Concept

Projective representation

Related lectures (19)

Wigner's Theorem and Temporal Inversion Operator

Explores Wigner's Theorem and temporal inversion operator in quantum mechanics.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Quantum Mechanics Rotations

Delves into quantum mechanical rotations, discussing SU(2), SO(3), group representations, and topological properties.

Complex Gaussian Signals

Delves into complex Gaussian signals and their properties in communication systems.

Quantum Physics I

Covers the fundamental concepts of quantum physics and diagonalization of operators.

Information Representation: conventions and basics

Covers information representation, including universal representation, symbol and number representation, and the significance of the binary system.

Wigner Theorem & Time Inversion

Explores the Wigner theorem and time inversion in group theory.

Geometric Projections: Understanding Monge's Method

Covers geometric projections using Monge's method, focusing on representing three-dimensional points through their orthogonal projections.

Poincaré Irreps 2: Little Group and Induced Representation

Explores Poincaré irreducible representations, Little Group, and induced representation in the context of momentum eigenstates.

Spinorial Representations of Lorentz Group

Explores spinorial representations of the Lorentz group and the transformation of fields under Lorentz, emphasizing a constructive approach towards spinors.

Group representations constructions

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Vector Representation of Signals

Explores the vector representation of signals, orthogonal functions, and Fourier series.

Circle Orthogonal & Poincaré Disk

Covers circle orthogonal and Poincaré disk concepts in geometry.

Quantum Field Theory: Heisenberg Representation and Noether Charges

Explores the Heisenberg representation of a free massive real scalar field and the time independence of Noether charges.

Balanced Realization: SISO Case

Covers the concept of balanced realization in the SISO case, focusing on system observability and controllability.

Lie Algebra: Bilinearity and Jacobi Identity

Covers Lie algebra, bilinearity, Jacobi identity, and Ado's theorem.

Generators of Groups

Explains the concept of generators of groups and their mathematical properties.

Group Theory & Quantum Mechanics

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

Quantum Physics I

Explores quantum state evolution, unitary operators, Heisenberg representation, spin precession, and observable averages.