Coadjoint Orbits of the Poincaré Group for Discrete-Spin Particles in Any Dimension

• Main Authors: Ismael Ahlouche Lahlali, Nicolas Boulanger, Andrea Campoleoni
• Format: Article
• Language: English
• Published: MDPI AG 2021-09-01
• Series: Symmetry
• Subjects: coadjoint orbit method; unitary irreducible representations of the Poincaré group
• Online Access: https://www.mdpi.com/2073-8994/13/9/1749
• ISSN: 2073-8994

Considering the Poincaré group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>S</mi><mi>O</mi><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula> in any dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>></mo><mn>3</mn><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula>, we characterise the coadjoint orbits that are associated with massive and massless particles of discrete spin. We also comment on how our analysis extends to the case of continuous spin.