Wydział Fizyki UW > Badania > Seminaria i konwersatoria > Exact Results in Quantum Theory

Exact Results in Quantum Theory

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Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

A.V. Kiselev (U. Groningen)

The Kontsevich star-product for affine Poisson brackets: new rational form

The Kontsevich star-product admits a well-defined restriction to the class of affine – in particular, linear – Poisson brackets; its graph expansion consists only of Kontsevich’s graphs with in-degree ≤ 1 for aerial vertices. We obtain the formula *aff mod ō(ℏ7) with harmonic propagators for the graph weights (over n ≤ 7 aerial vertices); we verify that all these weights satisfy the cyclic weight relations by Shoikhet–Felder–Willwacher, that they match the computations using the kontsevint software by Panzer, and the resulting affine star-product is associative modulo ō(ℏ7). We discover that the Riemann zeta value ζ(3)2/π6, which enters the harmonic graph weights (up to rationals), actually disappears from the analytic formula of *aff mod ō(ℏ7) because all the Q-linear combinations of Kontsevich graphs near ζ(3)2/π6 represent differential consequences of the Jacobi identity for the affine Poisson bracket, hence their contribution vanishes. We thus derive a ready-to-use shorter formula *red mod ō(ℏ7) with only rational coefficients. We also discover that the mechanism of associativity for the star-product up to ō(ℏ6) is different from the mechanism at order 7. Namely, at lower orders the needed consequences of the Jacobi identity are immediately obtained from the associator mod ō(ℏ6), whereas at order (ℏ7) and higher, some of the necessary differential consequences are reached from the Kontsevich graphs in the associator in strictly more than one step. (Joint work with R. Buring, see arXiv:2209.14438, arXiv:2309.16664, and arXiv:1702.00681 in Experimental Mathematics.)

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Ignacio Agustín Aucar (Groningen & Nikhef & Conicet)

owards an absolute NMR shielding scale: Relativistic effects on its relationship with nuclear spin-rotation constants

The talk will be also broadcasted via zoom

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Mikołaj Misiak (IFT UW)

Effective Quantum Field Theories. Part III: From pNRQED to the Lamb shift

I have been asked to present basic points of my full-semester lecture on effective quantum field theories in a couple of seminar talks. In the third (and last) talk, I am going to apply the already presented pNRQED action to derive the leading-order Lamb shift with the help of dimensional regularization. Broadcast via zoom

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Manizheh Botshekananfard (Bogazici University, Istanbul)

Induced energy-momentum tensor of Dirac field in 2-dimensional de Sitter quantum electrodynamics

The expectation value of the energy-momentum tensor in the in-vacuum state of the Dirac field, which is quantized in the Poincaré patch of 2-dimensional de Sitter space-time in the presence of a uniform electric field background, has been computed. The ultraviolet divergences are removed by applying the adiabatic regularization method. Then, we obtain the finite and continuous expressions of the parameters electric field and Dirac field mass for the energy-momentum tensor components. We show that the off-diagonal components of the energy-momentum tensor vanish, and the absolute values of the diagonal components increase as the electric field increases and decrease as the Dirac field mass increases, except in the very near vicinity of points at which these expressions become zero. We have computed the trace anomaly of the energy-momentum tensor, which agrees precisely with the trace anomaly derived earlier in the literature. In this talk, I will discuss the back-reaction effect of the induced energy-momentum tensor on the gravitational field of the 2-dimensional de Sitter spacetime.

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Michał Dereziński (University of Michigan)

Randomized Algorithms for Linear Systems: Going Beyond Krylov Subspace Methods

Solving large systems of linear equations has numerous applications across many areas, from partial differential equations to numerical optimization and beyond. Krylov subspace methods such as conjugate gradient have long been the gold standard in this area, thanks to their ability to exploit clusters and outliers in the spectrum of the input matrix to achieve fast convergence. Yet, our recent results have shown that it is possible to improve upon Krylov methods by introducing randomness into the algorithmic procedure. In this talk, I will survey the advantages of randomized algorithms in solving large linear systems, including our new randomized variant of the linear solver originally proposed by Stefan Kaczmarz in 1937, showing that this algorithm exploits large outlying eigenvalues provably better than any Krylov subspace method.

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Mikołaj Misiak (IFT UW)

Effective Quantum Field Theories. Part II: From HQET to pNRQED

I have been asked to present basic points of my full-semester lecture on effective quantum field theories in a couple of seminar talks. In the second talk, I am going to complete the description of the Heavy Quark Effective Theory (HQET), and pass to the Non-Relativistic QED (NRQED) as well as its "potential" version (pNRQED). Their sample application to be discussed later will be computing the Lamb shift with the help of dimensional regularization. The seminar is also transmitted by zoom

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Erik Skibsted (Aarhus University)

Scattering subspace for time-periodic N-body Schroedinger operators

We propose a definition of a scattering subspace for N-body Schrödinger operators with time-periodic short-range pair-potentials. This in given in geometric terms. We claim that all channel wave operators exist, and that their ranges span the scattering subspace. This may possibly serve as an intermediate step for proving the longstanding open problem of asymptotic completeness, which may be reformulated as the assertion that the scattering subspace is the orthogonal subspace of the pure point subspace of the monodromy operator. There will be also broadcast via zoom

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Jan Dereziński (KMMF)

Are tachyons physical

The short answer is: they are not. I will give a long answer. After a definition of what I mean by "physical", I will explain the flaws of various attempts to define tachyonic quantum field theory. My talk is inspired by recent discussions in our Faculty about tachyons.

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Trond Saue (IFT UW)

Towards molecular QED

the hybrid format – the speaker will give the talk online with two-way audio and video available in room 1.40

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Mikołaj Misiak (IFT UW)

Effective Quantum Field Theories. Part I: From WET to HQET

I have been asked to present basic points of my full-semester lecture on effective quantum field theories in a couple of seminar talks. In the first talk, I am going to discuss the simplest examples, namely the Weak Effective Theory (WET) and the Heavy Quark Effective Theory (HQET). They will serve as a starting point for future discussion of Non-Relativistic QED and its application to evaluating the Lamb shift with the help of dimensional regularization.

Zapraszamy na spotkanie o godzinie 14:15

Krzysztof Jodłowski (IBS, Daejeon, Republic of Korea)

Covariant quantum field theory of tachyons is unphysical II

Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This may have changed with the recent works of Dragan et al., who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM) because they require introducing non-determinism and wave-like behavior at the fundamental level. Unfortunately, we show that the tachyon quantum field theory proposed as a part of this program is not quantum since the tachyon field commutes at all points and the canonical commutations relations of a quantum scalar field are not satisfied. We also discuss other authors' theories, e.g., we show that the Dhar-Sudarshan's formula for the Feynman propagator violates unitarity, and we apply the LSZ formalism to tachyons for the first time, where we find that one cannot prove the LSZ asymptotic condition just by replacing plane waves with wavepackets.Zoom link: https://uw-edu-pl.zoom.us/j/2780321940

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Krzysztof Pachucki (IFT UW)

Testing fundamental interactions with light muonic atoms

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Gregory S. Adkins (Franklin & Marshall College, USA)

High Order Calculation of Energy Levels for Two-Body QED Bound Systems

Powerful methods have been developed recently for the exact evaluation of Feynman integrals. In this talk I will describe one set of methods that allows for the calculation of recoil corrections to the energy levels of two-body bound systems such as positronium and muonium. The results obtained at a given order in the fine structure constant are exact in the masses of the particles involved, and will be useful for comparison with the results of upcoming experiments. Room 1.40 and on zoom Zoom link: https://uw-edu-pl.zoom.us/j/2780321940

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Vladimir Yerokhin (MPIK, Heidelberg, Germany)

Two-loop electron self-energy without expansion in binding field and Rydberg constant

The two-loop electron self-energy is one of the most problematic effects in the hydrogen Lamb shift, whose theory is the cornerstone for determination of the Rydberg constant [1]. Its contribution is presently obtained from combining the numerical all-order (in the nuclear binding field) calculations [2] and the calculations based on the expansion in the binding field [3,4]. The accuracy of the all-order calculations is limited by the convergence of the partial-wave expansion, whereas the accuracy of the expansion calculations is limited by the unknown higher-order contributions. Recently, methods with improved the partial-wave expansion convergence were developed for the one-loop self-energy problem [5,6]. I will discuss the recent developments in all-order two-loop calculations [7] and their consequences for the determination of the Rydberg constant. [1] E. Tiesinga, P. J. Mohr, D. B. Newell, and B. N. Taylor, Rev. Mod. Phys. 93, 025010 (2021). [2] V. A. Yerokhin, Phys. Rev. A 80, 040501(R) (2009). [3] K. Pachucki and U. D. Jentschura, Phys. Rev. Lett. 91, 113005 (2003). [4] S. G. Karshenboim, A. Ozawa, and V. G. Ivanov, Phys. Rev. A 100, 032515 (2019). [5] V. A. Yerokhin, K. Pachucki, and V. M. Shabaev, Phys. Rev. A 72, 042502 (2005). [6] J. Sapirstein, K. T. Cheng, Phys. Rev. A 108, 042804 (2023). [7] V. A. Yerokhin, Z. Harman, Ch. Keitel, submitted.

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Krzysztof Jodłowski (IBS, Daejeon, Republic of Korea)

Covariant quantum field theory of tachyons is unphysical

Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This changed with the recent work of Dragan and Ekert, who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM), since they require introducing non-determinism and wave-like behavior at the fundamental level. In fact, both classical and quantum field theory of tachyons have been constructed. Unfortunately, we will show that the latter theory contains several flaws, mostly caused by adapting incorrect results due to other authors, which puts the aforementioned program in question. In particular, unlike Feinberg, we show that tachyon microcausality violation spoils fundamental features of QFT such as statistical independence of distant measurements, and it negatively affects constructing Lorentz invariant scattering theory of tachyons. Moreover, the Feynman propagator, which was adapted from Dhar and Sudarshan, is shown to violate unitarity, the tachyonic vacuum is unstable due to radiatively generated tachyon self-interactions, and an interpolating tachyon field likely does not satisfy the LSZ asymptotic condition. Our analysis indicates that a covariant QFT of tachyons seems impossible, hence superluminal observers are unphysical and cannot be used to derive QM.

Zapraszamy do sali 1.40, ul. Pasteura 5 o godzinie 14:15

Jan Dereziński (KMMF FUW)

Lamb shift as a problem in mathematical physics

I will try to formulate the problem of bound states as a rigorous problem in (perturbative) QED. These proposals are based on my conversations with prof. Pachucki and Shabaev. I will also tell some entertaining anecdotes related to this question.