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E-raamat: Introduction to Strings and Branes

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(King's College London)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 05-Jul-2012
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139415293
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Introduction to Strings and BranesSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 05-Jul-2012
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781139415293
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Supersymmetry, strings and branes are believed to be the essential ingredients in a single unified consistent theory of physics. This book gives a detailed, step-by-step introduction to the theoretical foundations required for research in strings and branes. After a study of the different formulations of the bosonic and supersymmetric point particles, the classical and quantum bosonic and supersymmetric string theories are presented. This book includes accounts of brane dynamics and D-branes and the T, S and U duality symmetries of string theory. The historical derivation of string theory is given as well as the sum over the world-sheet approach to the interacting string. More advanced topics include string field theory and Kac–Moody symmetries. The book contains pedagogical accounts of conformal quantum field theory, supergravity theories, Clifford algebras and spinors, and Lie algebras. It is essential reading for graduate students and researchers wanting to learn strings and branes.

Supersymmetry, strings and branes are believed to be the essential ingredients in a single unified consistent theory of physics. This book gives a detailed, step-by-step introduction to the theoretical foundations required for research in this field and is essential reading for graduate students and researchers.

Arvustused

'This single-volume new textbook on string theory will provide a solid and broad foundation to those who aspire to learn essential physical aspects on string theory with efficiency and depth. It is refreshing to see that this textbook contains lots of material which rarely appears in other string theory textbooks. This textbook is very helpful and pedagogical and it is strongly recommended for individuals and coursework.' Jihye Seo, Mathematical Reviews 'In recent years attempts to find a unified description of all physical phenomena have embraced not only one-dimensional strings but higher-dimensional membranes called 'branes'. Few are more qualified than Peter West to write an introduction to these fields he does not disappoint. This masterly exposition provides an essential guide for graduate students and researchers.' Michael J. Duff, FRS, Imperial College London 'Peter West's Introduction to Strings and Branes has the same virtues that made his book on supersymmetry and supergravity such a resounding success: it is remarkably clear, self-contained and covers a lot of ground. After having mastered its content, the serious student will be well-equipped for research in the field.' Glenn Barnich, Université Libre de Bruxelles

Muu info

Detailed, step-by-step introduction to the theoretical foundations of strings and branes, essential reading for graduate students and researchers.
Preface xi
1 The point particle
1(35)
1.1 The bosonic point particle
1(7)
1.1.1 The classical point particle and its Dirac quantisation
1(4)
1.1.2 The BRST quantization of the point particle
5(3)
1.2 The super point particle
8(16)
1.2.1 The spinning particle
9(8)
1.2.2 The Brink-Schwarz superparticle
17(4)
1.2.3 Superspace formulation of the point particle
21(3)
1.3 The twistor approach to the massless point particle
24(12)
1.3.1 Twistors in four and three dimensions
25(4)
1.3.2 The twistor point particle actions
29(7)
2 The classical bosonic string
36(16)
2.1 The dynamics
36(13)
2.1.1 The closed string
42(4)
2.1.2 The open string
46(3)
2.2 The energy-momentum and angular momentum of the string
49(1)
2.3 A classical solution of the open string
50(2)
3 The quantum bosonic string
52(29)
3.1 The old covariant method
54(10)
3.1.1 The open string
55(7)
3.1.2 The closed string
62(2)
3.2 The BRST approach
64(17)
3.2.1 The BRST action
64(8)
3.2.2 The world-sheet energy-momentum tensor and BRST charge
72(5)
3.2.3 The physical state condition
77(4)
4 The light-cone approach
81(19)
4.1 The classical string in the light-cone
81(8)
4.2 The quantum string in the light-cone
89(3)
4.3 Lorentz symmetry
92(7)
4.4 Light-cone string field theory
99(1)
5 Clifford algebras and spinors
100(20)
5.1 Clifford algebras
100(1)
5.2 Clifford algebras in even dimensions
101(5)
5.3 Spinors in even dimensions
106(5)
5.4 Clifford algebras in odd dimensions
111(3)
5.5 Central charges
114(2)
5.6 Clifford algebras in space-times of arbitrary signature
116(4)
6 The classical superstring
120(23)
6.1 The Neveu-Schwarz-Ramond (NS-R) formulation
121(12)
6.1.1 The open superstring
125(5)
6.1.2 The closed superstring
130(3)
6.2 The Green-Schwarz formulation
133(10)
7 The quantum superstring
143(17)
7.1 The old covariant approach to the open superstring
144(6)
7.1.1 The NS sector
146(2)
7.1.2 The R sector
148(2)
7.2 The GSO projector for the open string
150(3)
7.3 The old covariant approach to the closed superstring
153(7)
8 Conformal symmetry and two-dimensional field theory
160(50)
8.1 Conformal transformations
161(10)
8.1.1 Conformal transformations in D dimensions
161(2)
8.1.2 Conformal transformations in two dimensions
163(8)
8.2 Conformally invariant two-dimensional field theories
171(10)
8.2.1 Conformally invariant two-dimensional classical theories
171(2)
8.2.2 Conformal Ward identities
173(8)
8.3 Constraints due to global conformal transformations
181(3)
8.4 Transformations of the energy-momentum tensor
184(3)
8.5 Operator product expansions
187(2)
8.6 Commutators
189(3)
8.7 Descendants
192(4)
8.8 States, modes and primary fields
196(3)
8.9 Representations of the Virasoro algebra and minimal models
199(11)
9 Conformal symmetry and string theory
210(30)
9.1 Free field theories
210(12)
9.1.1 The free scalar
210(9)
9.1.2 The free fermion
219(3)
9.2 First order systems
222(5)
9.3 Application to string theory
227(8)
9.3.1 Mapping the string to the Riemann sphere
227(5)
9.3.2 Construction of string theories
232(3)
9.4 The free field representation of the minimal models
235(5)
10 String compactification and the heterotic string
240(32)
10.1 Compactification on a circle
240(7)
10.2 Torus compactification
247(6)
10.3 Compactification in the presence of background fields
253(4)
10.4 Description of the moduli space
257(4)
10.5 Heterotic compactification
261(3)
10.6 The heterotic string
264(8)
11 The physical states and the no-ghost theorem
272(21)
11.1 The no-ghost theorem
272(9)
11.2 The zero-norm physical states
281(4)
11.3 The physical state projector
285(2)
11.4 The cohomology of Q
287(6)
12 Gauge covariant string theory
293(27)
12.1 The problem
294(6)
12.2 The solution
300(6)
12.3 Derivation of the solution
306(4)
12.4 The gauge covariant closed string
310(5)
12.5 The gauge covariant superstring
315(5)
13 Supergravity theories in four, ten and eleven dimensions
320(100)
13.1 Four ways to construct supergravity theories
321(25)
13.1.1 The Noether method
323(8)
13.1.2 The on-shell superspace method
331(8)
13.1.3 Gauging of space-time groups
339(3)
13.1.4 Dimensional reduction
342(4)
13.2 Non-linear realisations
346(15)
13.3 Eleven-dimensional supergravity
361(5)
13.4 The IIA supergravity theory
366(8)
13.5 The IIB supergravity theory
374(9)
13.5.1 The algebra and field content
375(3)
13.5.2 The equations of motion
378(2)
13.5.3 The SL(2, R) version
380(3)
13.6 Symmetries of the maximal supergravity theories in dimensions less than ten
383(7)
13.7 Type I supergravity and supersymmetric Yang-Mills theories in ten dimensions
390(2)
13.8 Solutions of the supergravity theories
392(28)
13.8.1 Solutions in a generic theory
392(16)
13.8.2 Brane solutions in eleven-dimensional supergravity
408(3)
13.8.3 Brane solutions in the ten-dimensional maximal supergravity theories
411(2)
13.8.4 Brane charges and the preservation of supersymmetry
413(7)
14 Brane dynamics
420(40)
14.1 Bosonic branes
420(4)
14.2 Types of superbranes
424(6)
14.3 Simple superbranes
430(4)
14.4 D-branes
434(1)
14.5 Branes in M theory
435(9)
14.6 Solutions of the 5-brane of M theory
444(8)
14.6.1 The 3-brane
445(3)
14.6.2 The self-dual string
448(4)
14.7 Five-brane dynamics and the low energy effective action of the N = 2 Yang-Mills theory
452(8)
15 D-branes
460(25)
15.1 Bosonic D-branes
461(8)
15.2 Super D-branes in the NS-R formulation
469(6)
15.3 D-branes in the Green-Schwarz formulation
475(10)
16 String theory and Lie algebras
485(65)
16.1 Finite dimensional and affine Lie algebras
485(27)
16.1.1 A review of finite-dimensional Lie algebras and lattices
485(17)
16.1.2 Representations of finite dimensional semi-simple Lie algebras
502(7)
16.1.3 Affine Lie algebras
509(3)
16.2 Kac-Moody algebras
512(4)
16.3 Lorentzian algebras
516(3)
16.4 Very extended and over-extended Lie algebras
519(5)
16.5 Weights and inverse Cartan matrix of En
524(2)
16.6 Low level analysis of Lorentzian Kac-Moody algebras
526(6)
16.6.1 The adjoint representation
526(2)
16.6.2 All representations
528(4)
16.7 The Kac-Moody algebra E11
532(9)
16.7.1 E11 at low levels
532(4)
16.7.2 The l1 representation of E11
536(3)
16.7.3 The Cartan involution invariant subalgebra of a Kac-Moody algebra
539(2)
16.8 String vertex operators and Lie algebras
541(9)
17 Symmetries of string theory
550(62)
17.1 T duality
550(6)
17.2 Electromagnetic duality
556(13)
17.3 S and U duality
569(4)
17.4 M theory
573(8)
17.5 E theory
581(31)
17.5.1 The eleven-dimensional theory
581(5)
17.5.2 The IIA and IIB theories
586(9)
17.5.3 The common origin of the eleven-dimensional, IIA and IIB theories
595(3)
17.5.4 Theories in less than ten dimensions
598(3)
17.5.5 Duality symmetries and conditions
601(4)
17.5.6 Brane charges, the l1 representation and generalised space-time
605(4)
17.5.7 Weyl transformations of E11 and the non-linear realisation of its Cartan sub-algebra
609(3)
18 String interactions
612(54)
18.1 Duality, factorisation and the origins of string theory
612(21)
18.2 The path integral approach
633(14)
18.3 The group theoretic approach
647(10)
18.4 Interacting open string field theory
657(9)
18.4.1 Light-cone string field theory
657(5)
18.4.2 Mapping the interacting string
662(2)
18.4.3 A brief discussion of interacting gauge covariant string field theory
664(2)
Appendix A The Dirac and BRST methods of quantisation
666(7)
A.1 The Dirac method
666(2)
A.2 The BRST method
668(5)
Appendix B Two-dimensional light-cone and spinor conventions
673(3)
B.1 Light-cone coordinates
673(1)
B.2 Spinor conventions
674(2)
Appendix C The relationship between S2 and the Riemann sphere
676(3)
Appendix D Some properties of the classical Lie algebras
679(5)
D.1 The algebras An-1
679(1)
D.2 The algebras Dn
680(1)
D.3 The algebra E6
681(1)
D.4 The algebra E7
681(1)
D.5 The algebra E8
682(1)
D.6 The algebras Bn
682(1)
D.7 The algebras Cn
683(1)
Chapter quote acknowledgements 684(1)
References 685(21)
Index 706
Peter West is a Professor at King's College London. He is a pioneer in the development of supersymmetry and its application to strings and branes.
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