Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Group Repetition Theory: Character Representations

In course

PHYS-314: Quantum physics II

The aim of this course is to familiarize the student with the concepts, methods and consequences of quantum physics. ...

Description

This lecture covers the theory of group repetition, focusing on character representations and their properties, such as irreducibility and equivalence. It explains how characters are associated values and how they relate to conjugation classes and abelian groups. The lecture also discusses the choice of base and the concept of mutual orthogonal vectors in the context of group representations.

Instructors (3)

Vincenzo Savona

Vincenzo Savona studied physics in Pisa at the Scuola Normale Superiore and the University of Pisa, prior to completing his PhD at the EPFL's Institute of Theoretical Physics. Subsequently he did post-doctoral work, first at the EPFL and then in the physics department of the Humboldt University of Berlin. In 2002, he returned to the EPFL to create his own research group, receiving a "professeur boursier" fellowship from the Swiss National Science Foundation. In 2006, he was appointed tenure-track assistant professor at the EPFL and joined the NCCR for Quantum Photonics. In 2010 he was appointed associate professor. Currently he directs the Laboratory of Theoretical Physics of Nanosystems.

Florent Gérard Krzakala

Zoë Holmes

Official source

Ontological neighbourhood

Mathematics

Algebra: Representation theory, Abstract algebra

Related concepts (32)

Abelian group

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.

Character theory

In mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix realization of representations themselves.

Mathematical formulation of quantum mechanics

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.

Particle physics

Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, although ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos.

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Related lectures (37)

Lemma of Schur: Group Repetition Theory

Explores irreducible and reducible representations in group repetition theory and the lemma of Schur in quantum physics.

Irreducible Representations of Rotations Group

Explores irreducible representations of the rotations group and their mathematical properties.

Group Representations Theory Application Overview

Covers the application of group representations theory in quantum physics.

Group Theory: Reducible and Irreducible Representations

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Symmetry and Group Theory