Gau Thors Elmary Parcl Physcs Sro Iraco Fomoloy o Bo cadmc yar -
Gau Ivarac
Gau Ivarac Whr do Laraas or Hamloas com from? How do w kow ha a cra raco should dscrb a acual hyscal sysm? Why s h lcromac raco du o a masslss s- arcl b xchad bw lcrcally chard objcs? Ths qusos hav b aswrd wh h framwork of au hors. I hs hors h srucur of h raco s drmd by h varac rors udr cra rasformaos.. Bo Fomoloa Irazo For
. Bo Fomoloa Irazo For 4 Classcal Elcrodyamcs V E B V V ) ; ( V Gau Trasformaos
Gau Ivarac Quaum Thory Sc obsrvabls dd o w ca dmad ha h srucur of h hory b vara udr h rasformao: whr s a cosa. Global Gau Trasformao., x x, x, x, Ths s calld a local au rasformao.. Bo Fomoloa Irazo For 5
. Bo Fomoloa Irazo For 6 x x m,, x V x m,, V V V x x x,,, Th Schrödr s o vara udr local au rasformaos! For lcrcally chard arcls h rsc of a lcromac fld w modfy h Schrödr quao o b: Ths quao s vara udr h smulaous rasformaos: '
Th local au varac of h hory rqurs h rsc of a fld. Sc h fld wll hav a xaso rms of arcl crao ad dsruco oraors hr mus b a assocad s- arcl (sc h fld s dscrbd by a four vcor). Sc h sam ffc occurs for ay chard arcl h raco of h w arcl (h hoo) s h sam wh ay chard arcl,.. s uvrsal. Th local au varac of h hory for lcrcally chard arcls rqurs h xsc of h hoo ad of h lcromac raco! Ths fac wll allow us o wr h assocad raco Laraa. Wha w do o kow y s udr whch au rasformaos h hory should b vara. lravly: w cao dsush bw h ffcs of a local has cha ad h ffcs of a w vcor fld.. Bo Fomoloa Irazo For 7
. Bo Fomoloa Irazo For 8 Covara rvavs V m ) ( ) ( V ; Covara rvav rasforms as a wav fuco. y quao wr rms of wll auomacally b au-vara. Rad alcaos of sll v a au-vara quao.
Gral Cas Suos w wa h hory o b vara udr a rc au rasformao U. U U U U U U U U U U U U U U. Bo Fomoloa Irazo For 9
No-bla Gau Thors
Sro Isos Hsbr (9): Proo ad uro cosdrd as dffr char subsas of o arcl h Nuclo. w quaum umbr s roducd, sos, cosrvd sro racos, o cosrvd lcromac (ad wak) racos. Th sos assm for h uclo s: I I m m 98.7 MV m 99. 57 MV m I. Bo Fomoloa Irazo For Th sro raco s vara udr roaos sos sac
. Bo Fomoloa Irazo For N L L us wr a raco Laraa o dscrb h mos ral N raco. W wa hs Laraa o b vara udr roaos sos sac. By aaloy wh s w us h Paul marcs o form h vcor N N cras a roo or dsroys a aroo + dsroys a + or cras a -. c. N N L (=,,) Paul marcs
. Bo Fomoloa Irazo For N N : :: : : : L
L us wr a has raformao sos sac (SU()):, j jk k SU() / a a a /. Bo Fomoloa Irazo For 4 a a a o-abla rasformaos (hy do o commu),,, Thr s o horcal rcl, a rs, whch lls us whch ral sacs o xam. Each ral sac whr arcls carry orval quaum umbrs lads o a raco bw arcls, mdad by a w s of au bosos. Prsly SU() color [SU()U()] lcrowak. 8
No bla Local Gau Trasformaos (Ya-Mlls Thors) x x,, s bfor, o fr arcl ca hav a varac udr a o-bla local au rasformao. W df aa a covara drvav: SU() wak sos x, SU() W Th coul s a arbrary facor whch wll drm h raco srhs. Th local au varac rqurs h roduco of h vcor flds S- arcls. marx quao.. Bo Fomoloa Irazo For 5 W
. Bo Fomoloa Irazo For 6 Ths xrsso for coas wo rms: h frs o s h aaloous of for h abla cas (U()) (sld 6) h scod corrsods o h rasformao of a vcor udr roaos. Ths quao s wr wh h udrsad ha wll ac o h doubl rrsao of SU(). I fac w wll u lf-hadd frmos SU() doubls (wak sos). Th hory s vara udr rasformaos hs wak sos sac. To drm how h rasform udr a au rasformao w sar from h rqurm: W ) ( x W W W k j jk W W W
Form of for a dffr rrsao of SU(). If s a sa of wak sos wh + comos, l T b h marx oraor rrsao of SU() ha bass. Th: T W For s ½ : T Form of for varac udr SU(). L F b h rou raors ( ( -)-dmsoal vcor). SU() color SU() wak sos F, Fj cjk Fk F G. Bo Fomoloa Irazo For 7
Y B W a G a =,, a =,..,8,, arbrary ral umbrs (coul srhs). Oc hy ar fxd for ay rrsao hy ar kow for all rrsaos. For xaml, masur wh muo dcay fxs for quark racos. Y hyrchar U() raor of U() (umbr) For h bla U() symmry w hav wr h fld ha mus b roducd as B rahr ha sc w do o kow a ror ha h U() varac corrsods rcsly o lcromasm. s a four-vcor, lk all ohr rms. Ths xrsso for uaras au varac h hr sacs U(), SU(), SU() ad mls h xsc of h s- au bosos corrsod o h flds B (), W () ad G (8). ll hs bosos hav b obsrvd xrmally.. Bo Fomoloa Irazo For 8