rpp2010-rev-young-diagrams

rpp2010-rev-young-diagrams - 38. SU(n) multiplets and Young...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
38. SU(n) multiplets and Young diagrams 1 38. SU( n ) MULTIPLETS AND YOUNG DIAGRAMS Written by C.G. Wohl (LBNL). This note tells (1) how SU( n ) particle multiplets are identifed or labeled, (2) how to fnd the number oF particles in a multiplet From its label, (3) how to draw the Young diagram For a multiplet, and (4) how to use Young diagrams to determine the overall multiplet structure oF a composite system, such as a 3-quark or a meson-baryon system. In much oF the literature, the word “representation” is used where we use “multiplet,” and “tableau” is used where we use “diagram.” 38.1. Multiplet labels An SU( n ) multiplet is uniquely identifed by a string oF ( n 1) nonnegative integers: ( α,β,γ,. .. ). Any such set oF integers specifes a multiplet. ±or an SU(2) multiplet such as an isospin multiplet, the single integer α is the number oF steps From one end oF the multiplet to the other ( i.e. , it is one Fewer than the number oF particles in the multiplet). In SU(3), the two integers α and β are the numbers oF steps across the top and bottom levels oF the multiplet diagram. Thus the labels For the SU(3) octet and decuplet 1 1 0 3 are (1,1) and (3,0). ±or larger n , the interpretation oF the integers in terms oF the geometry oF the multiplets, which exist in an ( n 1)-dimensional space, is not so readily apparent.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

rpp2010-rev-young-diagrams - 38. SU(n) multiplets and Young...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online