Frontier Quantum Theory (FYS902)

Content

The course consists of two modules chosen each year, depending on the composition of the PhD student body, among the following three:

Module 1 (5ECTS - option1): Advanced Quantum Field Theory

• Renormalization and renormalization group
• Non-Abelian Gauge theory
• Spontaneous symmetry breaking and the Higgs mechanism
• Standard model of electroweak and strong interactions
• Thermal field theory
• Selected advanced topics (anomalies, topological defects, phase transitions)

Module 2 (5ECTS - option2): Numerical Simulation Methods

• Statistical Mechanics and Spin Models
• Monte-Carlo Methods
• Deterministic Partial Differential Equations
• Stochastic Processes and Stochastic PDEs
• Data Analysis methods

Module 3 (5ECTS - option3): Lattice Field Theory

• Statistical Mechanics and Spin Models
• Renormalization in the Ising Model
• Scalar Lattice Field Theory
• Gauge Lattice Field Theory
• Fermions on the Lattice
• Real-Time Methods and Challenges
• Sign-Problem

Literature:

Module 1: Michael Kachelriess: Quantum Fields, From the Hubble to the Planck Scale, Oxford University Press, 2017

Module 2: notes by the lecturer, Kloeden and Platen, Numerical Solution of Stochastic Differential Equations, Springer 1992

Module 3: Jan Smit, Introduction to quantum fields on a lattice (Cambridge Lecture Notes in Physics), Cambridge University Press, 2002, Montvay and Munster, Quantum fields on a lattice, Cambridge University Press, 1994

Learning outcome

The course consists of two modules chosen each year, depending on the composition of the PhD student body. The learning outcome then consists of the corresponding two of the three modules below.

Module 1: After having taken this module, the student will be versatile enough to understand the main quantitative properties of a quantum field theory, defined by a given Lagrangian. They will have the skills, among others, to find the ground state of the theory and decide whether it spontaneously breaks some symmetry or not, renormalize the theory and quantify the effects of quantum corrections such as running of the couplings, and map out the phase diagram of the theory.

Module 2: When the student has finished this course module, the following learning outcomes should be achieved: Feel confident to discuss central concepts of statistical physics using a simple spin model. Easily recall challenges in discretising common deterministic partial differential equations arising in physics. See no difficulty in explaining the basic properties of stochastic processes and the different challenges they pose for numerical solution; Have a basic theoretical and practical understanding of Monte-Carlo methods to evaluate highly dimensional integrals; Have gained a good understanding of the concepts underlying data analysis and am aware of common pitfalls in the interpretation of simulation data; Feel confident to deploy the numerical simulation tools from this course to the study of real-world problems relevant to each individual PhD project.

Module 3: When the student has finished this course module, the following learning outcomes should be achieved: Feel confident to discuss central concepts of statistical physics using a simple spin model; See no difficulty in explaining the basic concepts of lattice regularised field theory using scalar fields as an example; Have a basic understanding of the concept of renormalization and am aware of its application in lattice field theory and spin models; Have gained a first look into the structure and principles underlying lattice gauge theory as well as fermions on the lattice; Feel excited and empowered to study real-world problems encountered in master's or PhD thesis work using lattice field theory methods.

Required prerequisite knowledge

Recommended prerequisites

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Literature