The Bessel operator, that is, the Schroedinger operator on the half-line with a potential proportional to 1/x^2, has been extensively studied in the momentum representation. It has been noticed that it can be used as an illustration of K. Wilson's approach to renormalization.I will explain the mathematics that underlies the Wilsonian renormalization applied to inverse-square potentials. I will discuss how to make the momentum approach rigorous, including all its tools such as cut-offs and counterterms, and how it relates to the self-adjoint realizations of the operator in the position space.
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Paweł Duch (Universitaet Leipzig)
Stochastic quantization is a method of constructing models of Euclidean quantum field theory with the use of stochastic partial differential equations driven by a random force called the white noise. Stochastic quantization equations of nontrivial QFT models are typically ill-posed. They require renormalization and admit only distributional solutions. A general solution theory for such equations was developed only recently by Martin Hairer. His breakthrough work triggered much interest in singular stochastic PDEs in the mathematical community and was awarded the Fields Medal in 2014.
In the first part of the talk, I will give a short introduction to the stochastic quantization technique. In the second part, I will outline a new method of constructing solutions of singular stochastic PDEs. I will illustrate the method with the example of the stochastic quantization equation of the Phi^4 model in 3 dimensions. A distinctive feature of my construction is the use of the Wilsonian renormalization group theory and the Polchinski flow equation.
room 1.40, Pasteura 5 at 14:15
Abhishek Goswami (Department of Mathematics, SUNY)
In the Standard Model of particle physics, the interaction of a particle with the Higgs boson is responsible for its mass generation. This principle is known as the Higgs mechanism. Fermions interact with the Higgs boson through a Yukawa coupling constant. The presences of a Higgs-like particle and the Yukawa coupling have now been confirmed at the CERN Large Hadron Collider (LHC). In this talk, I will discuss rigorous, non-perturbative proof of the fermion mass generation. I will start with a weakly coupled U(1) Higgs-Yukawa theory on a unit lattice in d=4 and show exponential decay of two-point fermion correlation function. This is the mass gap. Mass gap implies that all the particles in the theory i.e. the U(1) gauge boson, the Higgs boson and the fermions have a non-zero physical mass.
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room 1.40, Pasteura 5 at 14:15
Maciej Łebek (IFT UW + CFT PAN)
Quantum mechanics is a theory that provides us with the wave picture of matter and it explicitly brings phenomena such as interference into the description of particles. These aspects are thoroughly illustrated by the phenomenon of quantum carpet. Quantum carpets are highly coherent interference patterns found in the evolution of the wave function describing particles in certain confined geometries. I will review known results and the most important concepts such as quantum revivals. In particular, recently carpets were found in many-body fermionic systems. Then, I will move on to new results in interacting bosonic systems, where we study carpets for all values of interaction between particles using exact Gaudin's solutions constructed with the Bethe ansatz techniques.
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room 1.40, Pasteura 5 at 14:15
Yik Man Chiang (Hong Kong University of Science and Technology)
We give a geometric interpretation about the method of resolving apparent singularities of Heun equations, a class of Fuchsian type linear differential equations. It turns out that the resolving singularity technique are used in various branches of applied mathematics and mathematical physics. We shall briefly introduce the use of Heun equations and its confluent counterparts in some of these applications. In particular, we apply the geometric interpretation in connecting the hypergeometric-type expansions solutions to Heun equations obtained by Erdelyi from the 1940s.
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room 1.40, Pasteura 5 at 14:15
Yik Man Chiang (Hong Kong University of Science and Technology)
The classical Picard theorem (A meromorphic function that misses three values must reduce to a constant) can be regarded as a result about differential operators. We introduce the recent rejuvenation of the classical result to include various difference operators related to special functions. We shall deduce these new results as consequences of relevant Nevanlinna theories. We shall also discuss potential implications and what we still do not understand of these theories.
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Chiu-Yin Tsang (The University of Hong Kong)
It is well-known that Heun equations always admit a power series (local) solution at a regular singularity. On the other hand, such a local solution can be expanded into an infinite sum of hypergeometric functions. In this talk, we will give a unified approach to these series, which mimic the construction of
p-adic numbers. Also, we will discuss its algebraic interpretations of the series of hypergeometric functions.
Link:
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(IFT UW)
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Paweł Caputa (IFT UW)
Exactly solvable deformations in Quantum Theory & Gravity
I will give a short introduction to the so-called "TT-bar" deformations of quantum field theories in two dimensions. I will describe how, using Burger's equation and geometric methods, one can derive the energy spectrum and a few other aspects of deformed theories. Finally, I will discuss the interpretation of these results from the perspective of gravity in Anti-de Sitter spacetimes.
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Carlos Tamarit (Technische Universität München)
While CP violation has never been observed in the strong interactions, the QCD Lagrangian admits a CP-violating topological interaction proportional to the so called theta angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of theta ≤ 10^(-10)which constitutes the so-called strong CP problem. In this talk we challenge this view and argue that in the infinite volume limit the theta angle drops out of correlation functions, so that it becomes unobservable and CP remains a good symmetry. We arrive at this result either by using instanton computations or by constraining the dependence of the partition function on the spacetime volume and the fermion masses by imposing cluster decomposition and compatibility with the index theorem. We further show that in large but finite spacetime volumes, cluster decomposition can be satisfied up to volume-suppressed corrections without the need to sum over topological sectors. The resulting partitions functions lead again to no CP violation. Zoom Meeting ID: 861 0663 2208, Passcode: 673023
room 1.40, Pasteura 5 at 14:15
Maciej Lisicki (IFT UW)
Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. On the other hand, chemically active surfaces can lead to microscale flow generation, bacoming an effective pumping mechanism in inertia-less small-scale flows. In this talk, I will review briefly both phenomena relating to the same concept of phoretic flow generation. Asymmetry needed for the flow to be initiated can be induced by geometry or by chemical patterning. I will show examples of both ways and some developments in biomimetic systems of phoretic swimmers.
The link to join the meeting is:
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Avery Ching (Hong Kong University of Science and Technology)
Certain classical special functions can be expressed by Rodrigues' type formulas, such as the Jacobi polynomials, generalized Laguerre polynomials, and Hermite polynomials (do not forget the most important example: monomials with negative powers.). In this talk, we will explore the common topological nature behind these formulas. Various orthogonal properties will become direct consequences from this viewpoint.
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Adam Bednorz (IFT UW)
We will argue that free will or the freedom of choice is a necessary concept in physics. Free will with locality leads to the no-signaling principle,but it is in conflict with local hidden variables in quantum physics.It can be shown by Bell paradoxes — a violation of certain inequalities or equalities. The equalities are used in the Conway-Kochen free will theorem and Greenberger-Horne-Zeilinger experiment. We will discuss also various done and not yet done experiments testing free will.Zoom ID: 861 0663 2208 Passcode: 673023
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Marcin Napiórkowski (KMMF)
We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in the large particle number limit, and provide the optimal convergence rate. Based on joint work with P.T. Nam, J. Ricaud and A. Triay.
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Jerzy Lewandowski (IFT UW)
Zoom. Meeting ID: 861 0663 2208, Passcode: 673023