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

Lecture

Poincaré Group and Lorentz Subgroup

In course

PHYS-431: Quantum field theory I

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions. ...

Description

This lecture covers the Poincaré group, Lorentz subgroup, and their properties in the context of theoretical physics, focusing on the mathematical aspects of spacetime transformations and symmetries. The instructor discusses the Lorentz subgroup as a special case of the Poincaré group, emphasizing its significance in relativistic physics and quantum field theory.

Instructors (2)

Riccardo Rattazzi

Riccardo Rattazzi was born in Novara (Italy) in 1964. He studied physics at the University of Pisa, where he received the Laurea cum laude in 1987, and at the Scuola Normale Superiore where he received the Diploma in Scienze and carried out graduate research in theoretical physics. After having been a post-doctoral research associate at the Lawrence Berkeley Laboratory, at Rutgers University and at CERN, in 1998 Riccardo obtained a permanent research position at the Istituto Nazionale di Fisica Nucleare in Pisa. From 2001 to 2006 he was a staff member at the Theory Division of CERN. In 2006 he was appointed professor of physics at EPFL.

Francesco Riva

Official source

Ontological neighbourhood

Physics

Relativity: Special relativity

Related concepts (32)

Poincaré group

The Poincaré group, named after Henri Poincaré (1906), was first defined by Hermann Minkowski (1908) as the group of Minkowski spacetime isometries. It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics. A Minkowski spacetime isometry has the property that the interval between events is left invariant. For example, if everything were postponed by two hours, including the two events and the path you took to go from one to the other, then the time interval between the events recorded by a stop-watch you carried with you would be the same.

Lorentz transformation

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.

History of Lorentz transformations

The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval and the Minkowski inner product . In mathematics, transformations equivalent to what was later known as Lorentz transformations in various dimensions were discussed in the 19th century in relation to the theory of quadratic forms, hyperbolic geometry, Möbius geometry, and sphere geometry, which is connected to the fact that the group of motions in hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group.

Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe).

Lorentz group

In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry: The kinematical laws of special relativity Maxwell's field equations in the theory of electromagnetism The Dirac equation in the theory of the electron The Standard Model of particle physics The Lorentz group expresses the fundamental symmetry of space and time of all known fundamental laws of nature.

Related lectures (30)

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 Field Theory: Poincaré Group

Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.

Lorentz-Minkowski Spacetime

Covers Lorentz-Minkowski spacetime, speed of light interpretation, isometries, and special relativity principles.

Quantum Field Theory: Lecture 9

Covers relativistically normalized states, Lorentz invariance, and scalar field representations in quantum field theory.

Lie Algebra Representation