Sommerfeld Theory Colloquium (ASC)

Latest Episodes:

Pulling Yourself by your Bootstraps in Quantum Field Theory Jan 30, 2019

Show notes

Quantum field theory (QFT) is the universal language of theoretical physics, underlying the Standard Model of elementary particles, the physics of the early Universe and a host of condensed matter phenomena such as phase transitions and superconductivity. A great achievement of 20th-century physics was the understanding of weakly coupled quantum field theories where interactions can be treated as small perturbations of otherwise freely moving particles. Critical challenges for the 21st century include solving the problem of strong coupling and mapping the whole space of consistent QFTs. In this lecture, I will overview the bootstrap approach, the idea that theory space can be determined from the general principles of symmetry and quantum mechanics. This strategy provides a new unifying language for QFT and has allowed researchers to make predictions for physical observables even in strongly coupled theories. I will illustrate the general framework in a few examples, ranging from the concrete (boiling water) to the abstract (supersymmetric theories in various spacetime dimensions).

Space-Time-Matter: Finite Projective Geometry as a Quantum World with Elementary Particles Dec 06, 2018

Show notes

A unified theory for space-time and matter might be based on finite projective geometries instead of differentiable manifolds and gauge groups. Each point is equipped with a quadratic form over a finite Galois field which define neighbors in the finite set of points. Due to the projective equivalence of all quadratic forms this world is necessarily a 4-dimensional Lorentz-invariant space-time with a gauge symmetry G(3)xG(2)xG(1) for internal points which represent elementary particle degrees of freedom. Matter appears as a geometric distortion by an inhomogeneous field of quadrics and all physical properties (spins, charges) of the standard model seem to follow from its geometric structure in a continuum limit. The finiteness inevitably induces a fermionic quantization of all matter fields and a bosonic for gauge fields. This unity of space-time and matter was already sought 1918 by Hermann Weyl in a gauge theory as an extension of Einstein’s general theory of relativity, but not found - probably because of the assumption of a continuous geometry.

R-matrix Quantization of the Ruijsenaars-Schneider Models Nov 27, 2018

Show notes

I describe an algebraic scheme for quantizing the Ruijsenaars-Schneider models in the R-matrix formalism. It is based on a special parametrization of the cotangent bundle over GL(n,C). In new variables the standard symplectic structure is described by a classical (Frobenius) r-matrix and by a new dynamical r¯-matrix. Quantizing these r-matrices, I will exhibit the quantum L-operator algebra and construct its particular representation corresponding to the RuijsenaarsSchneider system. I will also indicate a couple of open problems.

Black holes as harbingers of new gravitational physics Oct 10, 2018

Show notes

The apparent crisis of black holes inconsistency with foundational physical principles provides a sharp focus for the conflict between quantum mechanics and classical spacetime. Various resolutions have been proposed; a very plausible one is that small interactions can transfer sufficient information between the black hole and outgoing radiation, with a quantum enhancement from the enormous number of black hole states. Such interactions must however violate conventional notions of locality, perhaps as a symptom of the more basic subtlety of information localization in quantum gravity, and hinting at aspects of the fundamental structure of quantum gravity. An intriguing question is whether further clues can be found from new observational windows on black holes.

Black Holes, Quantum Information, and Unification Jun 21, 2018

Show notes

The study of black holes has revealed a deep connection between quantum information and spacetime geometry. Its origin must lie in the quantum theory of gravity, which offers a valuable hint in our search for a unified theory. Precise formulations of this relation recently led to new insights in Quantum Field Theory, some of which have been rigorously proven. An important example is our discovery of the first universal lower bound on the local energy density. The energy near a point can be negative but it is bounded below by a quantity related to the information flowing past the point.

High order correlation and what we can learn about the solution for many body problems from experiment Jan 18, 2018

Show notes

The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I will give examples how one can apply this powerful theoretical concept in experiment. A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system of two 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble [2]. This is verified through phase correlations up to 10th order. Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon / massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize [3]. This allowed us to characterize the essential features of the model solely from our experimental measurements: detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the quasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve a non-trivial quantum field theory. Our examples establish a general method to analyse quantum systems through experiments. It thus represents a crucial ingredient towards the implementation and verification of quantum simulators. Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg). Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and the EU: ERC-AdG QuantumRelax [1] M. Gring et al., Science, 337, 1318 (2012); [2] T. Langen et al., Science 348 207-211 (2015). [3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126

Gauge Theories and Non-Commutative Geometry Nov 09, 2017

Show notes

We shall review the attempts to extend the quantum mechanical property of non-commutativity from phase space to ordinary space. These attempts took a more precise form in the case of gauge theories for which some concrete results have been obtained. In flat space they amount to a reformulation of the theory which looks interesting but they have not given so far any novel physical results. However, the introduction of gravity gives a richer structure and may offer some new insights.

Emergent cosmology from quantum gravity: the universe as a quantum condensate Oct 19, 2017

Show notes

The construction of a quantum theory of gravity remains an open problem despite decades of efforts. In time, the very perspective on this problem evolved. From quantising General Relativity, the goal is now mostly understood to be unraveling a more fundamental microstructure of spacetime, based on non-geometric building blocks, and to show how spacetime and matter emerge as effective, approximate notions. Given some candidate building blocks, the task becomes analogous to that of extracting the macroscopic, collective behaviour of the atoms of a condensed matter system, but even more challenging since we cannot use the usual spacetime intuition and no direct observational input is available to guide theory construction. Lacking a fundamental theory of quantum gravity, existing cosmological models which have proven extremely successful in accounting for the observed features of the very early universe (via CMB data) remain without a solid foundation, having to make a number of assumptions about a physical regime (close to the big bang), where the quantum nature of gravity and spacetime is expected to be relevant. This is all the LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN SEITE 2 VON 2 more unfortunate, since the very early universe is also where any proposed quantum theory of gravity has the highest chance of finding its observational test-bed. The gap needs to be bridged. In this talk I will first of all review the basic aspects of the problem of quantum gravity, and of some current approaches. I will then focus on one specific formalism for quantum gravity, so-called group field theories (strictly related to a number of other modern approaches). I will introduce its main features, trying to clarify the nature of the suggested building blocks of spacetime and their mathematical description. Next, I will outline a general strategy to extract an effective cosmological dynamics from quantum gravity, within this formalism. In this setting, the universe emerges as a quantum condensate of the fundamental “atoms of spacetime”, and cosmology is its corresponding hydrodynamics. Finally, I will summarize the recent results obtained along this research direction.

Modeling microbial diversity Jul 06, 2017

Show notes

Metagenomics has revealed hundreds to thousands of microbial species coexisting in almost all microbiota. It is increasingly appreciated that microbial communities condition their own environments. To better understand the role of this environmental conditioning in promoting diversity, we physically model the population dynamics of microbes that compete for steadily supplied resources. In a model where cells require multiple nutrients, we find that population dynamics generally leads to the coexistence of different metabolic types, which satisfy an extended competitive exclusion principle. Moreover, we establish that these consortia of metabolic types act as cartels, whereby population dynamics pins down resource concentrations at values for which no other strategy can invade. Strikingly, these cartels also yield maximum biomass, constituting a microbial example of Adam Smith’s “invisible hand” leading to collective optimal usage of resources. Curiously, in a model where only total resource acquisition is considered, diversity can arbitrarily exceed that predicted by the competitive exclusion principle.

From Emergent Gravity to Dark Energy and Dark Matter Jun 08, 2017

Show notes

The observed deviations from the laws of gravity of Newton and Einstein in galaxies and clusters can logically speaking be either due to the presence of unseen dark matter particles or due to a change in the way gravity works in these situations. Until recently there was little reason to doubt that general relativity correctly describes gravity in all circumstances. In the past few year insights from black hole physics and string theory have lead to a new theoretical framework in which the gravitational laws are derived from the quantum entanglement of the microscopic information that is underlying space-time. An essential ingredient in the derivation is of the Einstein equations is that the vacuum entanglement obeys an area law, a condition that is known to hold in Anti-de Sitter space due to the work of Ryu and Takayanagi. We will argue that in de Sitter space due to the positive dark energy, that the microscopic entanglement entropy also contains also a volume law contribution in addition to the area law. This volume law contribution is related to the thermal properties of de Sitter space and leads to a total entropy that precisely matches the Bekenstein-Hawking formula for the cosmological horizon. We study the effect of this extra contribution on the emergent laws of gravity, and argue that it leads to a modification compared to Einstein gravity. We provide evidence for the fact this modification explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

Our TOPPODCAST Picks

Follow Us

Stay Connected

Sommerfeld Theory Colloquium (ASC)

Related Podcasts

Links

Stay Connected