Faculty of Physics University of Warsaw > Events > Seminars > Exact Results in Quantum Theory & Gravity

Exact Results in Quantum Theory & Gravity

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room 1.40, Pasteura 5 at 14:15

Jan Głowacki (Oxford)

Towards relational foundations for Quantum Field Theory

In this talk, I want to introduce a newly developed relational approach to relativistic quantum physics steaming from the theory of operational quantum reference frames (QRFs). I will begin by introducing the QRF framework in the context of Special Relativity by taking the Poincare group as the underlying symmetry structure. From these considerations, a novel and relational perspective on the notion of a quantum field emerges, which is then extended to curved geometries by replacing the Poincare group with a Lorentz bundle. The formalism is also capable of dealing with indefinite background geometries when formulated in the context of the frame bundles.

The talk is based on a recent preprint http://arxiv.org/abs/2405.15455.

room 1.40, Pasteura 5 at 14:15

Christian Gass (KMMF)

Two-point functions from operator theory and alpha vacua in de Sitter space

I will introduce two different operator-theoretic settings which can be used to describe various two-point functions of quantum fields. These settings are not common points of view but they have several advantages. For example, they can be used to give rigorous meaning to expressions that are in the usual interpretation zero divided by zero, or they can serve to distinguish certain states in Quantum Field Theory on curved spacetimes. As example, I will discuss is a scalar field on de Sitter space. This example at the same time exhibits a rich structure and is comparably simple.

room 1.40, Pasteura 5 at 14:15

Maciej Kolanowski (UC Santa Barbara)

Where do Schwarzian modes live?

We calculate one-loop corrections to the nearly extremal black hole thermodynamics directly in the bulk. In this way, we confirm previous near-horizon calculations of the one-loop determinant. In particular, we find a family of modes that become zero modes in the extremal limit. In that limit, they localize at a finite distance from the horizon. Thus, we may interpret them as bulk counterparts of the Schwarzian modes that arise in the near-horizon geometry due to the SL(2,R) symmetry. Along the way, we explain certain confusions regarding the count of rotational zero modes (that contribute to the log corrections to the entropy).

room 1.40, Pasteura 5 at 14:15

Paweł Jakubczyk (IFT UW)

The derivative expansion of the nonperturbative RG

I will review the application of the nonperturbative renormalization group to analyze the critical behavior of the Ising universality class. I will highlight points, where mathematical clarifications would be welcome.

room 1.40, Pasteura 5 at 14:15

Krzysztof Mysliwy (IFT UW)

Simulating critical anion chemistry with indirect excitons

The maximal ionization problem is a basic open question in quantumchemistry: given a nucleus of charge Z, what is the maximal number ofelectrons that this nucleus can bind? Based on observations, it isconjectured that this number equals Z+C, where C is a universal constantindependent of Z, most likely equal to unity. Nobody has succeeded inproving such a bound to date and only partial results in this directionexist. Some theoretical work has also been performed on a slightlyreformulated version of this problem, that is, given N electrons, whatis the minimal value of the nuclear charge Z, treated as a continuousparameter, that is able to bind them? It is known, for instance, thatthis Z is about 0.91e for N=2. In this talk, we are going to discuss apossible experimental platform for the study of this basic yetsurprisingly difficult question. Joint work with K. Jachymski.

room 1.40, Pasteura 5 at 14:15

Christian Gass (KMMF)

Point potentials on symmetric spaces in any dimension

(joint work with Jan Dereziński and Błażej Ruba)

In dimensions d≥4, the Laplacian perturbed by a point potential cannot be defined as a self-adjoint operator. However, in any dimension, there exists a natural family of functions that can be interpreted as Green’s functions of the Laplacian with a spherically symmetric point potential. In dimensions 1, 2, 3 they are the integral kernels of the resolvent of well-defined self-adjoint operators. In higher dimensions they are not even integral kernels of bounded operators.
I will describe two methods to construct these Green functions. The first resembles dimensional regularization in the minimal subtraction scheme, the second resembles the point-splitting method. Both methods can be viewed as toy models illustrating various aspects of renormalization in Quantum Field Theory. It is expected that the obtained Green functions approximate the Green functions of true Schrödinger operators with a potential of shrinking support.

room 1.40, Pasteura 5 at 14:15

Krzysztof Pachucki (IFT UW)

Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

A general quantum electrodynamic method for derivation of nuclear recoil corrections in hydrogenic systems, which are exact in the nuclear charge parameter Z α, is introduced. The exemplary derivation is presented for the O(m/M) nuclear pure recoil correction to the hyperfine splitting. The obtained result is verified by comparison to the known (Z α)^5 contribution.

join us at 14:15

Long Meng (École de Ponts, ParisTech)

Rigorous justification of the Dirac–Fock model from Mittleman's definition of QED

In this talk, we study the relationship between Dirac-Fock energy and electron-positron Hartree-Fock energy. We prove the longstanding conjecture due to Mittleman: the Dirac-Fock model is an approximation of QED when the fine structure constant α is small and the velocity of light c is large. We also prove some properties about Dirac-Fock model. In addition, we will talk about some perspectives on the Dirac many-body problem.

Link: https://uw-edu-pl.zoom.us/j/96778397094?pwd=bTZneUdLSS9ZUTJxWlhhbGRlQzdwUT09
Meeting ID: 967 7839 7094
Passcode: 090952

room 1.40, Pasteura 5 at 14:15

Paweł Duch (UAM)

Construction of Gross-Neveu model using Polchinski flow equation

The Gross-Neveu model is a quantum field theory model of Dirac fermions in two dimensions with an interaction term of quartic type. The model is barely renormalizable and asymptotically free. I will present a new construction of this model in Euclidean signature in infinite volume. The construction is based entirely on the renormalization group flow equation. I express the Schwinger functions of the model in terms of the effective potential and construct the effective potential by solving the flow equation using the Banach fixed point theorem. In order to define a suitable space of functionals, in which the flow equation can be solved, I use the filtered non-commutative probability space. The construction does not involve cluster expansion or discretization of phase-space and is applicable to other barely renormalizable and asymptotically free purely fermionic theories such as the symplectic fermion model.

join us at 14:15

Nguyen Viet Dang (Université Paris Sorbonne)

The Phi43 measure on Riemannian manifolds

I will describe a joint work with Bailleul, Ferdinand and To where we construct the $\phi^4_3$ quantum field theory measure on compact Riemannian 3-manifolds, as invariant measure of some stochastic partial differential equation. This gives an example of nonperturbative, interacting, non topological quantum field theory constructed on 3 manifolds.

https://uw-edu-pl.zoom.us/j/93686861281?pwd=ZG9iN3pqL3RVbTJ2QVVDc1RyMEZCdz09
Meeting ID: 936 8686 1281
Passcode: 227184

room 1.40, Pasteura 5 at 14:15

Nicola Pinamonti (U. Genova)

Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models

Based on arXiv:2007.14665

We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical approximation, the backreaction of matter to curvature is taken into account by equating the Einstein tensor to the expectation values of the stress-energy tensor in a suitable state. We impose initial conditions for the scale factor at finite time and we show that a regular state for the quantum matter compatible with these initial conditions can be chosen. Contributions with derivative of the coefficient of the metric higher than the second are present in the expectation values of the stress-energy tensor and the term with the highest derivative appears in a non-local form. This fact forbids a direct analysis of the semiclassical equation, and in particular, standard recursive approaches to approximate the solution fail to converge. In this paper we show that, after partial integration of the semiclassical Einstein equation in cosmology, the non-local highest derivative appears in the expectation values of the stress-energy tensor through the application of a linear unbounded operator which does not depend on the details of the chosen state. We prove that an inversion formula for this operator can be found, furthermore, the inverse happens to be more regular than the direct operator and it has the form of a retarded product, hence causality is respected. The found inversion formula applied to the traced Einstein equation has thus the form of a fixed point equation. The proof of local existence and uniqueness of the solution of the semiclassical Einstein equation is then obtained applying the Banach fixed point theorem.

room 1.40, Pasteura 5 at 14:15

Andrzej Herdegen (UJ)

Infrared structure beyond locality in electrodynamics

Infrared problems in QED are related to fundamental, conceptual physical questions, such as: what is a charged particle, completeness of particle interpretation of electromagnetic field, existence of vacuum, or quantum status of long range degrees of freedom. Answers to these questions, based on locality paradigm, do not seem to be fully convincing (despite the existence of procedures for avoiding infrared infinities incalculations). This talk briefly characterizes perspectives which openwith an admission of nonlocal variables residing in infinity, or at theboundary of spacetime after compactification.Recently, this line of investigation gains popularity.

room 1.40, Pasteura 5 at 14:15

Christian Gerard (Université Paris-Saclay)

The Euclidean vacuum state for linearized gravity on de Sitter spacetime II

I will give more details about the construction and properties of the Euclidean vacuum state for linearized gravity on de Sitter. In particular the various elliptic operators appearing in after Wick rotation and their properties will be discussed in details.

room 1.40, Pasteura 5 at 14:15

Syed Naqvi (UJ)

Chaos and Einstein-Rosen gravitational waves

We demonstrate the existence of chaotic geodesics for the Einstein-Rosen standing gravitational waves. The complex dynamics of massive test particles are governed by a chaotic heteroclinic network. We present the fractal associated with the system under investigation. Gravitational standing waves produce intricate patterns through test particles in a vague analogy to mechanical vibrations generating Chladni figures and complicated shapes of Faraday waves.

join us at 14:15

Christian Gérard (Université Paris-Saclay)

The Euclidean vacuum state for linearized gravity on de Sitter spacetime

We study the quantization of linearized gravity on de Sitter spacetime.We work in the transverse-traceless gauge and consider the (pseudo-) state obtained by Wick rotation, called the Euclidean vacuum. We show that the Euclidean vacuum is not fully gauge invariant and does not generate a positive state on the physical phase space. This fact can be traced back to the existence of Killing isometries.We show how to modify the Euclidean vacuum to obtain a fully gauge invariant and positive Hadamard state. The modified state is however not invariant under the full symmetry group of de Sitter space.

Link: https://uw-edu-pl.zoom.us/j/92533160394?pwd=dmsyNVVrelhjbDJpRmJtaGFaR1BmQT09
Meeting ID: 925 3316 0394
Passcode: 839945

room 1.40, Pasteura 5 at 14:15

Markus Fröb (Universität Leipzig)

All-order existence of and recursion relations for the operator product expansion in Yang-Mills theory

In four-dimensional Euclidean Yang-Mills theory, I show the existence of Wilson's operator product expansion (OPE) as a short-distance expansion to all orders in perturbation theory. I demonstrate that the Ward identities are reflected in the expansion, such that the OPE of gauge-invariant composite operators only involves again gauge-invariant composite operators. Furthermore, I derive novel (renormalized) recursion relations which allow to construct the OPE coefficients order by order in perturbation theory, starting from the known free-theory objects. Joint work with J. Holland, based on arXiv:1603.08012.

room 1.40, Pasteura 5 at 14:15

Mikołaj Korzyński (CFT PAN)

Redshift drift, position drift and parallax in general relativity

I will discuss the redshift and the position drifts in general relativity, i.e. the temporal variations of the redshift and the position on the sky of a light source, as registered by an arbitrary observer. With the recent advancements in astrometry, the drifts of distant sources are likely to become important observables in cosmology in the near future. In my lecture I will present the derivation of exact relativistic formulas for the drifts. I will show how the drifts may be expressed in terms of the kinematical variables characterising the motions of the source and the observer, i.e. their momentary 4-velocities and 4-accelerations, as well as the spacetime curvature along the line of sight. The formulas we derive are completely general and involve automatically all possible GR effects. They may be regarded as the counterpart of the Sachs optical equations for temporal variations of the standard observables. I will discuss their physical consequences and their possible applications to the gravitational lensing theory, cosmology and pulsar timing. The talk is based on the graduate course in Chęciny this year.

room 1.40, Pasteura 5 at 14:15

Tom Devereaux (Stanford)

Transport and Superconductivity in Strongly Interacting Quantum Matter: Role of Exact and Un-biased Numerical Simulations

"Distinguished Lectures on Complex Systems and Quantum Physics"

Lev Landau's reduction of weakly interacting electrons intoquasiparticles - essentially renormalized but otherwise free particles- forms the basis for a standard model of condensed matter systems.However, a theory to describe transport in strongly interactionsystems has been lacking. Moreover, the notion of "bad metals" hasbeen plausibly linked to "high temperature" superconductivity by PhilAnderson, which has formed a cental tenet for an understanding of thecuprates, for example. Despite multiple decades of effort, there hasbeen no theoretically derived link between the two.Yet, a tremendous amount of advancement in exact and un-biasednumerical methods has been made just in the last 5-10 years. In thistalk I will review some of this work that sheds light into the groundstate and transport properties of simple models for stronglycorrelated electrons. While much remains unresolved, I will give astatus update and discuss a link between transport properties andsuperconductivity.

room 1.40, Pasteura 5 at 14:15

Dawid Maskalaniec (FUW)

Collinear limits and infinite tower of soft graviton symmetries

Celestial holography conjectures a duality between the gravitational S-matrix and correlators in a two-dimensional conformal field theory (so-called celestial CFT). In this talk, after a brief review of soft theorems and asymptotic symmetries I will show the equivalence between them and formulate the holographic dictionary. Next, I will discuss how celestial OPE indicates new asymptotic symmetry algebras in the bulk theory.

room 1.40, Pasteura 5 at 14:15

Paweł Jakubczyk (IFT UW)

Casimir amplitudes and scaling functions for Bose gases with nonstandard dispersions

I will discuss the Casimir effect in mean-field Bose gases. Afterdemonstrating how varying the dispersion influences the Casimir effectfor realistic cases, I will analyse dispersions characterised byarbitrary power-law-type low-momentum asymptotic behavior. I will showthat the Casimir amplitudes are not well defined for the general caseand the physically relevant results are recovered by cancellation ofsingular factors.

room 1.40, Pasteura 5 at 14:15

Błażej Ruba (University of Copenhagen)

Semiclassical analysis of SU(2)-invariant quantum channels

Quantum channels are maps between spaces of (mixed) quantum states which can be realized as unitary evolutions in an extended system. That is, they arise from unitaries by tracing out degrees of freedom, just as density matrices arise from pure states. In my talk I will discuss invariant channels between density matrices acting on irreducible representations of SU(2). I will show how they can be analyzed using coherent state quantization methods, for example how one can compute the von Neumann entropy of output states.

room 1.40, Pasteura 5 at 14:15

Wojciech Kamiński (IFT UW)

On classification of conformal anomalies

I will describe classification of conformal anomalies and how the result can be proven.