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**Time: ** 19. May 2023, 12:00h

**Place: ** Institute of Physics, room 360

**Speaker: ** Maja Buric

**Title: ** Scalar fields on fuzzy de Sitter space

**Abstract:**

After a short introduction of fuzzy de Sitter geometry, we present general solution to the Klein-Gordon equation on this noncommutative space.

**Time: ** 19. May 2023, 11:00h

**Place: ** Institute of Physics, room 360

**Speaker: ** Vladislav Kupriyanov

**Title: ** Homotopy algebras, symplectic embeddings and noncommutative gauge theory

**Abstract:**

The problem of the consistent definition of noncommutative gauge theory on spaces with non-constant noncommutativity parameters has attracted the attention of theoretical physicists and mathematicians for more than two decades. Nevertheless, this theory is still not completely understood in full generality. In recent years we have formulated two new approaches to consistent non-commutative and non-associative deformations of gauge theory. The first one employs the framework of homotopy algebras and is a powerful tool for the construction of order by order noncommutative deformation. The second approach makes use of the elements from the symplectic geometry and is better adapted for obtaining the explicit all-order expressions. Several interesting results have been obtained and published in this direction. In this talk I will briefly describe the two approaches and discuss the recent progress in noncommutative gauge theories.

**Time: ** 18. May 2023, 16:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Richard Szabo

**Title: ** Homotopy double copy of noncommutative gauge theories

**Abstract:**

This talk will summarise recent work attempting to understand how standard noncommutative gauge theories, such as those which arise naturally from string theory, fit into the paradigm of colour-kinematics duality and the double copy of gauge theory to gravity. The treatment will focus on the elegant formulation of the double copy prescription using homotopy algebras. Along the way we shall encounter some novel noncommutative scalar field theories with rigid colour symmetry that have no commutative counterparts, whose double copies are deformations of some known topological theories such as the special Galileon theory in two dimensions and self-dual gravity in four dimensions.

**Time: ** 18. May 2023, 15:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Igor Prlina

**Title: ** Amplitugicians: using (non-magic) tricks to find scattering amplitudes

**Abstract:**

This talk will introduce the audience to the goals and methods of the so-called Amplitudes project, where alternatives to the Feynman diagram approach are used to calculate scattering amplitudes in different theories. Some common themes in the Amplitudes approach are symmetry adapted variables, recursive relations and geometric interpretation. These themes will be illustrated by introducing spinor helicity formalism, BCFW recursion, momentum twistors, and the Amplituhedron. Finally, some of the lecturer's own results on the connection of the boundaries of the Amplituhedron with amplitude singularities will be presented.

**Time: ** 12. May 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Voja Radovanovic

**Title: ** Batalin-Vilkovisky formalism and quantization of gauge field theories (part 4)

**Abstract:**

In these series of lectures we will review the Batalin-Vilkovisky (BV) formalism and its applications. This formalism is a generalization of the BRST quantization and it is frequently used in field theory and quantum mechanics. One of the advantages of the BV formalism is that it provides a well defined quantization for theories that cannot be quantized by the Faddev-Popov path integral approach. In particular, gauge field theories with complicated gauge symmetries (reducible and/or with an open algebra) are quantized in the framework of this formalism.

In the fourth lecture we will discuss quantization of field theories in the BV formalism.

**Time: ** 28. April 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** James Fullwood

**Title: ** On quantum states over time

**Abstract:**

While in relativity theory space evolves over time into a single entity known as spacetime, quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a quantum state into a single "state over time". Recently there is an emerging interest in the formulation of such dynamical quantum states, resulting in various approaches to their construction. In our work with Arthur Parzygnat, we have developed a general approach which we have recently shown is equivalent to the pseudo-density matrix formalism of Fitzsimons, Jones and Vedral, which was initially introduced to treat temporal and spatial correlations in quantum theory on equal footing. In this talk, we review the general theory of such states over time, and go over some recent applications, such as a dynamical quantum Bayes' rule, time-reversal for quantum systems, and quantum mechanical world lines. We then conclude with some ideas on how quantum states over time may yield "spacetime states" associated with a causal set.

**Time: ** 21. April 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Voja Radovanovic

**Title: ** Batalin-Vilkovisky formalism and quantization of gauge field theories (part 3)

**Abstract:**

In these series of lectures we will review the Batalin-Vilkovisky (BV) formalism and its applications. This formalism is a generalization of the BRST quantization and it is frequently used in field theory and quantum mechanics. One of the advantages of the BV formalism is that it provides a well defined quantization for theories that cannot be quantized by the Faddev-Popov path integral approach. In particular, gauge field theories with complicated gauge symmetries (reducible and/or with an open algebra) are quantized in the framework of this formalism.

In the third lecture we will discuss some examples of reducible and/or open gauge symmetries. Then we will introduce notions of antifields, antibracket and BV Laplacian, derive their properties and discuss the classic and the quantum master equations and their solutions. Finally, we will present few relevant examples: Yang-Mills theory, toplogical Yang-Mills theory and the antisymmetric tensor field theory.

**Time: ** 31. March 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Voja Radovanovic

**Title: ** Batalin-Vilkovisky formalism and quantization of gauge field theories (part 2)

**Abstract:**

In these series of lectures we will review the Batalin-Vilkovisky (BV) formalism and its applications. This formalism is a generalization of the BRST quantization and it is frequently used in field theory and quantum mechanics. One of the advantages of the BV formalism is that it provides a well defined quantization for theories that cannot be quantized by the Faddev-Popov path integral approach. In particular, gauge field theories with complicated gauge symmetries (reducible and/or with an open algebra) are quantized in the framework of this formalism.

In the second lecture we will discuss some examples of reducible and/or open gauge symmetries. Then we will introduce notions of antifields, antibracket and BV laplacian, derive their properties and discuss the classic and the quantum master equations and their solutions. Finally, we will present few relevant examples: Yang-Mills theory, toplogical Yang-Mills theory and the antisymmetric tensor field theory.

**Time: ** 24. March 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Voja Radovanovic

**Title: ** Batalin-Vilkovisky formalism and quantization of gauge field theories (part 1)

**Abstract:**

In these series of lectures we will review the Batalin-Vilkovisky (BV) formalism and its applications. This formalism is a generalization of the BRST quantization and it is frequently used in field theory and quantum mechanics. One of the advantages of the BV formalism is that it provides a well defined quantization for theories that cannot be quantized by the Faddev-Popov path integral approach. In particular, gauge field theories with complicated gauge symmetries (reducible and/or with an open algebra) are quantized in the framework of this formalism.

In the first lecture we will describe the standard field theory approach to the BV quantization. To start with, we will introduce notions of antifields, antibracket and BV Laplacian and derive their properties. Then we will discuss the classical and the quantum master equations and their solutions. Finally, we will present a few relevant examples: Yang-Mills theory, toplogical Yang-Mills theory and the antisymmetric tensor field theory.

**Time: ** 10. March 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Pavle Stipsic

**Title: ** Symmetry breaking mechanisms for 3BF action

**Abstract:**

In the process of construction of the action for the physical theory of Standard Model coupled to gravity, in the language of 3-groups, we begin from the topological action and impose simplicity constraints. These constraints explicitly break the initial symmetry of the topological action all the way to the symmetry of the Standard Model. Aside from the explicit symmetry breaking, we demonstrate also the equivalent of BEH mechanism of spontaneous symmetry breaking of electroweak interaction.

**Time: ** 24. February 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to category theory and n-groups (part 6)

**Abstract:**

In the final lecture of the series, we will present a theorem relating a 2-group, a path 2-groupoid, a 2-connection and a principal 2-bundle. This theorem generalizes some concepts of differential geometry, specifically the notion of parallel transport and holonomy, by introducing the so-called surface parallel transport and surface holonomy. Such a generalization represents a new tool to build gauge theories in physics, and has direct applications for the constructions of models of quantum gravity.

The lectures are based on material from papers arXiv:q-alg/9705009 and arXiv:1003.4485.

**Time: ** 10. February 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to category theory and n-groups (part 5)

**Abstract:**

In the fifth lecture, we will introduce the notion of a 2-group, and provide a few examples how to use 2-groups to describe symmetries in physics. In particular, we will study in detail the example of the Poincaré 2-group. We will also comment on some properties of 2-groups and their equivalence to crossed modules.

The lectures are based on material from papers arXiv:q-alg/9705009 and arXiv:1003.4485.

**Time: ** 20. January 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to category theory and n-groups (part 4)

**Abstract:**

In the fourth lecture, we finally perform the first step in the categorical ladder procedure. We will first introduce the notion of a 2-category (both the strict and weak versions), the notion of a 2-group, and the notion of a crossed module. Then we will discuss various properties specific to strict 2-groups, their equivalence to crossed modules, and a couple of examples relevant for physics.

The lectures are based on material from papers arXiv:q-alg/9705009 and arXiv:1003.4485.

**Time: ** 13. January 2023, 11:00h

**Place: ** Faculty of Physics, room 665

**Speaker: ** Marko Vojinovic

**Title: ** Introduction to category theory and n-groups (part 3)

**Abstract:**

In the third lecture, we will discuss three important examples of categories and functors between them. These examples illustrate an important relationship between category theory, Lie groups, and differential geometry --- primarily in the context of the path groupoid category, which will be defined and discussed in detail. The material of this lecture is important as a preparation for the remainder of the course, which will focus on higher categories and generalizations of structures in differential geometry using higher category theory.

The lectures are based on material from papers arXiv:q-alg/9705009 and arXiv:1003.4485.

**Seminars for the year:**
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007

**Follow our seminars online via:** GPF BigBlueButton server