The QMat Student Seminars are courses organized by QMat students at the Faculty of Physics and Engineering, in partnership with the Tutoring Division of the ARIANE, the GeQS group and the Strasbourg Students Physical Letters.

They are intended to foster a better understanding of theoretical aspects of quantum sciences among physics students. When not stated otherwise, all seminars are held at the Institut de Physique in Strasbourg, and the proceedings are published in the 2SPL.

For more information regarding the QMat Student Seminars, please contact Simon BEAUDOIN.

2025 Symposium on Quantum Sciences

3 June 2025

Salle 103, Institut de Physique

10h15: Welcome of the students

Loris Delafosse

10h30: Wigner Quantum Mechanics: A phase-space formalism

Maxence Pandini

Multiple formalisms of quantum mechanics have been developed during the last century to overcome difficulties as in many-body systems. One of the most appealing formalism for physicists would be one mapping quantum mechanics to the usual phase-space of classical mechanics, this is the aim of the formalism introduced by Eugene Wigner in the 1930s. He introduced a quasi-probability distribution in phase-space known as the Wigner function that is exactly equivalent to the density matrix and describes entirely quantum mechanics. We will introduce this formalism and apply it to simple models. Current use of this formalism in modern physics will be also presented (quantum tomography, many-body dynamics).

Slides

13h30: Quantization and Path Integrals

Loris Delafosse

The path integral, developed by Feynman in the 1940s, is one of the best-known and most widely used formulations of quantum mechanics. It owes its success to the elegant physical interpretation it provides for quantization, and to the fact that it describes both non-relativistic quantum mechanics and quantum field theory. However, despite this great success, path integrals usually happen to be ill defined as mathematical objects. This seminar aims at presenting the challenge of quantization, the way it is tackled by path integration, and the issues faced by this formalism.

Slides

15h15: The subtle art of counting holes

Loris Delafosse

The notion of singularity is omnipresent in physics. Whether we're interested in crystalline impurities, magnetic monopoles or cosmic strings, the study of "holes" is of paramount importance. But what is a hole? How do you find one? We want to give here some physical intuition behind the concepts of algebraic topology.

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2024-2025 Second semester

20th March (10h-12h): Symmetries and representations in high-energy physics

Target audience: L3-M2

Room 130 (SAP Master classroom), Building 26, IPHC, Cronenbourg Campus

The theory of groups and their representations leads to numerous applications, notably in high-energy physics. Lie groups and their associated Lie algebras allow us to represent continuous symmetries. Representations of the Poincaré group are used to classify particles according to their spin, defining concepts such as fermions and bosons, but also associating different types of tensors and spinors to different particles. The "calculus of representations" is also the basis of the quark model, used to predict the existence of hadrons and to compute their quantum numbers. In the end, the seminar aims to answer the question "What is a particle?"

27th March (10h-12h): Elements of classical field theory II (Gauge theories)

Target audience: M1-M2

Room 103

After the discussion of Noether’s theorem in the first seminar (15/10/2024), we introduce gauge theories as a very general procedure allowing us to extend the perimeter of some field theories. Several examples are discussed, and gauge theories are shown to be the current best mathematical description of fundamental interactions. The relation of classical field theory with relativistic quantum mechanics and general relativity is discussed, although no previous knowledge of these domains is assumed. Attendance at the first seminar is not required to understand the notions discussed here, since general results on field theories and Noether's theorem will be recalled at the beginning (it helps, though).

1st April (9h-10h30): Structure formation in cosmology

Target audience: L3-M2

Room 130 (SAP Master classroom), Building 26, IPHC, Cronenbourg Campus

The matter of our universe is concentrated into galaxies and galaxy clusters. At even larger scales, those galaxy clusters are distributed on a complex network of filaments, walls and voids called the cosmic web. How could all these structures emerge from a nearly uniform density ? The aim of this seminar is to provide some answers to this question. We will first present a classical model based on newtonian gravity, and then give elements of the more complete theory of gauge invariant cosmological perturbations. In the final part of the seminar, we will discuss some observational tensions related to the large scale structure of the universe, and that may motivate new physics beyond the standard model of cosmology.

2024-2025 First Semester

27th September (16h-17h30): Tensor calculus for physicists

Target audience: L3-M1

Fresnel Amphitheater

Tensors are quite general mathematical objects, used in almost all areas of physics, from continuum mechanics to general relativity and quantum physics. Beginning with a reminder of some useful concepts of linear algebra, this seminar introduces the notion of tensor, discusses its relation with metrics, covariance and contravariance in Euclidean and Minkowski spaces, and eventually presents tensor products in the context of quantum mechanics.

15th October (14h-16h): Elements of classical field theory I (Formalism and symmetries)

Target audience: M1-M2

Fresnel Amphitheater

Classical field theory is the branch of mathematical physics dealing with non-quantized fields as representations of physical objects. The first historical motivation for using fields was of course Maxwell’s theory of electromagnetism,which revealed how powerful this kind of formalism might be. This seminar first introduces the mathematical notion of field, and how it can be connected to physics through Lagrangians. The consequences of field symmetries are investigated, namely Noether’s theorem on conserved currents and charges.

2nd December (10h-12h): Construction of the quantum state space

Target audience: L3-M2

Room 103

The first postulate of Quantum Mechanics states that a system’s state is completely characterized by some vector, which is an element of an abstract space called the state space. The features of this space may vary considerably from one system to another, and even for simple systems, the physical interpretation of the state vectors is not always straightforward. This seminar aims at elaborating a rigorous, step-by-step, construction of the state space associated to real space variables, first for systems with 1 degree of freedom (one particle evolving in one dimension), and then for 3D and many-body systems. Generalized kets (non-normalizable states) are tackled from the mathematical and physical point of views. The state space associated to spin variables is introduced in a second part, allowing us to discuss the notions of quantum entanglement and indistinguishability.

2024 GeQS Seminar on Quantum Sciences

4 June 2024

Salle 103, Institut de Physique

10h30: Welcome and presentation

10h40: Semi-classical approaches in quantum mechanics

Loris Delafosse

Before the establishment of quantum mechanics, physicists attempted to modify the paradigm of classical mechanics to include the quantization phenomena discovered by experimentalists. This “old quantum theory” led to models still in use today that simplify the mathematical treatment of quantum effects.
 
Slides

14h00: Spinors, geometry and space-time

Loris Delafosse

Giving a correct geometric interpretation to the mathematical concepts of physics can serve as a guide for developing and understanding physical theories, particularly in quantum mechanics (notoriously difficult to understand) and general relativity (where geometry plays a central role). These considerations led to the development of twistor theory, which generates spacetime from spinors representing light rays.

Slides

16h30: Introduction to the Higgs mechanism

Simon Beaudoin

The Standard Model of particle physics predicts massless gauge bosons, which experiment refutes for the W and Z bosons. Brout, Englert, and Higgs have devised a mechanism that is currently the best resolution of this inconsistency. The (recent!) detection of the Higgs boson was a major step forward in our understanding of the concept of mass, but introduces new unresolved questions in the Standard Model.

Slides