# Search result: Catalogue data in Spring Semester 2022

Mathematics Master | ||||||||||||||||||||||||||||||||||||||||||||||||||||||

Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||

Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | ||||||||||||||||||||||||||||||||||||||||||||||||||||||

Selection: Mathematical Physics, Theoretical Physics | ||||||||||||||||||||||||||||||||||||||||||||||||||||||

Number | Title | Type | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||||||||||||||||||||
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402-0206-00L | Quantum Mechanics IIIn 2022 the lectures will be held separately from UZH. A different class under the same name will be taught by a different lecturer at UZH. | W | 10 credits | 3V + 2U | R. Renner | |||||||||||||||||||||||||||||||||||||||||||||||||

Abstract | Many-body quantum physics rests on symmetry considerations that lead to two kinds of particles, fermions and bosons. Formal techniques include Hartree-Fock theory and second-quantization techniques, as well as quantum statistics with ensembles. Few- and many-body systems include atoms, molecules, the Fermi sea, elastic chains, radiation and its interaction with matter, and ideal quantum gases. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Learning objective | Basic command of few- and many-particle physics for fermions and bosons, including second quantisation and quantum statistical techniques. Understanding of elementary many-body systems such as atoms, molecules, the Fermi sea, electromagnetic radiation and its interaction with matter, ideal quantum gases and relativistic theories. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Content | The description of indistinguishable particles leads us to (exchange-) symmetrized wave functions for fermions and bosons. We discuss simple few-body problems (Helium atoms, hydrogen molecule) und proceed with a systematic description of fermionic many body problems (Hartree-Fock approximation, screening, correlations with applications on atomes and the Fermi sea). The second quantisation formalism allows for the compact description of the Fermi gas, of elastic strings (phonons), and the radiation field (photons). We study the interaction of radiation and matter and the associated phenomena of radiative decay, light scattering, and the Lamb shift. Quantum statistical description of ideal Bose and Fermi gases at finite temperatures concludes the program. If time permits, we will touch upon of relativistic one particle physics, the Klein-Gordon equation for spin-0 bosons and the Dirac equation describing spin-1/2 fermions. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Literature | G. Baym, Lectures on Quantum Mechanics (Benjamin, Menlo Park, California, 1969) L.I. Schiff, Quantum Mechanics (Mc-Graw-Hill, New York, 1955) A. Messiah, Quantum Mechanics I & II (North-Holland, Amsterdam, 1976) E. Merzbacher, Quantum Mechanics (John Wiley, New York, 1998) C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics I & II (John Wiley, New York, 1977) P.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (Mc Graw-Hill, New York, 1965) A.L. Fetter and J.D. Walecka, Theoretical Mechanics of Particles and Continua (Mc Graw-Hill, New York, 1980) J.J. Sakurai, Modern Quantum Mechanics (Addison Wesley, Reading, 1994) J.J. Sakurai, Advanced Quantum mechanics (Addison Wesley) F. Gross, Relativistic Quantum Mechanics and Field Theory (John Wiley, New York, 1993) | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Prerequisites / Notice | Basic knowledge of single-particle Quantum Mechanics | |||||||||||||||||||||||||||||||||||||||||||||||||||||

402-0844-00L | Quantum Field Theory IIUZH students are not allowed to register this course unit at ETH. They must book the corresponding module directly at UZH. | W | 10 credits | 3V + 2U | A. Lazopoulos | |||||||||||||||||||||||||||||||||||||||||||||||||

Abstract | The subject of the course is modern applications of quantum field theory with emphasis on the quantization of non-abelian gauge theories. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Learning objective | The goal of this course is to lay down the path integral formulation of quantum field theories and in particular to provide a solid basis for the study of non-abelian gauge theories and of the Standard Model | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Content | The following topics will be covered: - path integral quantization - non-abelian gauge theories and their quantization - systematics of renormalization, including BRST symmetries, Slavnov-Taylor Identities and the Callan-Symanzik equation - the Goldstone theorem and the Higgs mechanism - gauge theories with spontaneous symmetry breaking and their quantization - renormalization of spontaneously broken gauge theories and quantum effective actions | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Literature | M.E. Peskin and D.V. Schroeder, "An introduction to Quantum Field Theory", Perseus (1995). S. Pokorski, "Gauge Field Theories" (2nd Edition), Cambridge Univ. Press (2000) P. Ramond, "Field Theory: A Modern Primer" (2nd Edition), Westview Press (1990) S. Weinberg, "The Quantum Theory of Fields" (Volume 2), CUP (1996). | |||||||||||||||||||||||||||||||||||||||||||||||||||||

402-0822-13L | Introduction to Integrability | W | 6 credits | 2V + 1U | N. Beisert | |||||||||||||||||||||||||||||||||||||||||||||||||

Abstract | This course gives an introduction to the theory of integrable systems, related symmetry algebras and efficients calculational methods. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Learning objective | Integrable systems are a special class of physical models that can be solved exactly due to an exceptionally large number of symmetries. Examples of integrable models appear in many different areas of physics including classical mechanics, condensed matter, 2d quantum field theories and lately in string- and gauge theories. They offer a unique opportunity to gain a deeper understanding of generic phenomena in a simplified, exactly solvable setting. In this course we introduce the notion and formulation of integrability in classical and quantum mechanics. We discuss various efficient methods for constructing solutions and eigenstates in these models. Finally, we elaborate on the enhanced symmetries that underly integrable models. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Content | * Classical Integrability * Algebraic Methods for Integrability * Classical Spin Chains * Spectral Curves and Inverse Scattering * Quantum Spin Chains * Bethe Ansatz * Classical and Quantum Algebra | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Literature | * V. Chari, A. Pressley, "A Guide to Quantum Groups", Cambridge University Press (1995) * O. Babelon, D. Bernard, M. Talon, "Introduction to Classical Integrable Systems", Cambridge University Press (2003) * N. Reshetikhin, "Lectures on the integrability of the 6-vertex model", http://arxiv.org/abs/1010.5031 * L.D. Faddeev, "How Algebraic Bethe Ansatz Works for Integrable Model", http://arxiv.org/abs/hep-th/9605187 * D. Bernard, "An Introduction to Yangian Symmetries", Int. J. Mod. Phys. B7, 3517-3530 (1993), http://arxiv.org/abs/hep-th/9211133 * V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, "Quantum Inverse Scattering Method and Correlation Functions", Cambridge University Press (1997) * C. Gómez, M. Ruiz-Altaba, G. Sierra, "Quantum Groups In Two-Dimensional Physics", Cambridge University Press (1996) * L. D. Faddeev, L. A. Takhtajan, "Hamiltonian Methods in the Theory of Solitons", Springer (2007) * Lecture of HS16: https://moodle-app2.let.ethz.ch/course/view.php?id=2601 | |||||||||||||||||||||||||||||||||||||||||||||||||||||

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401-4816-22L | Geometric Methods in Mathematical Physics | W | 4 credits | 2V | M. Schiavina | |||||||||||||||||||||||||||||||||||||||||||||||||

Abstract | The course will cover selected topics in mathematical physics, focusing on their geometric underpinning. The main common denominator will be the notion of quantisation and the course material will range through several techniques to make sense of it from a mathematical standpoint. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Learning objective | The objective of this course is to expose master and graduate students in mathematics and physics to a number of successful geometric techniques in mathematical physics. The course will provide a foundation to essential topics in symplectic and Poisson geometry and its application to fundamental questions in classical and quantum physics. It is aimed at mathematics/physics masters and graduate students with an interest but no previous background in symplectic geometry, and students who want to focus on more formal aspects of classical and quantum physics. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Content | In progress: Basics of Symplectic and Poisson geometry. Geometric structure of coadjoint orbits. Hamiltonian group actions, equivariant momentum maps and symplectic reduction. Elements of geometric and deformation quantisation. | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Literature | S. Bates and A. Weinstein, Lectures on the geometry of Quantisation, Berkeley Mathematics Lecture notes, Volume 8, AMS. A. Weinstein, Lectures on Symplectic manifolds, Regional Conference Series in mathematics, Number 29, CBMS, AMS. J-P. Ortega and T. Ratiu, Momentum Maps and Hamiltonian Reduction, Progress in Mathematics, volume 222, Springer To be completed | |||||||||||||||||||||||||||||||||||||||||||||||||||||

Prerequisites / Notice | Required: Basics of Classical Mechanics Basics of Differential Geometry Useful: Quantum mechanics (will not be used, but we will refer to it when looking at particular results) Basics of Lie theory (will be briefly recalled) |

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