Description and contextualization of the subject

El curso examina la problemática de compatibilizar la Relatividad General con la Mecánica Cuántica y explora los métodos y enfoques propuestos para resolver esta cuestión fundamental de la Física. La estructura del curso incluye una introducción a la mecánica Hamiltoniana de la Relatividad General, seguida de un análisis de la cuantización canónica de esta teoría, con énfasis en la Gravedad Cuántica de Lazos y por último la Teoría de Cuerdas. En la sección de Gravedad Cuántica Canónica, se analizarán sistemas con restricciones y su cuantización. La Gravedad Cuántica de Lazos se presentará como una cuantización de la formulación Hamiltoniana de la RG en términos de las variables de Ashtekar. Se definirán y estudiarán los operadores geométricos asociados con áreas y volúmenes, y se comentarán los resultados físicos obtenidos en el contexto de la física de agujeros negros y la cosmología. En la sección dedicada a la Teoría de Cuerdas, se presentan la teoría clásica y cuántica de las cuerdas relativistas, mostrando cómo surgen el gravitón y los campos gauge en el espectro de estados cuánticos de la cuerda. Se abordan también la supersimetría, el concepto de supergravedad como límite de baja energía, y el papel fundamental de los objetos supersimétricos extendidos, como las p-branas. Por último, se discuten las dualidades en Teoría de Cuerdas y el concepto de "democracia de branas".

Learning outcomes of the subject

Knowledge or content:

RCO1. Demonstrate the ability to explain the fundamental principles of the quantum world, both at a basic and technical level.

RCO2. Have a basic knowledge of the relevant literature in quantum mechanics and be capable of effectively reading and understanding research articles.

RCO3. Be able to initiate the development of original ideas and applications within the context of quantum physics research.

RCO4. Possess the capacity for independent research, synthesis, and be able to present in a clear and structured way complex issues related to the various areas of quantum mechanics addressed in this Master¿s program.

RCO5. Under supervision, demonstrate the ability to write and defend original work that meets the quality standards required for publication in high-impact indexed journals.

RCO8. Know the basic literature and demonstrate the ability to solve standard problems in the field of Quantum Field Theory.

RCO10. Know the basic literature and demonstrate the ability to solve standard problems in the field of Fields and Particle Physics.



Competencies:

RC1. Possess and understand knowledge that provides a basis or opportunity for developing and/or applying original ideas, often in a research context.

RC2. Apply acquired knowledge and problem-solving skills in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.

RC3. Demonstrate the ability to integrate knowledge and address the complexity of formulating judgments based on incomplete or limited information, including reflection on social and ethical responsibilities linked to the application of their knowledge and judgments.

RC4. Communicate conclusions, as well as the underlying knowledge and rationale, clearly and unambiguously to both specialized and non-specialized audiences.

RC5. Possess learning skills that enable continued study in a largely self-directed or autonomous manner.



Abilities or skills:



RHE1. Demonstrate proficiency in using tools for bibliographic resource searches.

RHE2. Exhibit critical capacity to read research articles and incorporate their findings into one¿s own work.

RHE3. Write and present original work in one of the official languages and in English.

RHE4. Communicate scientific concepts and results clearly and effectively to both specialized and non-specialized audiences, through presentations and publications.

RHE5. Demonstrate the ability for autonomous learning and staying current with scientific and technological advances.





RHT1. Understand and apply the fundamental principles of quantum mechanics to analyze and solve problems in basic research in quantum science.

RHT3. Effectively integrate into a fundamental or applied research project involving quantum aspects, and solve problems in multidisciplinary environments.

RHT4. Evaluate and select appropriate tools and techniques for research in fundamental physics.

Temary

1. HAMILTONIAN FORMALISM IN CLASSICAL FIELD THEORIES WITH CONSTRAINTS

2. CANONICAL QUANTIZATION OF CONSTRAINED SYSTEMS

3. DIFFERENTIAL GEOMETRY AND HAMILTONIAN FORMALISM OF GENERAL RELATIVITY

4. CANONICAL QUANTIZATION OF GENERAL RELATIVITY

5. LOOP QUANTUM GRAVITY AND APPLICATIONS: BLACK HOLES AND COSMOLOGY

6. BOSONIC STRING. Classical and Quantum mechanics. Nambu-Goto and Polyakov actions, Hamiltonain mechanics and quantization

Quantum state spectrum. Gauge fields and gravity in string theory. Critical dimension D=26 and techion problem in bosonic string model.

7. SUPERSTRING. Supersymmetry and superspace, Superparticle as particle in superspace, Superstring as string in superspace, Quantum spectrum of superstring(s). No tachions. Critical dimension D=10.

8. LOW ENERGY ACTIONS OF STRING THEORY. 10D Supersymmetric gauge theory (SYM) and SUPERGRAVITY. Dimensional reduction down to D=4.

9. P-BRANES (supersymmetric extended objects), Dirichlet p-branes (Dp-BRANES) and Dualities. Worldvolume p-brane actions and coupling to supergravity. Solutions of supergravity equations. Brane Democracy concept. Dualities.

10. *M-THEORY and DUALITIES.11D supergravity. Supermembrane (M2-brane) and M5-brane in D=11. Unification of consistent string models: M-theory

11. *PRESENT STATE OF ART IN STRING/M-THEORY. Landscape vs Swampland tec.

*Advanced topics which will be addressed in case of having time.

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Bibliography

Basic bibliography

1. M. Henneaux, C. Teitelboim, Quantization of Gauge Systems, Princeton University Press 2020.

2. P. A. M. Dirac, Lectures on Quantum, Mechanics, Dover ed. 2001.

3. C. Kiefer, Quantum Gravity, Oxford Univ. Press 2012.

4. R. M. Wald, ¿General Relativity¿, Chicago Press 1984.

5. M. Bojowald, ¿Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity¿, CUP 2010.

6. R. Gambini, J. Pullin, ¿A first course in Loop Quantum Gravity¿, Oxford Univ. Press 2011.

7. Barton Zwiebach, ¿A First Course in String Theory¿, CUP 2004.

8. R. Blumenhagen, D. Lust and S. Theisen, ``Basic concepts of string theory,'' 2013. doi:10.1007/978-3-642-29497-6 (hay PDF en Biblioteca del UPV/EHU)

9. Clifford Johnson, `¿D-branes¿¿, CUP 2003.

In-depth bibliography

1. T. Thiemann, "Modern Canonical Quantum General Relativity", CUP 2007.

2. C. Rovelli, "Quantum Gravity", CUP 2004.

3. Michael Green, John H. Schwarz, Edward Witten, "Superstring Theory", V1,2. CUP 1987 (1987, ..., 2012).

4. Katrin Becker, Melanie Becker, John H Schwarz, "String theory and M-theory : a modern introduction", CUP 2007.

5. L.E Ibanez, A. Uranga, String Theory and Particle Physics: an Introduction to String Phenomenology, 2012.

Journals

1. C. Teitelboim, How Commutators of Constraints Reflect the Spacetime Structure, Annals of Physics 79, 542 (1973).

2. N. Bodendorfer, An Elementary Introduction to Loop Quantum Gravity, 2016. arXiv:1607.05129.

3. J. F. Barbero G., D. Pranzetti, Black Hole Entropy in Loop Quantum Gravity, 2022. arXiv:2212.13469.

4. I. Agullo, P. Singh, Loop Quantum Cosmology: A brief review, 2016, arXiv:1612.01236 .

5. P. Goddard, J. Goldstone, C. Rebbi and C.B. Thorn, Quantum dynamics of a massless relativistic string,

Nucl. Phys. B 56 (1973), 109-135, doi:10.1016/0550-3213(73)90223-X

6. A.M. Polyakov,``Quantum Geometry of Bosonic Strings,'' Phys. Lett. B 103 (1981), 207-210

doi:10.1016/0370-2693(81)90743-7

7. M.B. Green and J.H. Schwarz, ``Covariant Description of Superstrings,'' Phys. Lett. B 136 (1984), 367-370 doi:10.1016/0370-2693(84)92021-5

8. E. Witten, "String Theory Dynamics in Various Dimensions," Nucl. Phys. B443 (1995) 85 [hep-th/9503124].

9. P.K. Townsend,``P-Brane Democracy,'' in PASCOS / HOPKINS 1995 (Joint Meeting of the International Symposium on Particles, Strings and Cosmol-ogy and the 19th Johns Hopkins Workshop on Current Problems in Particle Theory), 271-285 doi:10.1201/9781482268737-33 [arXiv:hep-th/9507048 [hep-th]].

10. N.A. Obers and B. Pioline,``U duality and M theory,'' Phys. Rept. 318 (1999), 113-225 doi:10.1016/S0370-1573(99)00004-6 [arXiv:hep-th/9809039 [hep-th]].

11. M. Cicoli, J.P. Conlon, A. Maharana, S. Parameswaran, F. Quevedo and I. Zavala, ``String cosmology: From the early universe to today,'' Phys. Rept. 1059 (2024), 1-155 doi:10.1016/j.physrep.2024.01.002 [arXiv:2303.04819 [hep-th]]

Links

https://arxiv.org/list/hep-th/new

https://inspirehep.net