Hatfield B. — Quantum field theory of point particles and strings :: Электронная библиотека попечительского совета мехмата МГУ

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Hatfield B. — Quantum field theory of point particles and strings

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Название: Quantum field theory of point particles and strings

Автор: Hatfield B.

Аннотация:

The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. Allof the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization andapplication of quantum field theory for point particles to strings.

Язык:

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 734

Добавлена в каталог: 10.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Gauge-fixed action, superstring      697
Gauge-fixed action, Yang — Mills      356 357
Gauss — Bonnet theorem, global      561 623
Gauss — Bonnet theorem, local      557
Gauss's law constraint, free electromagnetic field      212
Gauss's law constraint, QED      255
Gauss's law constraint, relation to gauge invariance      212 245
Gauss's law constraint, use in solving Schrodinger eq.      249 258
Gauss's law constraint, Yang — Mills      245
Gaussian curvature      556—558
Gaussian effective potential      462
Genus      536 546
Geodesic      553
Geometric structure      543—544
Ghost states in covariant bosonic string      532
Ghost-free gauge      359
Ghosts (negative normed states)      89—90
Ghosts (negative normed states) no ghosts in the electrodynamic Lorentz gauge      92
Ghosts (negative normed states) representation of Faddeev — Popov determinant      356
Goldstone bosons      443
Grassmann variables      190
Grassmann variables $\delta$ -functional, definition      192
Grassmann variables supersurface $\delta$ -function      715
Grassmann variables, differentiation      191
Grassmann variables, functional derivative      192
Grassmann variables, in fermionic wave functionals      219
Grassmann variables, integration      191 323
Gravitino      693
Greena's function for $\Delta_{g}$ , conformal dependence      660
Greena's function for $\Delta_{g}$ , genus 0      659—660
Greena's function for $\Delta_{g}$ , genus 1      666
Greena's function for $\Delta_{g}$ , short-distance behavior      660
GSO projection      719
gyromagnetic ratio      417
Hadrons      5
harmonic oscillator      16—19
Harmonic oscillator, classical Green's function      291 311
Harmonic oscillator, Heisenberg picture      16—18
Harmonic oscillator, path integral representation      286—294
Harmonic oscillator, Schrodinger representation      18—19
Hausdorff space      539
Heat kernel, perturbative expansion      618—619
Heat kernel, role of zero modes      620—621
Heat kernel, use in evaluation of determinants      613—615 617—621
Higg's mechanism      471
Holomorphic      564
Holomorphic differential      599
Holomorphic factorization      644
Homeomorphism      540
Homology group      597
Homology group, basis      599 651
Homotopic      561
Hyperbolic metric      574
Image      539
In-out fields, electromagnetic      162
In-out fields, fermionic      159
In-out fields, scalar      113—114
Indiscrete topology      538
Induced world-sheet metric      492 505
Infrared divergences in QED      410
Injective (1—1)      539
Instantaneous Coulomb energy      152 338
Integral curves      592
Intersection matrix      598
Intersection product      598
Isothermal      571 584 648 645
Isothermal, coordinates and complex structure      584—585
Jacobi $\vartheta$ -functions      666
Killing vector field      596
Killing vector field, conformal      596
Klein — Gordon, current      37
Klein — Gordon, equation      36
Klein — Gordon, propagator      53
Lamb shift      408
Landau ghost      428
Laplace — Beltrami operator      611
Leptons      5
Levi — Civita connection      555
Lie derivative      593
Lie derivative, metric tensor      595 606
Lie derivative, scalar      594
Lie derivative, vector      594
Lie dragged      594
Linear fractional transformation      568
Liouville model      629 637 670
Liouville model, quantization in conformal gauge      672—674
Liouville model, supersymmetric extension      717—718
Loop expansion, as expansion in powers of $\hbar$       374
Loop expansion, scalar field theory      374
Lorentz algebra      57
Lorentz gauge propagator      91
Lorentz generators, scalar field      56
Lorentz generators, spinor field      75—76
Lorentz group, spinorial representations      691
Magnetic moment of electron      416
Mandelstam variables      663
Manifold      540
Manifold, differentiable      542
Manifold, Riemannian      543
Mapping class group      587 600
Mapping Class group, torus (genus 1)      591
Meromorphic      565
Meromorphic differential      599
Mesons      5
Metric tensor      544 554
Metric tensor, flat supersurface      698
Metric tensor, spinorial      696
Metric, on space of metrics      592 605
Microcausality      47 72
Mobius transformation      568
Mode expansion, bosonic string      507 508 510 517
Mode expansion, free electromagnetic field      83—84 88
Mode expansion, free scalar field      43—45
Mode expansion, free spinor field      70 318
Mode expansion, functional rep (bosonic string)      520
Mode expansion, functional rep (photon)      216
Mode expansion, functional rep (scalar)      207
Mode expansion, functional rep (spinor)      218—219
Modular function      584
Modular group      578
Moduli space      537 578 587 588
Moduli space, dimension      596
Moduli space, genus 1 (torus)      581
Moduli space, in bosonic string partition function      638
Moduli space, of cylinder      655
Moduli space, one-point compactification      645
Modulus of a basis      580
Momentum operator, functional representation      207
Momentum operator, scalar field      56
Moving frame field      559 689
Moving frame field nonuniqueness      690
Nambu — Goto action      492
Negative energy problem      39
Nonabelian phase factor      480
Nonabelian phase factor, transformation property      480
Nonlinear Schrodinger model      30—34
Nonlinear Schrodinger model 2-Body Sector      34
Nonlinear Schrodinger model, thermodynamic limit      32
Nonlinear sigma model      98
Normal ordering      45 513 529
Nother's theorem      22
On mass shell      365
One-particle irreducible diagram      371
Operator product expansion      32 34
Operator-valued distribution      45
Parallel transport      553
Parity      102
Parity, Dirac fields      103—104
Parity, electromagnetic field      104
Parity, scalar fields      102—103

Partition function, bosonic string      603 631 638 639 641 645 671
Partition function, bosonic string (genus $\geq$ 2)      638 645
Partition function, bosonic string (genus 0)      611 629
Partition function, bosonic string (genus 1)      639 641 643 644 645
Partition function, perturbative expansion      631
Partition function, reduction to integral over moduli      638
Partition function, superstring      708 717 718
Path integral in qm, anharmonic oscillator integral      298—300
Path integral in qm, constructive def      271—276
Path integral in qm, forced harmonic oscillator      293
Path integral in qm, free particle integral      285
Path integral in qm, harmonic oscillator integral      289
Path integral in qm, matrix elements      280
Path integral in qm, perturbative expansion      294—297
Path integral in qm, recovering diagrams      296
Path integral in qm, recovering wave functions      289 299
Path integral in qm, symmetric operator ordering      277
Path integral in qm, vacuum expectation values      279
Path-ordered exponential      480
Pauli — Villars regularization      382—383
Pauli — Villars regularization, applied to QED chiral anomaly      426
Pauli — Villars regularization, applied to vacuum polarization      385
PCAC hypothesis      421
PCT theorem      106
Period matrix      599 645 651
Perturbation theory, operator representation      125—132
Perturbation theory, path integral rep      294—297 330 339
Perturbation theory, Schrodinger rep      227
Perturbed wave functionals, $\lambda\varphi^{4}$ direct solution from Schrod. eq.      234—237 458 460
Perturbed wave functionals, $\lambda\varphi^{4}$ from Rayleigh — Schrodinger pert theory      230—234
Perturbed wave functionals, QED direct solution from Schrod. eq.      257—260
Perturbed wave functionals, Yang — Mills direct solution from Schrod. eq.      247—251
Planck length      477
Planck mass      485
Poincare half-plane      574
Polyakov action      492 604 629
Proper diagrams      371
Proper functions      373
Proper vertex      373
Proper vertex, asymptotic behavior      467
Properly discontinuous      578
QCD 1/N expansion      680
QCD 1/N expansion, connection to free strings      683
QCD 1/N expansion, double-line representation      681
QED, chiral anomaly      420
QED, chiral, Coulomb gauge quantization      155—158 336—338
QED, chiral, counterterms      402
QED, chiral, Faddeev — Popov procedure      351
QED, chiral, gauge-fixed action      353
QED, chiral, generating functional      336 339
QED, chiral, operator rep      155
QED, chiral, path integral rep      336
QED, chiral, regularized action      383
QED, chiral, renormalized action      402
QED, chiral, Schrodinger rep      255
QED, chiral, temporal gauge      255
Quantum field theory, nonrelativistic      23—27
Quantum field theory, relativistic      38—42
quantum mechanics      11—16
Quantum mechanics, Heisenberg (operator) representation      15
Quantum mechanics, path integral representation      271—276
Quantum mechanics, Schrodinger representation      14
Rayleigh — Schrodinger perturbation theory      227
Rayleigh — Schrodinger perturbation theory, applied to $\lambda\varphi^{4}$       228—234
Rayleigh — Schrodinger perturbation theory, failure in gauge theories      246 256
Reduction formula, electromagnetic      162
Reduction formula, fermionic      161
Reduction formula, scalar      124
Regge trajectory      663
Regularization, dimensional      382
Regularization, introduced      362
Regularization, momentum cutoff      266 450
Regularization, Pauli — Villars      382—383
Regularized photon propagator      384
Relativistic point particle, classical action      487—489
Renormalization group      463
Renormalization group equations, for asymptotic behavior of proper vertices      466 468
Renormalization group equations, for interacting scalar fields      465 470
Renormalization group equations, for massless $\phi^{4}      $464
Renormalization group equations, use      465—466
Renormalization of electron mass, from Schrodinger rep      265—268
Renormalization prescription, for electron propagator      409
Renormalization prescription, for QED vertex correction      412
Renormalization prescription, for vacuum polarization      405
Renormalization prescription, introduced      368
Renormalization, basic idea      362
Renormalization, of $\lambda\varphi^{4}$ via effective potential      444 449—450
Renormalization, of Coulomb's law      408
Renormalization, of electric charge      401
Renormalization, of electron mass      266 398
Renormalization, of photon propagator      399 405
Renormalization, of QED electron propagator      397 409—412
Renormalization, of QED vertex      400 412
Renormalization, of surface tension in string partition function      629
Ricci tensor      556
Riemann mapping theorem      575
Riemann sphere      566
Riemann surface      544
Riemann surface, topological classification      545—546
Riemann tensor      556
Riemann — Roch theorem      596
Rigid strings, $\vartheta$ term      684
Rigid strings, action      684
Rigid strings, partition function      684
RNS gauge-fixed action (supersurface)      700
Running coupling constant      407
S-matrix      107 118—120
S-matrix, operator representation      129 182
S-matrix, Schrodinger rep      238
Scalar curvature      556
Scalar field theory, $\lambda\varphi^{4}$       111—112
Scalar field theory, $\lambda\varphi^{4}$ , Schrodinger rep      226
Scalar field theory, free      42—48
Schottky problem      600
Schrodinger equation, $\lambda\phi^{4}$ , renormalized      460
Schrodinger equation, free photon field theory      211 214
Schrodinger equation, free scalar field theory      201 209
Schrodinger equation, free spinor field theory      217 219
Schrodinger equation, Yang — Mills      244 252
Sdet'( $-\Delta_{n}^{\pm_}$ )      717
Second fundamental form      684
Second quantization      20—30
Second quantization, relation to first quantization      27—28
Second quantization,of the nonrelativistic Schrodinger equation      20 23—27
Second structural equation      560 692
Shapiro — Virasoro model      519
Siegel modular group      600
Siegel upper half-plane      599
Simplices      597
Simplicial homology group      597
Smooth covering surface      575 732
Sommerfeld — Watson transformation      642
Spectral density      116 160
Spin and statistics      71—72
Spin connection, covariant derivative      691 693
Spin connection, first structuial equation      692
Spin connection, relation to Christoffel symbols      691
Spin connection, second structural equation      692
Spin connection, with torsion      692 694
Spin structure      719
Spinor field theory, free      69—72
Spinor metric      696
Spontaneous breakdown of symmetry      441
Spontaneous breakdown of symmetry, relation to Goldstone bosons      443
Stabilizer      570
Standard homology basis      599 651
Static quark potential, from Nambu — Goto model      680
Static quark potential, relation to Wilson loop      677—678
Static quark potential, universal string Coulombic piece      679
Stress-energy tensor      56

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