Modern Topics in Quantum Field Theory

Note: The seminars take place at 4pm ct (i.e. 4:15pm), in Hörsaal 2.

The seminar covers three topics in Quantum Field Theory that are not part of the regular QFT course. These represent important developments and tools in modern applications of QFT in high-energy physics.

Prerequisites: Quantum Field Theory (including functional integral, renormalization)

Time/Location: Wednesdays 16-18, 11.11.--16.2., not on 23.12., 30.12.,6.1 in Hörsaal 2

Presentations start in mid-November. To allow for enough time for preparation, students should register as soon as possible in September by sending an E-mail to mbeneke AT (Formal registration through TUM campus follows later) Topics will be assigned on a first-come / first-serve basis.

Depending on the number of participants, teams of three to four students prepare and present three to four lectures on each topic.

Topic 1: On-shell Effective Field Theories (Supervisor: Prof. Beneke), 9.12., 16.12., 13.1., 20.1.

Abstract: On-shell EFT represents an extension of the EFT concept to the physics at multiple scales when the high scale, which is integrated out, is still present through the external states. Examples are heavy quarks, the QFT of non-relativistic systems, and high-energy scattering etc. The corresponding EFTs, heavy-quark, non-relativistic and soft-collinear effective field theory have revolutionized and systematized the way of thinking and calculations in quantum chromodynamics. For example, they turn the problem of infrared divergences and large logarithms
into an (albeit sometimes unconventional) ultraviolet renormalization problem. The construction of these EFTs, matching and the renormalization group/all-order resummation is covered with some physics applications.

9.12. Jonathan Kley: Heavy Quark Effective Theory

16.12. Fabian Wagner: On-shell EFTs II: NRQCD

13.01., 20.01. Anca Preda: pNRQCD, SCET

20.01. Fabian Wagner: On-Shell EFTs III: Applications of Soft-Collinear Effective Theory

Topic 2: Exact Renormalization Group and Asymptotic Safety (Supervisor: Prof. Garbrecht), 27.1., 3.2., 10.2., 17.2.

Abstract: The idea of Wilson of evolving an action by integrating out all fluctuations above a certain energy scale is called the exact renormalization group because it (in principle) encompasses the evolution of all relevant, marginal and irrelevant operators. The approach can be put in practice using a cutoff proposed by Polchinski or based on the effective action following by Wetterich. Weinberg proposed that nonrenormalizable theories that have nontrivial ultraviolet fixed points may be considered as complete or "asymptotically safe". It stands as a logical possibitlity but it is presently unknown whether gravity (in connection with the Standard Model) has this property. We shall review these basic concepts as well as the present understanding and speculations.

27.1., 03.02. Anja Stuhlfauth: Exact Renormalization Group and Asymptotic Safety I

03.02. Juan Sebastián Valbuena Bermúdez: Euclidean Anharmonic Oscillator

10.02. Juan Sebastián Valbuena Bermúdez: Exact Renormalization Group and Asymptotic Safety II- Bosonization

10.02., 17.02.Juan Mauricio Valencia Villegas: Exact Renormalization Group Equation, and Asymptotic Safety Part 1  Part 2

Topic 3: Amplitudes from Spinor-Helicity and Unitarity Methods (Supervisor: Prof. Weiler), 11.11., 18.11., 25.11., 2.12.

Abstract: Many scattering amplitudes are actually uniquely fixed by kinematic constraints like Lorentz invariance and momentum conservation. During recent years, the study of the scattering amplitudes program has revealed a menagerie of alternative variables (like spinor helicity or twistors). By recasting expressions into the appropriate variables, one can achieve massive simplifications which reveal otherwise invisible structures. We review basic kinematical concepts like the spinor helicity formalism and explain how to bootstrap tree-level scattering amplitudes. Afterwards, we discuss on-shell recursion relations and soft theorems. We can arrive at the celebrated equivalence principle of Einstein without the ethical pitfalls of hurling unsuspecting test subjects into the dead of space in an elevator. We will emphasize their broad applicability to gravity, gauge theory, and effective field theories. Remarkably, using only Lorentz invariance, locality and dimensional analysis, we can bootstrap an enormous amount of physics: on-shell recursion relations (BCFW), generalized unitarity, dual conformal invariance, or gravity as a dual copy of gauge theories.

11.11. Thomas Bader: Amplitudes and the Spinor-Helicity Formalism

18.11. Andrea Sanfilippo: Three-Point Amplitudes, On-Shell Recursion Relations and Double Copy

25.11. Dominik Haslehner: Amplitudes from Spinor-Helicity and Unitarity Methods