliary field
6
1.3
Disconnected diagrams
8
1.4
Simple external field problem
9
1.5
Path integral for a free particle
11
1.6
Path integral for a general quadratic action
13
1.7
Spreading of a wave packet
16
1.8
Path integral for a harmonic oscillator
17
1.9
Path integral for a partition function
21
1.10
Partition function for an SHO system
23
1.11
Non-standard path-integral representation
25
1.12
Weyl ordering of operators
26
1.13
Generating functional for a scalar field
32
1.14
Poles in Green's function
35
2
Renormalization
2.1
Counterterms in
λφ4
theory and in QED
37
2.2
Divergences in non-linear chiral theory
39
2.3
Divergences in lower-dimensional field theories
41
2.4
n-Dimensional
'spherical' coordinates
43
2.5
Some integrals in dimensional regularization
46
2.6
Vacuum polarization and subtraction schemes
49
2.7
Renormalization of
λφ3
theory in
η
dimensions
53
2.8
Renormalization of composite operators
57
2.9
Cutkosky rules
59
3
Renormalization group
3.1
Homogeneous renormalization-group equation
63
3.2
Renormalization constants
64
3.3
/S-functionforQED
67
3.4
Behaviour of
g
near a simple fixed point
69
3.5
Running coupling near a general fixed point
70
3.6
One-loop renormalization-group equation in massless
λφ4
theory
7
1
3.7
/S-function for the Yukawa coupling
72
3.8
Solving the renormalization-group equation by Coleman's method
75
3.9
Anomalous dimensions for composite operators
77
viu
Contents
4
Group
theory and the quark model
4.1
Unitary and hermitian matrices
78
4.2
SUCn) matrices
79
4.3
Reality of
811(2)
representations
79
4.4
An identity for unitary matrices
81
4.5
An identity for SU(2) matrices
82
4.6
SU(3)
algebra in terms of quark fields
83
4.7
Combining two spin- \ states
85
4.8
The SU(2) adjoint representation
87
4.9
Couplings of SU(2) vector representations
89
4.10
Isospin breaking effects
90
4.11
Spin wave function of three quarks
93
4.12
Permutation symmetry in the spin-isospin space
96
4.13
Combining two fundamental representations
97
4.14
SU(3) invariant octet baryon-meson couplings
100
4.15
Isospin wave functions of two
pions
105
4.16 Isospins
in non-leptonic weak processes
107
5
Chiral symmetry
5.1
Another derivation of Noether'
s
current
110
5.2
Lagrangian with second derivatives 111
5.3
Conservation laws in a non-relativistic theory
113
5.4
Symmetries of the linear
σ
-model
115
5.5
Spontaneous symmetry breaking in the
σ
-model
122
5.6
PCAC in the
σ
-model
123
5.7
Non-linear
σ
-model
I
126
5.8
Non-linear
σ
-model
II
128
5.9
Non-linear
σ
-model
III
130
5.10
SSB by two scalars in the vector representation
133
6
Renormalization and symmetry
6.1
Path-integral derivation of axial anomaly
136
6.2
Axial anomaly and
η
—>
γγ
140
6.3
Soft symmetry breaking and renormalizability
142
6.4
Calculation of the one-loop effective potential
143
7
The
Parton
model and scaling
7.1
The Gottfried sum rule
146
7.2
Calculation of OPE Wilson coefficients
147
7.3
atot(e+e~
—>·
hadrons) and short-distance physics
151
7.4
OPE of two charged weak currents
155
7.5
The total decay rate of the W-boson
156
8
Gauge symmetries
8.1
The gauge field in tensor notation
158
8.2
Gauge field and geometry
161
8.3
General relativity as a gauge theory
163
Contents ix
8.4
0(и)
gauge theory
165
8.5
Broken generators and
Goldstone
bosons
167
8.6
Symmetry breaking by an adjoint scalar
169
8.7
Symmetry breaking and the coset space
171
8.8
Scalar potential and first-order phase transition
172
8.9
Superconductivity as a Higgs phenomenon
173
9
Quantum gauge theories
9.1
Propagator in the covariant
Щ
gauge
175
9.2
The propagator for a massive vector field
176
9.3
Gauge boson propagator in the axial gauge
177
9.4
Gauge boson propagator in the Coulomb gauge
178
9.5
Gauge
invariance
of a scattering amplitude
180
9.6
Ward identities in QED
180
9.7 Nilpotent BRST
charges
184
9.8
BRST
charges and physical states
186
10
Quantum chromodynamics
10.1
Colour factors in QCD loops
188
10.2
Running gauge coupling in two-loop
191
10.3
Cross-section for three-jet events
193
10.4
Operator-product expansion of two currents
198
10.5
Calculating Wilson coefficients
201
11
Electroweak theory
11.1
Crural spinors and
helicity
states
205
11.2
The polarization vector for a fermion
206
11.3
The
pion
decay rate and
/π
208
11.4
Uniqueness of the standard model scalar potential
212
11.5
Electromagnetic and gauge couplings
213
11.6
Fermion mass-matrix diagonalization
214
11.7
An example of calculable mixing angles
215
11.8
Conservation of the
В
—
L
quantum number
216
12
Electroweak phenomenology
12.1
Atomic parity violation
218
12.2
Polarization asymmetry of
Z
-» ƒ ƒ 221
12.3
Simple
т
-lepton
decays
222
12.4
Electron neutrino scatterings
223
12.5
CP properties of kaon non-leptonic decays
225
12.6
Z
-*
H H
is forbidden
226
12.7
AI = ì
enhancement by short-distance QCD
227
12.8
Scalar interactions and the equivalence theorem
230
12.9
Two-body decays of a heavy Higgs boson
234
x
Contents
13
Topics
in f
lavourdynamics
13.1
Anomaly-free condition in a technicolour theory
238
13.2
Pseudo-Goldstone bosons in a technicolour model
239
13.3
Properties of
Majorana
fermions
239
13.4
μ
—*■
е у
and heavy neutrinos
244
13.5
Leptonic mixings in a vector-like theory
250
13.6
Muomum-antimuonium transition
252
14
Grand unification
14.1
Content of
SU(5)
representations
255
14.2
Higgs potential for
SU(5)
adjoint scalars
256
14.3
Massive gauge bosons in
80(5) 258
14.4 Baryon
number non-conserving operators
260
14.5
ЅО(и)
group algebra
260
14.6
Spinor representations of
ЅО(и)
263
14.7
Relation between
ЅО(2и)
and SU(n) groups
267
14.8
Construction of SO(2n) spinors
269
15
Magnetic
monopoles
15.1
The Sine-Gordon equation
275
15.2
Planar vortex field
280
15.3
Stability of soliton
282
15.4
Monopole
and angular momentum
283
16
Instantons
16.1
The saddle-point method
289
16.2
An application of the saddle-point method
292
16.3
A Euclidean double-well problem
295
References
301
Index
303 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Cheng, Ta-Pei Li, Ling-Fong |
| author_facet | Cheng, Ta-Pei Li, Ling-Fong |
| author_role | aut aut |
| author_sort | Cheng, Ta-Pei |
| author_variant | t p c tpc l f l lfl |
| building | Verbundindex |
| bvnumber | BV023183494 |
| classification_rvk | UO 4000 UO 4060 |
| classification_tum | PHY 417f PHY 003f |
| ctrlnum | (OCoLC)316000556 (DE-599)BVBBV023183494 |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | reprint. |
| format | Book |
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| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV023183494 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:02:18Z |
| indexdate | 2024-07-09T21:12:31Z |
| institution | BVB |
| isbn | 9780198506218 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016369994 |
| oclc_num | 316000556 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | X, 306 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Clarendon Press [u.a.] |
| record_format | marc |
| spelling | Cheng, Ta-Pei Verfasser aut Gauge theory of elementary particle physics, problems and solutions problems and solutions Ta-Pei Cheng and Ling-Fong Li reprint. Oxford [u.a.] Clarendon Press [u.a.] 2007 X, 306 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Eichtheorie (DE-588)4122125-4 gnd rswk-swf Elementarteilchenphysik (DE-588)4014414-8 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Eichtheorie (DE-588)4122125-4 s Elementarteilchenphysik (DE-588)4014414-8 s DE-604 Li, Ling-Fong Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016369994&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cheng, Ta-Pei Li, Ling-Fong Gauge theory of elementary particle physics, problems and solutions problems and solutions Eichtheorie (DE-588)4122125-4 gnd Elementarteilchenphysik (DE-588)4014414-8 gnd |
| subject_GND | (DE-588)4122125-4 (DE-588)4014414-8 (DE-588)4143389-0 |
| title | Gauge theory of elementary particle physics, problems and solutions problems and solutions |
| title_auth | Gauge theory of elementary particle physics, problems and solutions problems and solutions |
| title_exact_search | Gauge theory of elementary particle physics, problems and solutions problems and solutions |
| title_exact_search_txtP | Gauge theory of elementary particle physics, problems and solutions problems and solutions |
| title_full | Gauge theory of elementary particle physics, problems and solutions problems and solutions Ta-Pei Cheng and Ling-Fong Li |
| title_fullStr | Gauge theory of elementary particle physics, problems and solutions problems and solutions Ta-Pei Cheng and Ling-Fong Li |
| title_full_unstemmed | Gauge theory of elementary particle physics, problems and solutions problems and solutions Ta-Pei Cheng and Ling-Fong Li |
| title_short | Gauge theory of elementary particle physics, problems and solutions |
| title_sort | gauge theory of elementary particle physics problems and solutions problems and solutions |
| title_sub | problems and solutions |
| topic | Eichtheorie (DE-588)4122125-4 gnd Elementarteilchenphysik (DE-588)4014414-8 gnd |
| topic_facet | Eichtheorie Elementarteilchenphysik Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016369994&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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