12th Tux Winter Workshop on Quantum Gravity

10 Feb 2025, 13:30 → 14 Feb 2025, 21:00 Europe/Berlin

Tux Center

The 12th Tux Winter Workshop on Quantum Gravity will take place on February 10–14, 2025 in Tux (Austria).

In October 2024, Prof. Jerzy Lewandowski, founder and co-organizer of the Tux Winter Workshop series, passed away.

The forthcoming edition of the workshop will be held in his memory and will have a special focus on his work and research interests.

Manuscripts don't burn!

Mikhail Bulgakov, The Master and Margarita

Scope:

The workshops aim to bring together experts on loop quantum gravity and related topics. In general, the topics of the workshops include:

• All approaches to loop quantum gravity
• Other approaches to quantum gravity and their relation to LQG
• Quantum gravity phenomenology
• Quantum gravity topics of general interest
• General relativity and differential geometry topics of general interest

Invited speakers:

• Abhay Ashtekar * (Pennsylvania State University)
• Fernando Barbero * (CSIC Madrid)
• Bianca Dittrich * (Perimeter Institute)
• Kristina Giesel (FAU Erlangen-Nürnberg)
• Wojciech Kamiński (University of Warsaw)
• Yongge Ma (Beijing Normal University) 
• Guillermo Mena Marugán (CSIC Madrid)
• José Mourão (IST, University of Lisbon)
• Daniele Oriti (Universidad Complutense de Madrid)
• Jorge Pullin (Louisiana State University)
• Thomas Thiemann* (FAU Erlangen-Nürnberg)

* Online talk.

Funding:

Funding for the workshop is provided by Paderborn University, the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) and the German Research Foundation (DFG).

Earlier editions:

2024, 2023, 2022, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013

Financial support and Visas:

We cannot provide any financial support for participants.

Please note that we can not support visa applications.

Organizers:

Mehdi Assanioussi, Christian Fleischhack, Ilkka Mäkinen, Hanno Sahlmann, Wolfgang Wieland

Monday 10 February

1 Jurek's physics

Speaker: Jorge Pullin

15:10 Break

2 Mabuchi geodesics and mixed momentum space and holomorphic quantization for cotangent bundles of Riemannian symmetric spaces

The choice of a polarization in a quantum theory is equivalent to the choice of a (local) maximal abelian algebra of preferred observables. We recall how imaginary time Hamiltonian flows correspond to geodesics in the space of Kaehler polarizations and how this allows us to define mixed momentum space and holomorphic quantization for cotangent bundles of compact Riemannian symmetric spaces. In the noncompact case the same can be achieved with the infinite real time limit of the symmetric space geodesic flow.

Speaker: José Mourão

3 Observations on representations of the spatial diffeomorphism group and algebra (via Zoom)

The spatial diffeomorphism constraint plays a key role in the canonical approach to quantum gravity. In this talk, devoted to Jurek Lewandowski who has contributed substantially to this subject, we report partial results concerning its possible representations in the quantum theory.

Speaker: Thomas Thiemann (FAU Erlangen-Nuremberg)

17:20 Break

4 Solving quantum Hamilton constraints of LQG using neural network quantum states: review and developments

Obtaining and interpreting solutions to the quantum Hamilton constraint of LQG is a long-standing and difficult problem. In this talk, we review recent developments which approach this problem with novel numerical methods which harness the power of neural networks. We begin by introducing the basic idea of parameterising quantum states with a neural network. To illustrate its applicability, we consider 3d Euclidean gravity in Smolin’s weak coupling limit whereby the quantum theory is truncated by introducing a fixed graph and a cutoff on representations on account for computational feasibility. We then find and compare approximate solutions of the Thiemann regularised Hamilton constraint with a more naive regularisation and show that they quantitatively have much more in common than expected. Lastly, we present some preliminary results and work in progress in building towards finding solutions to the Thiemann regularised quantum Hamilton constraint of 4d gravity in Smolin’s weak coupling limit.

Speaker: Waleed Sherif

5 Shift charges, edge vectors and diffeomorphisms on the lattice

By analogy to 3D gravity, I present an attempt to get a hold of diffeomorphisms in lattice tetrad gravity: diffeomorphisms can be replaced by combinations of Lorentz and Shift symmetries, all of which can be covariantly defined, eliminating the seperation into spatial and timelike constraints.
I present these results, their implications for corner symmetries as well as some early ideas for how to implement these symmetries on a phase space toy model that includes discretised tetrads (edge vectors) explicitly.

Speaker: Simon Langenscheidt (LMU Munich)

6 Observable signatures of quantum spin connection foam

Quantum spin connection foam (SCF) arises within the precanonical quantization of general relativity as a description of the quantum geometry of spacetime in terms of the amplitudes on the spin connection bundle, derived from the precanonical Schr\"odinger equation. We show that it leads to observable signatures such as a small Milgromian acceleration $g_0 \sim 8\pi \hbar G \varkappa$ and a small cosmological constant $\Lambda \sim (8\pi \hbar G \varkappa)^2$. The smallness of these values is attributed to the hadronic scale of the constant $\varkappa$, which emerges in precanonical quantization on dimensional grounds and is related to the hadronic mass gap scale in nonabelian gauge theories of the Standard Model. By considering a nonrelativistic test particle moving in the gravitational field of a point mass on a background of the SCF described by the simplest solution of the precanonical Schr\"odinger equation for quantum gravity, we derive a modified Newtonian potential and recover the Milgromian MOND, which describes flat galactic rotation curves without dark matter. We also present estimations showing that the effects of SCF can already be tested in tabletop experiments, potentially be seen in anomalies of dynamics of the outer Solar System, and play a role in the dynamics and formation of large-scale structures in the Universe.

Based on:
DOI:10.1007/978-3-031-62407-0_26,
DOI:10.1088/1742-6596/2533/1/012037,
DOI:10.13140/RG.2.2.29652.72328/1,
DOI:10.1142/9789813226609_0352,
DOI:10.1063/1.4791728,
DOI:10.1142/9789813226609_0519.

Speaker: Igor Kanatchikov (Natl. Quantum Information Center in Gdansk)

Tuesday 11 February

7 Covariance in Spherically symmetric effective models and quantum black holes

Speaker: Yongge Ma

8 My recollections of Jurek: life and science (via Zoom)

In this talk I will go through the memories of a lifetime of friendship and science from the moment I became Jurek's office mate in the early months of 1992.

Speaker: Fernando Barbero

15:10 Break

9 The Enigma of Black Hole Horizons (via Zoom)

Speaker: Abhay Ashtekar

10 On the continuum dynamics of spin foams (via Zoom)

Speaker: Bianca Dittrich

17:20 Break

11 Unimodular quantum cosmology and late-time quantum corrections for the Universe

The application of unimodular quantum gravity to the model of a flat, homogeneous and isotropic Universe with a scalar field yields predictions for late-time quantum gravity effects. We could identify conditions on the classical dynamics of the scalar field that imply growing uncertainties for the cosmological observables. These conditions are in particular fulfilled for a scalar field determined by an exponential potential that can be considered as a phenomenological model for the matter in our Universe. We further investigate the dynamics of quantum corrections for the Hubble parameter and the matter density for the special cases of a de-Sitter and a stiff matter Universe.

Speaker: Natascha Riahi (Faculty of Physics, University of Vienna)

12 Revisiting semiclassical effective dynamics for quantum cosmology

In this talk we revisit the technique of semiclassical effective dynamics, focusing on the evaluation of the Poisson structure of central moments that encode quantum corrections. A systematic, pedagogical, and efficient algorithm for deriving these structures is presented. The resulting formulae are applied to a broad class of isotropic cosmological models, incorporating locally observable configuration variables for matter fields. This approach enables the formulation of a consistent and nontrivial procedure for the removal of the fiducial cell (infrared regulator) in models describing spatially noncompact spacetimes.

Speaker: Maciej Kowalczyk (University of Wrocław)

Wednesday 12 February

13 Cosmological acceleration from Quantum Gravity

Speaker: Daniele Oriti

14 Charges in asymptotically de Sitter spaces

I will describe joint work with Adam Bac, Jurek Lewandowski and Michalina Broda about Wald-Zoupas charges in asymptotically de Sitter spacetimes. Wald-Zoupas construction gives a definition of asymptotic charges in gravity provided that some natural choice of
renormalization of presymplectic current exists. Interestingly such current comes from conformal Einstein's equations. In dimension 4, it is given by special choice of presymplectic current for Bach equations and Yang-Mills equations for conformal Cartan connection.

Speaker: Wojciech Kamiński

15:10 Break

15 Regular black hole models and their relationship to polymerised models and mimetic gravity

In this talk, we discuss a reconstruction algorithm that allows for a given class of regular black hole models to reconstruct from a modified Schwarzschild metric the corresponding polymerisations of the effective spherically symmetric model. This provides a tool for systematically studying different types of regular black hole models and their physical implications. As applications, we discuss models with LQG-inspired polymerisations and also consider the Hayward and Bardeen metrics and discuss their corresponding polymerizations. Finally, we provide the associated extended mimetic model in Lagrangian form for these examples and discuss its generic marginally bound solution.

Speaker: Kristina Giesel

16 Vacuum state and relation between the inflationary and Planck scales

Recent observations about the cosmic microwave background show a clear discrepancy between the scale of inflation and the Planck scale expected in the conventional inflationary picture, based on simple chaotic inflationary models. I explore a possible resolution of this conflict by considering a slight modification of the standard general relativity scenario, which naturally incorporates a scale of power suppression consistent with observations. This last scale appears by the combined effect of the preinflationary background dynamics and an associated initial vacuum state for the cosmological perturbations which differs from the conventional Bunch-Davies state. Similarities with the situation found in cases of phenomonenological interest in Loop Quantum Cosmology are discussed.

Speaker: Guillermo A. Mena Marugán (IEM, CSIC)

17:20 Break

17 Perturbative gauge-invariants in the Schwarzschild interior for hybrid quantization

In this talk, we aim to present a Hamiltonian formulation for the interior perturbations of the Schwarzschild spacetime. Our analysis is based on a truncated action at quadratic order in perturbations. Both background and perturbative degrees of freedom are treated dynamically, forming a unified system endowed with the canonical structure derived from the truncated action. First-order perturbations of the metric are expressed through perturbative gauge-invariants, linear perturbative constraints, and their associated canonical variables. For the quantum description, we employ a hybrid approach: the background is quantized using loop quantum gravity techniques, while the perturbations are treated with conventional quantum field methods.

Speaker: Andrés Mínguez-Sánchez (IEM-CSIC)

18 Gauge-invariant symmetry reduction to bridge Cosmology and Loop Quantum Gravity

We address the problem of defining a proper cosmological sector within Loop Quantum Gravity. Using a symmetry-reduction approach, we characterize the classical cosmological phase space with tools from differential topology, drawing inspiration from Yang-Mills theories and avoiding the usual minisuperspace reduction. Specifically, we propose a symmetry-reduction method based entirely on geometric considerations, which preserves local gauge symmetries. Consequently, our quantization scheme mirrors the LQG framework, allowing spin-network states to naturally emerge with properties analogous to the standard cosmological states.

In this talk, after a brief review of the necessary mathematical formalism, we discuss the imposition of symmetries at the classical level, focusing on the formal definition of homogeneity for the Ashtekar variables. We observe that, under our mathematical interpretation of homogeneity, the SU(2) gauge symmetry of the theory is preserved. The resulting system possesses a set of constraints analogous to those in LQG, enabling quantization in terms of spin networks. Furthermore, we demonstrate that these spin networks exhibit a notion of homogeneity, where the homogeneous spin-network states depend on point holonomies in a manner similar to the usual states in Loop Quantum Cosmology.

Additionally, our ongoing analysis of the moduli space of symmetry-reduced connections reveals favorable topological properties, suggesting that it is possible to define an Ashtekar-Lewandowski measure on this space without resorting to the construction of the set of generalized connections.

As a result, the cosmological states we construct share significant properties with both the LQC and LQG frameworks. This provides a simplified yet physically meaningful setting to implement and test quantum dynamics approaches proposed within LQG.

Speaker: Matteo Bruno (Sapienza University of Rome)

Gravitational waves: from Newton through Einstein to the Nobel Prize

Public Talk

Convener: Jorge Pullin

Thursday 13 February

19 Entanglement in QFT: Lessons from Minkowski and de Sitter space

Entangled states in quantum field theory are not the exception but rather the norm. Even seemingly simple states such as the vacuum in Minkowski or Sitter spacetime are rich in the entanglement they contain. In this presentation, I will discuss recently developed techniques aimed at uncovering and characterizing the distribution of entanglement in field theory. These tools include the definition and computation of the "purifier" of a given mode from the complex structure of a pure state, and how these purifying modes can be leveraged to gain insights into the entanglement content of the state and its spatial distribution. These tools become useful in various scenarios, including black holes, the early universe, and potentially in understanding entanglement in quantum gravity. This talk will discuss some applications to the early universe.

Speaker: Ivan Agullo (LSU)

20 The one-loop effective action from the coherent state path integral of LQG

A great success from Quantum Field Theory methods lies in their ability to directly obtain the effective theory, where all degrees of freedom have been integrated out, starting from a UV-complete framework.
We adopt a new approach to combine path integral effective methods and Loop Quantum Gravity (LQG) by using the recently developed coherent state path integral formulation of LQG to compute the one-loop effective action. We highlight the differences between our approach and the standard Feynman-prescribed path integral. This investigation has two main objectives: to compare our findings with the divergences encountered in the one-loop calculations of Einstein gravity and to begin exploring the IR effective properties of LQG.
Based on work in collaboration with Muxin Han and Hongguang Liu.

Speaker: Renata Ferrero

21 Phenomenology of Effective Quantum Gravitational Collapse in Metric Variables

We study how the presence of an area gap, different than zero, affects the gravitational collapse of a dust ball in metric variables. The collapse is analyzed for both the flat and spherical Oppenheimer-Snyder models.
In both scenarios the formation of the singularity is avoided, due to the inversion of the velocity at finite values of the sphere surface. This can be attributed to the presence of a negative pressure, with origins at a quantum level, which is evident in metric variables.
The phenomenology concerning the collapse is analyzed in order to identify possible measurable effects that take place during the gravitational collapse.

Speaker: Lorenzo Boldorini (Sapienza University of Rome)

15:00 Break

22 Shell-crossing singularities in effective LQG star collapse

Classical star collapse leads generally to shell-focusing singularities, according to Penrose singularity theorems. However, once non-perturbative quantum gravitational effects are taken into account, the collapsing star core undergoes a bounce when its energy density becomes planckian. In this talk I will show that such bounce of the core is generally followed by the formation of shell-crossing singularities on the outer shells of the star for a very large class of star configurations, including dust (in the marginally and non marginally bound case), ideal and non ideal fluids. This gives a central role to shell-crossing singularities in effective gravitational star collapse and black hole physics.

Speaker: Francesco Fazzini (University of New Brunswick)

23 Stellar collapse with pressure in effective loop quantum gravity

I will explore the semiclassical scenario of fluid collapse with pressure in a framework of Loop Quantum Gravity.
It is shown, consistently with already existent models, that the singularity is replaced by a bounce occurring in the Planckian regime. However, it is seen that the presence of pressure does not prevent the formation of shell crossing singularities which feature the non-homogeneous dust collapse.
The model is studied both semi-analytically, in a simplified case, and numerically in a more general and realistic scenario.

Speaker: Luca Cafaro (University of Warsaw)

24 Quantum Gravity and Black Hole Evaporation

Hawking’s seminal result, that black holes behave as black bodies with a non-vanishing temperature, suggests that black holes should evaporate. However, Hawking’s derivation is incomplete, as it neglects the backreaction between radiation and geometry. In this talk, we will present a novel approach to black hole perturbation theory that incorporates backreaction and is valid to arbitrary order. The applications to the physics of evaporating black holes is discussed, and we explore potential experimental implications. The intention is to eventually derive corrections to semi-classical computations in the literature and to determine the fate of evaporating black holes.

Speaker: Jonas Neuser

20:15 Workshop Dinner

Friday 14 February

25 Type D Isolated Horizons

One of the most exciting predictions of general relativity are black holes. Although the first exact black hole solution has been derived by Schwarzschild soon after Einstein proposed his field equations, the description of general stationary black holes required much more time and effort. Finally, in the 1960's, novel techniques in differential topology and geometry developed by Penrose, Hawking, Geroch and others provided the characterization of the global structure of spacetimes containing a black hole. Many properties of black holes have been discovered due to the global definition of the event horizon, among them are uniqueness, rigidity, no-hair and area theorems, black hole thermodynamics and Hawking effect. However, the realistic black holes are not static nor stationary, and their description should not require a teleological knowledge of the future of the whole spacetime. Therefore, an alternative, local description was proposed by Pajerski and Newman in 1971, and really gained popularity in the late 90's. This framework is referred to as isolated horizons and provides many analogical properties to global black holes. It became one of the favorite research topics of Jerzy Lewandowski. I will present the theory of the isolated horizons and some of the results obtained by Lewandowski and Warsaw relativity group.

Speaker: Denis Dobkowski-Ryłko (University of Gdańsk)

26 Do we live inside a Hayward black hole?

I will discuss a (quantum mechanically) modified model for the Oppenheimer-Snyder collapse scenario where the exterior of the collapsing dust ball is a Hayward black hole spacetime and the interior is a dust Friedmann-Robertson-Walker cosmology. This interior cosmology is entirely determined by the junction conditions with the exterior black hole. It turns out to be non-singular, displaying a power-law contraction which precedes a de Sitter phase or, reversely, a power-law expansion followed by a de Sitter era. I will also analyse the global causal structure and the viability of the model. We will learn that cosmic inflation in the collapse setting is a (quantum) mechanism that decelerates the collapsing matter and prevents it from singularity formation.

Speaker: Michał Bobula (University of Wrocław)

27 Thinking inside the box

The covariant phase space formalism is a powerful framework for analyzing systems with boundaries. One of its key achievements is providing an elegant, one-line proof of the first law of thermodynamics, demonstrating its simplicity and wide applicability—even extending to black holes in the context of dynamical gravity.
Using Lanczos-Lovelock theories as a playground, we show how to derive integrated relations that require extensions of the phase space. We apply these considerations to give well-defined prescriptions for the thermodynamical potentials that enter the Smarr formula for Lanczos-Lovelock black holes and describe how the total energy depends on the couplings.

Speaker: Giulio Neri

15:00 Break

28 The 3BF state sum as a TQFT

We study a generalization of a 4-dimensional BF-theory in the context of higher gauge theory. We have defined the state sum $Z_{3BF}$ that is a topological invariant of 4-dimensional manifolds using the higher categorical structure of a 3-group. The definition of the state sum $Z_{3BF}$ is then extended to a new state sum $Z_\partial$, that corresponds to 4-dimensional manifolds with boundary, and it is demonstrated that this extended definition gives rise to a TQFT, by explicitly verifying the axioms. It is shown that it inherently defines a functor between two dagger symmetric monoidal categories equipped with a dual: the category of 4-dimensional cobordisms between 3-dimensional manifolds and the category of finite-dimensional Hilbert spaces.

Speaker: Tijana Radenković (Institute of physics Belgrade)

29 Particle masses and degenerate spacetime metrics

Internal spacetime geometry was recently introduced to model certain quantum phenomena using spacetime metrics that are degenerate. I will describe how the Ricci tensors of these metrics can be used to derive a ratio of the bare up and down quark masses, obtaining $m_u/m_d = 9604/19683 \approx .4879$. This value is within the lattice QCD value $.473 \pm .023$, obtained at $2 \operatorname{GeV}$ using supercomputers. Moreover, I will show how the Levi-Cevita Poisson equation can be used to derive ratios of the dressed electron mass and bare quark masses. For a dressed electron mass of $.511 \operatorname{MeV}$, these ratios yield the bare quark masses $m_u \approx 2.2440 \operatorname{MeV}$ and $m_d \approx 4.599 \operatorname{MeV}$, which are within/near the respective lattice QCD values $(2.20\pm .10) \operatorname{MeV}$ and $(4.69 \pm .07) \operatorname{MeV}$. Finally, I will describe how the $4$-accelerations of these metrics can be used to derive the ratio $\tilde{m}_u/\tilde{m}_d = 48/49 \approx .98$ of the constituent up and down quark masses. This value is within the $.97 \sim 1$ range of constituent quark models. All of the ratios obtained are from first principles alone, with no free or ad hoc parameters. Furthermore, and rather curiously, the derivations do not use quantum field theory, but only tools from general relativity.

Speaker: Charlie Beil (University of Graz)

30 Fermionic entanglement and Bells' inequality in loop quantum gravity

Entanglement between particles is a fundamental concept of quantum physics which one might expect to be predicted by the theory of loop quantum gravity. Famously, entanglement aborts the idea of locality the EPR paradox is based on. Technically locality implemented by hidden variables places an upper bound on the measurement correlations between two observers (Bell's inequality). However, as shown in theoretical and experimental setups, one can exceed this bound.

One simple setup includes two spacelike separated observers which each measure the spin projection of one half of a pair of qubits. We will present a loop quantum gravity version of this setup on the kinematical level, starting with the definition of a spin projection operator which will enable us to formulate the measurements of the two observers in a gauge invariant way. Defining the Hilbert space this operator acts on and calculating its spectrum will allow us to write down states that violate Bell's inequality. We will also give a geometric interpretation of the parameter that describes the amout of violation of the inequality.

Speaker: Martin Zeiß (Friedrich-Alexander Universität Erlangen-Nürnberg (FAU))

17:00 Break

31 Dynamics of single-vertex states in quantum-reduced loop gravity

We study the quantum dynamics of a simple class of states in quantum-reduced loop gravity. These states are based on a cubic graph consisting of a single six-valent vertex. The dynamics is governed by a Hamiltonian constraint operator, whose Lorentzian part is represented by the scalar curvature operator introduced by Jurek and myself a couple of years ago. We observe a certain formal similarity between the Euclidean part of the Hamiltonian acting on the single-vertex states, and the Hamiltonian constraint of anisotropic Bianchi I models in loop quantum cosmology. By extending this formal analogy to the Lorentzian part of the Hamiltonian, we are led to suggest a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part (corresponding to the scalar curvature of the spatial manifold) is not assumed to be identically vanishing and is represented by a non-trivial quantum operator.

Speaker: Ilkka Mäkinen (National Centre for Nuclear Research, Poland)

32 More on maximal luminosity

Speaker: Wolfgang Wieland