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A mathematical introduction to string theory : variational problems, geometric and probabilistic methods / Sergio Albeverio [and others].

Contributor(s): Albeverio, Sergio | London Mathematical SocietyMaterial type: TextTextSeries: London Mathematical Society lecture note series ; 225.Publication details: Cambridge ; New York : Cambridge University Press, ©1997. Description: 1 online resource (viii, 135 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781107362383; 1107362385Subject(s): String models -- Mathematics | Mathematical physics | SCIENCE -- Physics -- Nuclear | Mathematical physics | String models -- Mathematics | Snaartheorie | Modèles des cordes vibrantes (Physique nucléaire) | Physique mathématiqueGenre/Form: Electronic books. | Electronic books. Additional physical formats: Print version:: Mathematical introduction to string theory.DDC classification: 539.7/2 LOC classification: QC794.6.S85 | M38 1997ebOther classification: 31.29 Online resources: Click here to access online
Contents:
I.0. Introduction -- I.1. The two-dimensional Plateau problem -- I.2. Topological and metric structures on the space of mappings and metrics -- Appendix to I.2. ILH-structures -- I.3. Harmonic maps and global structures -- I.4. Cauchy-Riemann operators -- I.5. Zeta-function and heat-kernel determinants of an operator -- I.6. The Faddeev-Popov procedure. I.6.1. The Faddeev-Popov map. I.6.2. The Faddeev-Popov determinant: the case G=H. I.6.3. The Faddeev-Popov determinant: the general case -- I.7. Determinant bundles -- I.8. Chern classes of determinant bundles -- I.9. Gaussian measures and random fields -- I.10. Functional quantization of the Hoegh-Krohn and Liouville models on a compact surface -- I.11. Small time asymptotics for heat-kernel regularized determinants -- II. 1. Quantization by functional integrals -- II. 2. The Polyakov measure -- II. 3. Formal Lebesgue measures on Hilbert spaces -- II. 4. The Gaussian integration on the space of embeddings.
Summary: Classical string theory is concerned with the propagation of classical 1-dimensional curves 'strings', and the theory has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras have been used for such quantization. In this lecture note the authors give an introduction to certain global analytic and probabilistic aspects of string theory. It is their intention to bring together, and make explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.
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Includes bibliographical references (pages 126-132) and index.

I.0. Introduction -- I.1. The two-dimensional Plateau problem -- I.2. Topological and metric structures on the space of mappings and metrics -- Appendix to I.2. ILH-structures -- I.3. Harmonic maps and global structures -- I.4. Cauchy-Riemann operators -- I.5. Zeta-function and heat-kernel determinants of an operator -- I.6. The Faddeev-Popov procedure. I.6.1. The Faddeev-Popov map. I.6.2. The Faddeev-Popov determinant: the case G=H. I.6.3. The Faddeev-Popov determinant: the general case -- I.7. Determinant bundles -- I.8. Chern classes of determinant bundles -- I.9. Gaussian measures and random fields -- I.10. Functional quantization of the Hoegh-Krohn and Liouville models on a compact surface -- I.11. Small time asymptotics for heat-kernel regularized determinants -- II. 1. Quantization by functional integrals -- II. 2. The Polyakov measure -- II. 3. Formal Lebesgue measures on Hilbert spaces -- II. 4. The Gaussian integration on the space of embeddings.

Print version record.

Classical string theory is concerned with the propagation of classical 1-dimensional curves 'strings', and the theory has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras have been used for such quantization. In this lecture note the authors give an introduction to certain global analytic and probabilistic aspects of string theory. It is their intention to bring together, and make explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.

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