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Rajaraman R. Ч Solitons and instantons
Rajaraman R. Ч Solitons and instantons

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Ќазвание: Solitons and instantons

јвтор: Rajaraman R.


This book offers an elementary and unified introduction to the non-perturbative results obtained in relativistic quantum field theory based on classical soliton and instanton solutions. Such solutions are derived for a variety of models and classified by topological indices. The methods are then developed for quantizing solitons to obtain quantum particles. Vacuum tunneling, &ugr;-vacua and the dilute-instanton-gas approximation are described in detail. Other instanton effects related to quark-quark forces, confinement, the U(1) problem and Borel summability are also discussed. The emphasis is on presenting the basic ideas in a simple pedagogical way. Technical tools like functional methods, Grassman integrals, homotopy classification, collective co-ordinates etc. are developed ab initio.
The presentation of this work is kept at a fairly simple level and ideas are developed through illustrative examples. Techniques not covered in older field theory textbooks, such as functional integral methods, are presented in some detail to the necessary extent. These techniques are important in their own right. Although the book is mainly addressed to particle physicists and quantum field theorists, several portions will be of relevance to other branches of physics, particularly statistical mechanics. These include three chapters devoted to deriving classical soliton and instanton solutions and one on collective co-ordinates, as well as sections devoted to general techniques

язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1989

 оличество страниц: 409

ƒобавлена в каталог: 08.12.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
"Classical limit" of Fermi fields      264Ч265 272
"Classical limit" of Fermi fields, functional integrals over      272Ч273
"Elementary" bosons      208 209
"Elementary" bosons, disappearance of      216
$CP_N$ model      116
$CP_N$ model, gauge invariance in      117
$CP_N$ model, instantons of      122
$CP_N$ model, relationship to O(3) model      123
$\theta$-vacua and $\theta$-sectors      333Ч337 341Ч343
$\theta$-vacua and $\theta$-sectors and cluster decomposition      371Ч372
$\theta$-vacua and $\theta$-sectors, background field in      352Ч353 372Ч373
$\theta$-vacua and $\theta$-sectors, degeneracy and chiral symmetry      372
$\theta$-vacua and $\theta$-sectors, restoration of equivalence of      373
'tHooft Ч Polyakov monopoles and the Bogomol'nyi condition      69Ч70
'tHooft Ч Polyakov monopoles and the Dirac Ч Schwinger quantisation condition      67
'tHooft Ч Polyakov monopoles, as solitary waves      70
'tHooft Ч Polyakov monopoles, force between      83
'tHooft Ч Polyakov monopoles, generalisation to higher groups and other representations      73Ч74
'tHooft Ч Polyakov monopoles, homotopy analysis      62Ч63
'tHooft Ч Polyakov monopoles, mass of      70
'tHooft Ч Polyakov monopoles, topological current and charge      64Ч65
1/N expansion      115 349 384
Abelian (Higgs) gauge model      75 113 318
Abelian (Higgs) gauge model, $\theta$-vacua in      333Ч337
Abelian (Higgs) gauge model, confinement in      356Ч357
Abelian (Higgs) gauge model, in (2 + 1) dimensions      76
Abelian (Higgs) gauge model, instantons in (1 + 1) dimensions      114 331
Abelian (Higgs) gauge model, on Higgs phenomenon in      318Ч319
Abelian (Higgs) gauge model, solitons of      77Ч78
Abelian (Higgs) gauge model, topological |N> vacua in      325
Abelian (Higgs) gauge model, vacuum tunnelling in      331Ч332
Action-angle variables      41Ч42 200
Analyticity      225Ч226
anomalies      7 8 see
Anti-commuting c-numbers      see "Grassmann numbers"
Anti-instanton of PPP      306
Anti-instanton of the Yang Ч Mills system      104
asymptotic freedom      8
Asymptotic freedom of QCD      359
Asymptotic freedom of the O(3) model      115
Asymptotic freedom of the Yang Ч Mills system      347
Axial current anomaly      361 364Ч365
Axial current anomaly and vacuum tunnelling suppression      365Ч370
Axions      383
Backlund transformations      6 43Ч44
Backlund transformations for the sine-Gordon system      43Ч44
Binding energy of SG bound states      209Ч211
Binding energy of SG bound states by Bethe Ч Salpeter equation      210Ч211
Binding energy of SG bound states, non-relativistic limit      210
Bloch's theorem      305 332
Bloch's theorem, derivation using instantons      312
Bogomolnyi condition      69Ч70
Bohr Ч Sommerfeld condition, derivation using path integrals      183Ч187
Bohr Ч Sommerfeld condition, generalisation in field theory      195
Borel function      375
Borel function for GreenТs functions      376Ч377
Borel sum      375
Borel sum, generalisation      379
Borel summation procedure      374Ч375
Borel summation procedure, impact of instantons on      377Ч380
Bosonisation      217
Breather solutions of the sine-Gordon model      see "Doublet solutions"
CDD ambiguities      232
CDD ambiguities, removal of, for O(N) and GN models      235Ч236
CDD ambiguities, removal of, in the SG model      233Ч235
Charge conjugation      279 295Ч297
Charge conjugation, matrices      279 295
Charge conjugation, operator      296Ч297
Charge-monopole duality      74
Charged soliton solutions      27 249Ч252
Chiral SU(2) $\otimes$ SU(2) symmetry      360
Chiral SU(2) $\otimes$ SU(2) symmetry and massless quarks      360
Chiral SU(2) $\otimes$ SU(2) symmetry, spontaneous breaking of      360Ч361
Chiral U(1) charge and suppression of tunnelling      370
Chiral U(1) charge, gauge invariant ($Q_5$)      369
Chiral U(1) charge, gauge variant ($\bar{Q}_5$)      369
Chirality of operators      370
Cluster decomposition      370Ч372
Collective coordinates      237
Collective coordinates for general symmetries      262
Collective coordinates for translation symmetry      254
Collective coordinates in a U(1) symmetric model      246Ч247
Collective coordinates in Euclidean functional integral      390Ч393
Collective coordinates in non-relativistic quantum mechanics      238Ч243
Collective coordinates, Jacobian associated with      393
Colour group      358
Colour group, indices of      359
Colour group, suppression of indices of      360 363
confinement      3
Confinement and instantons in QCD      357Ч358
Confinement of charges by instantons      356Ч357
Confinement of quarks in QCD      3 348 351
Continuous symmetry and the semi-classical method      131 150Ч153
Continuous symmetry in a complex scalar field theory      244
Continuous symmetry in a non-relativistic problem      238
Crossing symmetry      225
Crossing symmetry for (1 + 1) dimensional O(N) models      227
Cubic identities for S matrices      223
Cubic identities for S matrices for O(N) models      227Ч228
Dilute instanton gas      313 331
Dilute instanton gas, difficulties with, in Yang Ч Mills theory      344Ч347
Dilute instanton gas, self consistency of, in PPP      313
Dirac field theory with quartic interaction      280 299Ч301
Dirac field theory, energy spectrum for free field      277
Dirac field theory, functional integral for free field      273Ч274
Dirac field theory, functional integral for interacting field      280
Dirac Hamiltonian (single particle)      275 278 285
Dirac matrices      274
Dirac matrices in (1 + 1) dimensions      291
Dirac matrices, a representation of      279
Doublet (or Breather) solutions, as bound states      209
Doublet (or Breather) solutions, as poles in the S-matrix      234
Doublet (or Breather) solutions, classical      40
Doublet (or Breather) solutions, interpretation of      208Ч213
Doublet (or Breather) solutions, quantisation of      203 208
Doublet (or Breather) solutions, quantum mass of      207
Doublet (or Breather) solutions, quantum statility of      211Ч212
Dyons      71Ч72
Energy band in a periodic potential      304Ч305
Energy band in a periodic potential, derivation using instantons      305Ч311
Euclidean action definition      85
Euclidean action definition and static energy functionals      112Ч113
Euclidean action definition for the $CP_N$ model      118
Euclidean action definition for the abelian Higgs model      326
Euclidean action definition for the Klein Ч Gordon system      85
Euclidean action definition for the pendulum      112
Euclidean action definition for the Yang Ч Mills system      88
Euclidean action definition of the sine-Gordon system      317
Euclidean systems, action of      85Ч86
Euclidean systems, definition      84Ч85
Euclidean systems, field equations of      85 88 118
Euclidean systems, functional integrals for      175 181Ч183
Exact S-matrices      225Ч236
Exact S-matrices for the Gross Ч Neveu model      236
Exact S-matrices for the non-linear O(3) model      236
Exact S-matrices for the SG model      233Ч235
Factorisation of S-matrices      223
Fermi fields, "classical limit" of      264Ч265
Fermi fields, functional integrals for      272Ч273
Fermi fields, soliton quantisation for      284Ч298
Fermions from Bose fields      73 214 218Ч219
Flavour      359
Floquet indices      287
Flux quantisation in superconductors      76Ч77
Form factors of soliton states      159Ч160
Functional integrals in field theory      176
Functional integrals in field theory and quantisation of static solitons      178Ч180
Functional integrals in field theory and quantisation periodic solitons      194Ч195
Functional integrals in field theory for abelian Higgs model      329
Functional integrals in field theory for Fermi fields      272Ч273 280
Functional integrals in field theory for the Yang Ч Mills theory      342
Functional integrals in field theory, boundary conditions      177
Functional integrals in field theory, Euclidean case      181Ч182
Functional integrals in field theory, gaussian approximation to      181
Functional integrals in field theory, stationary phase approximation (SPA) to      179
Gauge Fields      60
Gauge fields, matrix notation for      87 359
Gauge fixing terms      329 342
Gauge transformations, abelian      117Ч118 319
Gauge transformations, non-abelian      60 87 337
Gauge transformations, small and large      323
Gauge transformations, time-independent      323 338
Gauss' theorem and gauge equivalence, abelian      321Ч323
Gauss' theorem and gauge equivalence, non-abelian      339Ч340
Gaussian approximation      181 306
Goldstone bosons      360 151
Goldstone bosons and SU(2) $\otimes$ SU(2) symmetry      360
Goldstone bosons, absence of, for U(1) symmetry      361
Goldstone bosons, axions as      383
Grassmann algebra, definition      266
Grassmann algebra, generators of      266
Grassmann algebra, odd and even subsets of      266
Grassmann fields      265 271Ч272
Grassmann fields, functional integrals over      272Ч273
Grassmann numbers      265
Grassmann numbers, change of variables in integration      269
Grassmann numbers, derivatives with respect to      267
Grassmann numbers, exponential integral      270
Grassmann numbers, integration over      268
Gross Ч Neveu (GN) model      225 236
Gross Ч Neveu (GN) model, definition of      300
Gross Ч Neveu (GN) model, S-matrix of      236
Gross Ч Neveu (GN) model, semi-classical method for      301
Group measure for SU(2)      93Ч95
Half-integral charge, solitons with      295Ч298
Heavy quark potential      381
Higgs (scalar) fields, definition      60
Higgs mechanism      see "Higgs phenomenon"
Higgs phenomenon      318Ч319
Higgs phenomenon, prevention by instantons      320 337 352 357
Homotopy classification      see "Topological charge"
Homotopy classification and gauge equivalence      325 340
Homotopy classification in liquid crystals      79
Homotopy classification in the $CP_N$ model      119
Homotopy classification in the abelian Higgs model      76
Homotopy classification in the Euclidean Yang Ч Mills system      90Ч98
Homotopy classification in the O(3) model      53Ч54
Homotopy classification of classical gauge vacua      324Ч325 338
Homotopy classification of mappings of circles into circles      51Ч52
Homotopy classification of monopole solutions      62Ч63
Homotopy classification, some general results      74
Infra-red divergence in Yang Ч Mills instanton effects      344Ч347
Instantons of SU(N) gauge theories      114
Instantons of the $CP_N$ model      122
Instantons of the abelian Higgs model      113Ч114
Instantons of the Yang Ч Mills system      88 103
Instantons, absence of, in O(N) models      113
Instantons, general definition of      2 84Ч85
Instantons, relevance of finite size of      308 344Ч345
Internal space      49
Internal space, centrifugal effect in      252
Internal space, global rotations in      49Ч61
Internal space, local transformations in      59Ч61
Internal space, rotation in      249 252
Inverse scattering method      6 9 15
Inverse scattering method for the sine-Gordon system      41Ч42
Kink of $\phi^4$ - theory, anti-kink      20
Kink of $\phi^4$ - theory, classical solution      20
Kink of $\phi^4$ - theory, fluctuation modes about      140Ч141
Kink of $\phi^4$ - theory, form factors of      159Ч160
Kink of $\phi^4$ - theory, mass of classical solution      21
Kink of $\phi^4$ - theory, mass of the quantum kink      144Ч148
Kink of $\phi^4$ - theory, non-perturbative nature      23
Kink of $\phi^4$ - theory, quantisation of      137Ч150
Kink of $\phi^4$ - theory, quantum stability of      155
Landau Ч Ginzburg model      76
Langer modification      242
Localised solutions, definition of      13
Massive Thirring model      213
Massive Thirring model, bound states in strong coupling      215Ч216
Massive Thirring model, equivalence to SG model      213Ч215
Massive Thirring model, O(2) invariance of      233
Massive Thirring model, S-matrix of      233Ч235
Massless fermions and chiral symmetry      360Ч361 364
Massless fermions and suppression of vacuum tunnelling      368
Matrix notation for Yang Mills fields      87
Mechanical analogy to non-linear equations      17Ч20 24Ч27
Mechanical analogy to non-linear equations, orbits in      24Ч31
Meron solutions      348 383 384
Monopoles      see "'tHooft Ч Polyakov monopoles"
Non-abelian Higgs model      59Ч60 352 357
Non-linear O(3) model      49
Non-linear O(3) model, exact S-matrix of      236
Non-linear O(3) model, homotopy analysis in 2 dimensions      51Ч52
Non-linear O(3) model, relevance to ferromagnets      58 80
Non-linear O(3) model, static solitons in (2 + 1) dimensions      57
Non-topological solitons      33
Non-topological solitons, static      30
Non-topological solitons, time dependent      250
Normal modes of fluctuations      132
Normal modes of fluctuations in scalar field theory      134
Normal modes of fluctuations with zero frequency      see "Zero-modes"
Normal modes of fluctuations, around the kink solution      140
Normal modes of fluctuations, around the SG soliton      201
Normal ordering      146Ч147 202
Nuclear democracy      209
Operator ordering problem in quantum mechanics      243
Operator ordering problem in soliton quantisation      258 259
Parity symmetry and axions      383
Parity symmetry, violation by $\theta$-vacua      335 343 382
Particle on a circle (POC)      314Ч317
Particle on a circle (POC), $\theta$-dependcnt ground state      316
Particle on a circle (POC), similarity to $\theta$-vacua      335Ч336
Path integrals and the energy spectrum      170 174Ч175
Path integrals and the stationary phase approximation (SPA)      170Ч171
Path integrals, applied to the oscillator      172Ч174
Path integrals, definition      169
Path integrals, Euclidean      175Ч176
Path integrals, gaussian approximation to      306
Path-ordered exponentials      89 357
Periodic potential problem (PPP)      303
Periodic potential problem (PPP), derivation of energy band      305Ч311
Periodic potential problem (PPP), instanton of      306Ч307
Periodic potential problem (PPP), properties of      304Ч305
Periodic potential problem (PPP), restoration of symmetry in      314
Perturbation scries, Borel summation of      375
Perturbation scries, radius of convergence      373Ч379
Perturbation series, divergence of      374
Pontryagin index      91 338 341
Pontryagin index and fermion zero modes      367
Pontryagin index, current associated with      92
Pontryagin index, density of      92
Pontryagin index, gauge invariance of      97
Prasad Ч Sommerfield limit      69
Quantisation of static solitons by canonical operator methods      257Ч263 285Ч286 295Ч297
Quantisation of static solitons in higher dimensions      165
Quantisation of static solitons in the presence of Fermi fields      166 281Ч286 291Ч298
Quantisation of static solitons, as applied to the $\phi^4$-kink      137Ч150
Quantisation of static solitons, as applied to the sine-Gordon soliton      201Ч203
Quantisation of static solitons, general principles      133Ч135
Quantisation of static solitons, mass renormalisation in      144Ч150
Quantisation of static solitons, non-perturbative aspect of      124 149
Quantisation of static solitons, using functional integrals      178 180 281Ч285
Quantisation of time-dependent solitons in field theory      194
Quantisation of time-dependent solitons in non-relativistic quantum mechanics      183Ч193
Quantisation of time-dependent solitons in the presence of Fermi fields      286Ч288
Quantisation of time-dependent solitons, applied to sine-Gordon doublets      203Ч208
Quantum chromodynamics (QCD)      2Ч5
Quantum chromodynamics (QCD), definition of      358Ч359
Quantum chromodynamics (QCD), miniature version of      362
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