By Howard Georgi

Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) idea. This broadly revised and up to date variation of his vintage textual content makes the speculation of Lie teams available to graduate scholars, whereas delivering a viewpoint at the approach during which wisdom of such teams delivers an perception into the advance of unified theories of sturdy, susceptible, and electromagnetic interactions.

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**Lie algebras in particle physics**

Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) conception. This broadly revised and up-to-date version of his vintage textual content makes the speculation of Lie teams available to graduate scholars, whereas supplying a viewpoint at the means during which wisdom of such teams delivers an perception into the advance of unified theories of sturdy, susceptible, and electromagnetic interactions.

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The normalized eigenst,at,e of moment,iim operator fj is givon by Thc boundary condition that, up(x)is periodic in the range L gives p = (F) n,. e. the number of states within the interval E and E by d n = p ( E ) d E . In three dimensions, we have (&)"$ p(E)= dn = dE /d3p = (&)3p 2 + d E is given d~ dP / d o . 66) ' ' and only (n- 1)momenta are independent. With the normalization L = 27r, we can write from Eq. (65) n= / 63 [pi - ( p i + p ; + - . + p;)] d3p', d3p', . 67) Thus we can write + + + p:,)] [Pi - ( p i p ; x d3p', d3p; * * * d3p',.

7 ) and k, = 4 / 3 ( q q ) , 2/3(qqq)) is the single gluon exchange potential while V c ( r )is the confining potential (independent of the quark flavor), has been used in hadron spectroscopy with quite good success. 25 (GeV)2,obtained from the quarkonium spectroscopy. To sum up the most striking physical properties of QCD are asymptotic freedom and confinement, of quarks and gluons. The quark hypothesis, the electroweak theory and QCD form the basis for the "Standard Model" of elementary particles to which most of the book is devoted while Chap.

125. That the effective coupling constant, decreases at, short, distances is called the asymptotic freedom property of QCD. (m) The binding energy provided by one gluon exchange potential of the form mentioned above cannot be siifficient, to confine the quarks in a hadron since a s one can ionize an atom to knock out an electron, similarly a quark coiild be separated from a hadron if sufficient energy is supplied. e. impossibility of separating a quark from a hadron. The hope here is that the self interaction of color carrying gliions may give rise to long distance behavior of the potential in QCD completely different, from that in QED, where the electrically neutral phot,on has no self interaction.