Quantum & Fuzzy
Workshop in honour of the 65th birthday of Professor Maja Burić
4-5 April 2024, Belgrade, Serbia
Organization
The Workshop is organized by Group for Gravitation, Particles and Fields and Faculty of Physics, University of Belgrade, supported by the Ministry of Science, Technological Development and Innovations, Republic of Serbia.
Organizing committee
Marija Dimitrijević Ćirić (Faculty of Physics, University of Belgrade)
Larisa Jonke (Ruđer Bošković Institute, Zagreb)
Ilija Burić (University of Pisa)
Duško Latas (Faculty of Physics, University of Belgrade)
Voja Radovanović (Faculty of Physics, University of Belgrade)
Local Organizing committee
Bojana Brkić (Faculty of Physics, University of Belgrade)
Đorđe Bogdanović (Faculty of Physics, University of Belgrade)
Nikola Konjik (Faculty of Physics, University of Belgrade)
Programme
Lectures were held on Thursday and Friday, 4-5. April 2024, at the Faculty of Physics, Studentski Trg 12, Belgrade, lecture hall 661 (third floor).
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09:50 -- 10:00 |
Thursday, 4. April 2024. --- Opening of the workshop | |
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10:00 -- 10:50 |
Speaker: George Zoupanos (National Technical University, Athens) (lecture slides) |
Title: A realistic and testable Supersymmetric Model from the Dimensional Reduction of an N = 1, 10D, E8 Theory over a Modified Flag Manifold Abstract: We plan to review the Standard Model extension that results from the dimensional reduction of a 10D, N = 1, E8 gauge theory over the M4 × SU(3)/U(1) × U(1) × Z3 space, which leads to a 4D, N = 1, SU(3)3 × U(1)2 theory. Below the unification scale we obtain a Split NMSSM effective theory. The third generation quark and light Higgs masses are within the experimental limits at 2-loop level and the neutralino LSP mass is predicted < 800GeV. |
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10:50 -- 11:20 |
Coffee break | |
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11:20 -- 12:10 |
Speaker: Harald Grosse (Physics Department, University of Vienna) online (lecture slides) |
Title: Remarks on two "solvable" ncQFT models Abstract: For the quartic Euclidean scalar model with oscillator term (resulting from a curvature contribution, as shown by Maja and Michael Wohlgenannt) on a Euclidean deformed space-time, we prove, that it is a nontrivial QFT. Correlation functions follow blobbed topological recursions. In simple cases, the partition function obeys a differential equation. The "free" deformed Minkowski field shows wedge locality and the relative entropy between vacuum state and a state generated by the deformed field is calculated. |
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12:10 -- 13:00 |
Speaker: Dragan Prekrat (Faculty of Pharmacy, Belgrade) (lecture slides) |
Title: Matrix phase in non-commutative space: Between theory and numerical experiments Abstract: In this talk we will discuss the relationship between renormalizability and extent of the striped/matrix phase in non-commutative theories. As a main example, we will consider the matrix version of the Grosse-Wulkenhaar model on the truncated Heisenberg space. We will also present latest results on the structure of its phase diagram and new tools for its derivation. Finally, we will see how these results could help to formulate a renormalizable gauge model in non-commutative space. |
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13:00 -- 15:00 |
Lunch break | |
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15:00 -- 15:50 |
Speaker: Richard Szabo (Heriot-Watt University, Edinburgh) (lecture slides) |
Title: The BV formulation of fuzzy field theories Abstract: We apply the modern Batalin-Vilkovisky quantization techniques of Costello and Gwilliam to field theories on fuzzy spaces, treating in detail the examples of scalar field theory and Chern-Simons theory on the fuzzy sphere. We also demonstrate how these techniques extend to braided field theories on fuzzy spaces, treating in detail the example of braided scalar field theory on the fuzzy 2-torus. |
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15:50 -- 16:40 |
Speaker: Ilija Burić (University of Pisa) (lecture slides) |
Title: Quantum field on fuzzy de Sitter space I Abstract: Quantum gravitational effects relevant for inflationary cosmology may in part be captured by a weakly coupled quantum field on a noncommutative de Sitter background. Working with the fuzzy de Sitter, we pave the way for QFT calculations by constructing a de Sitter invariant vacuum and a complete set of field modes. The talk is based on joint work with Bojana Brkić, Maja Burić and Duško Latas. |
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16:40 -- 17:10 |
Coffee break | |
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17:10 -- 18:00 |
Speaker: Branislav Cvetković (Institute of Physics Belgrade) (lecture slides) |
Title: Entropy of black holes coupled to a scalar field Abstract: The Hamiltonian approach to black hole entropy, recently proposed in the framework of Poincaré gauge theory, is extended by including the scalar matter. The improved approach is used to analyse asymptotic charges and entropy of a typical black hole with scalar hair in two complementary dynamical settings, in GR and in the teleparallel gravity. In both cases, the results confirm the validity of the first law. |
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19:00 |
Conference dinner at Gradonačelnik restaurant, Dragoslava Jovanovića 9, Belgrade | |
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10:00 |
Friday, 5. April 2024. --- Second day of the workshop | |
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10:00 -- 10:50 |
Speaker: Fedele Lizzi (University Federico II, Naples) (lecture slides) |
Title: Quantum Spacetime, Noncommutative Geometry and Quantum Observers Abstract: Since the dynamical variable of general relativity is spacetime itself, it is natural to think that a quantization of gravity requires a quantization of spacetime, possibly described by a non-commutative geometry. Such a quantum spacetime requires quantum symmetries, and a quantization of observers/references frames. I will introduce the necessity for a quantum spacetime, and describe some instances for which symmetries and observers are likewise quantized. |
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10:50 -- 11:20 |
Coffee break | |
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11:20 -- 12:10 |
Speaker: Peter Schupp (Constructor University, Bremen) (lecture slides) |
Title: Quantum mechanics for nonassociative quantum algebras Abstract: We present a suitably general formulation of quantum mechanics that can handle nonassociative quantum algebras. The approach is naturally probabilistic, and it reduces to standard quantum theory in the traditional associative setting. The main difference to the usual formulation of quantum mechanics is a careful distinction between the algebra of operators on Hilbert space and the more fundamental algebra of observables that describe the quantum system. We formulate properties of states together with notions of trace and use them to develop GNS constructions. Traditional assumptions like power-associativity or alternativity are not needed, but the existence of a 3-cyclic trace is helpful. We describe Heisenberg and Schroedinger pictures of completely positive dynamics, and we illustrate our formalism for matrix Jordan algebras, octonion algebra, and even more general quantum algebras. |
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12:10 -- 13:00 |
Speaker: Marko Vojinović (Institute of Physics Belgrade) (lecture slides) |
Title: New type of closed timelike curves in quantum gravity Abstract: We will present a novel construction of the closed timelike curves (CTC) type of solutions, in the context of an abstract formalism of quantum gravity. The new CTC solutions are constructed via the quantum superposition of two regular configurations of the gravitational field in a globally hyperbolic spacetime topology, which is an unusual feature of CTC solutions. A quantum-mechanical particle traveling through such a superposed gravitational field behaves as traveling through a CTC, while also interacting with two agents (Alice and Bob) at two distinct spacetime points. Work done in collaboration with N. Paunković. |
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13:00 -- 15:00 |
Lunch break | |
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15:00 -- 15:50 |
Speaker: Tijana Radenković (Institute of Physics Belgrade) (lecture slides) |
Title: Insights from Higher Gauge Theory: the quest for Quantum Gravity with matter Abstract: Higher category theory can be employed to generalize the BF action to the so-called nBF action, obtained by passing from a notion of a gauge group to the notion of a gauge n-group. The n-groups are novel algebraic structures designed to generalize the notions of connection, parallel transport, and holonomy from curves to higher-dimensional manifolds. Therefore, they generalize the notion of gauge symmetry and give rise to the class of topological actions known as nBF actions. Constrained nBF actions are then defined by adding simplicity constraints to topological nBF actions. Specifically, we define constrained 2BF actions that describe the dynamics of gravitational and Yang-Mills fields and constrained 3BF actions that describe the Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained 3BF action, that is naturally split into a topological sector and a sector with simplicity constraints and therefore adapted for the spinfoam quantization method and nonperturbative quantization of both gravity and matter fields. Moreover, the 3-group structure gives novel gauge groups that specify the spectrum of matter fields in the theory, analogous to how the ordinary gauge group specifies the spectrum of gauge bosons in Yang-Mills theory, and have the potential to explain fermion families and other structures in the matter spectrum of the Standard Model. |
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15:50 -- 16:40 |
Speaker: Athanasios Chatzistavrakidis (Ruđer Bošković Institute, Zagreb) (lecture slides) |
Title: Higher structures and geometry for gauge systems Abstract: Generalizations of geometry have emerged in various forms in the study of field theory, gravity and quantization. In this talk I will give a brief overview of selected instances where higher structures such as homotopy algebras, algebroids and Q-manifolds appear in gauge theory. Emphasis will be given on ordinary and generalized sigma models in various dimensions and their relation to generalized symmetries and models of gravity. |
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16:40 -- 17:10 |
Coffee break | |
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17:10 -- 18:00 |
Speaker: Antun Balaž (Institute of Physics Belgrade) |
Title: Quantum fluctuations and stability of dipolar bosonic and fermionic systems Abstract: Quantum fluctuations usually lead to small, quantitative corrections to the properties of weakly interacting quantum systems at low temperatures. However, in the presence of dipole-dipole interactions, quantum fluctuations may even decide the fate of the system, including its stability and existence of the ground state. The delicate interplay and competition between the isotropic short-range contact interaction and the anisotropic long-range dipole-dipole interaction inspired the quest to explore novel phases of matter in bosonic systems, such as quantum droplets and supersolids. In fermionic systems, the presence of dipole-dipole interactions can lead to deformation of the Fermi sphere, while its stability strongly depends on geometry of the system and orientation of the dipoles. In this talk we will present our recently developed beyond-mean-field approaches for dipolar bosonic and fermionic systems and show how they can be used to study ultracold matter. We will demonstrate the emergence of quantum droplets and supersolidity in dipolar bosonic systems, and present a universal stability diagram for dipolar fermions. |
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18:00 -- 18:10 |
Final discussion and closing | |
Last update: Friday 26. April 2024, 02:09:30.
