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**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

**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