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Jost J. — Bosonic Strings: A mathematical treatment
Jost J. — Bosonic Strings: A mathematical treatment

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Название: Bosonic Strings: A mathematical treatment

Автор: Jost J.

Аннотация:

Presented in this book is a mathematical treatment of Bosonic string theory from the point of view of global geometry. As motivation, the author presents the theory of point particles and Feynman path integrals. He considers the theory of strings as a quantization of the classical Plateau problem for minimal surfaces. The conformal variance of the relevant functional, the Polyakov action or (in mathematical terminology) the Dirichlet integral, leads to an anomaly in the process of quantization. The mathematical concepts needed to resolve this anomaly via the Faddeev-Popov method are introduced, specifically the geometry of the Teichmu?ller and moduli spaces of Riemann surfaces and the corresponding function spaces, i.e., Hilbert spaces of Sobolev type and diffeomorphism groups. Other useful tools are the algebraic geometry of Riemann surfaces and infinite-dimensional determinants. Also discussed are the boundary regularity questions. The main result is a presentation of the string partition function as an integral over a moduli space of Riemann surfaces. Some new physical concepts, such as D-branes, are also discussed.

This volume offers a mathematically rigorous treatment of some aspects of string theory, employs a global geometry approach, systematically treats strings with boundary, and carefully explains all mathematical concepts and tools.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 101

Добавлена в каталог: 24.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
action      1 3 6 7 12 19 85 87
Albanese period map      70
Anomaly      7
Anticommutation relation      10
Antighost      10
Arakelov metric      70
Baily compactification      71
Beltrami differential      65 66
Bergman metric      70 71
Bosonic Gaussian      16
BRST cohomology      20
BRST cohomology group      11
BRST operator      10
BRST transformation      11 18
Canonical line bundle      56
Center of mass      86
Chern class      54
Chern form      53
Christoffel symbol      29
Clifford variable      8
Cohomology      10
Collar Lemma      68
Commutation relation      87
Compact Riemann surface      33
Compactification      88
Complex structure      64
Configuration space      7
conformal      23
Conformal anomaly      42 81
Conformal diffeomorphism      24
Conformal invariance      23 28
Conformal metric      26 56
Conformal parameter      24
Conformal structure      24
Conformal transformation      23
Conjugate momenta      86
Conjugate variable      3
Conserved current      19
Constraint      3
Converging integral      6
Coulomb quantization      5
Courant — Lebesgue lemma      36
Current      19
D-brane      90
Degree      54
density      6
Determinant      76 83
Determinant line      73
Determinant line bundle      72-74
Diffeomorphism      83
Diffeomorphism group      14 16 18 22 26 42 46 48
Dirichlet boundary condition      26 90
Dirichlet integral      22 26 38 41 82
Dirichlet membrane      90
Duality      90
Energy-momentum tensor      23
Equations of motion      85
Estimates of Masur      68
Euler characteristic      28
Euler — Lagrange equation      4 19 21 22 24 29
Faddeev — Popov determinant      7
Faddeev — Popov procedure      7 10 18 51 83
Fermionic Gaussian      16
Feynman path integral      2
Fredholm operator      72
Functional determinant      18
Functional integration      17
Fundamental result for the bosonic string      85
Gauge field      88
Gauge fixing      3 7
Gauge redundancy      10
Gauge slice      7
Gauge transformation      7
Gauss curvature      28
Gauss — Bonnet theorem      28
Gaussian integral      3
Ghost      10
Ghost number      10
Grassmann variable      7
Green function      71
Ground state      87
Gupta — Bleuler quantization      5
Hamiltonian      3
Harmonic      23
Harmonic Beltrami differential      27 65
Harmonic map      29
Harmonic oscillator algebra      87
Hartman — Wintner lemma      38
Hermitian metric      53
Hildebrandt's theorem      26 32
Holomorphic quadratic differential      25—27 33 49 50 57 62 64 65 84
Holomorphic section      53
INDEX      72
Infinitesimal decomposition      17
Infinitesimal diffeomorphism      18 27
Infinitesimal symmetry      1
Invariance      1
Jacobian      70
Klein — Gordon equation      5
Lagrange multiplier      3
Lagrangian      3
Laplace equation      87
Laplace — Beltrami operator      46 61
Left-moving part      88
Lie derivative      17 48
Light cone quantization      5
Line bundle      52
Local variation      4
Lorentz metric      85
Mapping class group      46 47 70
Mass      89
Massless particle      3
Massless scalar      89
Maximum principle      38
Measure      3 7 16 17 82 83
Meromorphic quadratic differential      70
Metric density      4
Minimal surface      32
Minkowski space      1
Modular group      46 47
Moduli space      47 64 67 68 72 84
Momenta      3
Mumford — Deligne compactification      71
Mumford — Deligne moduli space of stable curves      68
Nambu — Goto action      21
Neumann boundary condition      85 90
Neumann condition      28 63
Nilpotent      10 18
Noether's theorem      19
Nonlinear sigma model      29 33 41
Occupation number      89
Oscillatory path integral      6
Parametrization      1
Partition function      29 42 83 84
path integral      3
Path length      1
Periodic boundary condition      28 85
physical state      11
Picard group      56
Plateau boundary condition      22 26
Poincare Invariance      23
Polyakov action      22 32 41
Principally polarized abelian variety      70
Proper time      5
Puncture      67
Quantization      5
Quillen metric      77 79
Quillen norm      75 78
Quillen product      74
Radius of the compactification      88
Regge slope      28
Regularity      26 31 32 36
Relativistic point particle      1
Reparametrization      1 3—5
Riemann mapping theorem      27
Riemann surface      26 33
Riemann — Hilbert structure      13
Riemann — Roch theorem      57 60
Riemannian Hilbert manifold      45
Right-moving part      88
Satake — Baily — Borel compactification      71
Schottky double      43 44 47 52 62 76
Siegel upper half space      70
Sobolev embedding theorem      14 30-32
Sobolev space      13 30 32 82
String coupling constant      28
String scattering theory      72
T-duality      90
Teichmueller space      47 63-65 67 83
Trace theorem      32
Universal moduli space      72
Vertex operator      72
Wave equation      85
Weak derivative      30
Weak riemannian structure      13 15 16
Weil — Petersson metric      68 71
Weil — Petersson product      50
Weyl estimate      74
Weyl invariance      23
Wick rotation      2
Wiener path integral      2
Winding number      89
Zeta function      74
Zeta-function regularisation      75
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