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SUMMARY:Representations and subgroups of SL(4)\, with applications to phys
 ics - Robert Wilson (Queen Mary UL)
DTSTART:20200212T163000Z
DTEND:20200212T173000Z
UID:TALK138289@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:The real 15-dimensional Lie group SL(4\,R) contains pairwise d
 isjoint\nsubgroups GL(1\,R)\, SU(2)\, SL(3\,R) and SL(2\,C). Apart from a 
 technical\ndifference in the real form\, which can be adjusted by suitable
 \nmultiplications\nby i\, these are the same as the groups U(1)\, SU(2)\, 
 SU(3) and SL(2\,C) that\nare used in the standard model of particle physic
 s. By removing the naive\nassumption that disjoint groups necessarily comm
 ute\, it is possible to\nreproduce the entire group-theoretical foundation
  of particle physics\ninside SL(4\,R).\n\nThe failure of commutativity pro
 vides a mechanism for explaining (some of)\nthe unexplained parameters of 
 the standard model. The representation\ntheory of SL(4\,R) provides a clas
 sification of particles that is coarser\nthan\nthe standard model\, and th
 ereby permits a more flexible view of the\nrelationships between (for exam
 ple) electron\, proton and neutron.\n\nPutting all this together with the 
 local coordinate transformation group\nof general relativity\, which is al
 so isomorphic to SL(4\,R)\, suggests ways in\nwhich the two theories may n
 ot be as incompatible as has been thought\nfor the past 80 years or so.\n
LOCATION:MR12
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