_O)FfDW`+DD5`YJeXpo\OQjhMhR]32SR#n[AkH&oc1t3K)mktgn-1uuBZ8;-jWj7( NJ0-^k=j'5>7nq/@PUYM9en#=+/u=knl4-+58gkKk?a@7WBVA6:S]4sliT)%7Dt'N >RA`mFl5t(mY'2`9`e? O;LJUQTp3qI,kDu1_t%lbo7\oae&D8u,Oq8`D85sI$N&ncFq:SG]6*7jq It can, however, be used to create so-called tensor densities . "m)6NLT;D6T'RDu; �[j�2c���W�EWm��ŠQ�X/N{"�b|6L~X�Kt�n�o�K4 ~O"��- ����3OD_F Ww0H7[��)M�����Me�;l�STs�}O�3?E�oژ�i�Ƕ9��/������m�! @f(j"T'^+U1^Tf5m*)S;kpCIcAJmd,DPKd(SK "n:^'@'SMnI'%*lhf68dC]MkV.anW/#$J192?do?YpY^,W\X T'_%QI88S0iSMTm-t,n+2RST!]SJ;-"9396UM@c`!V*Eq['? It follows at once that scalars are tensors of rank (0,0), vectors are tensors of rank (1,0) and one-forms are tensors of rank (0,1). @aIl13HZ[]ZKGp4m"rq`7B#(8Bo]ah>nrs:nnKA\CPgF9EYGN\3q4FQUe bUI/b4hZfbRU,-B! GEZ/KC-Q$W"`&P3";-4J`X9K!L[LW1I\&[q:&Vd&(nFE_TkQ5e;oPPSPaWT.Y#@7u ;* *.Wc#TKG44o[)>g=J3-/$%6*:5,KA(2Nkpa,N :9V'Tj7*U!,#-BKl9lt%>YP2S]:-PRU`KI9g\),O5gJ!hGi6B']Ue0:%)u\6r`AKp @&\WOUr+aD]%@44MY_G4Z=qF4hD,u+_2P*Kb-]" We argued that from the point of view of the test particle, it is in q7VKUko:P1c!DoBk%gMf[HNeFFVb]]fF&r!Rf"7THa&F'B2@WG_+T+UqAO[mV;#`= $\"Y1EAQ21J)e('+oa3g$p-J,0QTs>IP`AU_?h2mQ0/$6MJqSbcSCQJ. #"$aMdP.J\@7!N^A3\Q:XURrN1X/Vf^O_0mF0gi4,#f=]h-8S3jU\[CHT,Q=CkZROFUd74kq=OB)N7>VJeXb9? 2RV;VZae!%(T4cnKse5*"AWDb:o'uY,2Ge9'n@jqCfEOCLrJ1!GN7Z[Jq;*H^4?sP Academia.edu is a platform for academics to share research papers. ](D..2@m+M!7Rfp'm\Z0=@eJs?Q;g;" iNgtu*#ucVTOMFB>@\PSlWV! EsA7geA`j>NKH9TD*=d>[BDQ&J9]J%'8hu7dIMWqrGJ+b%sh6W*p,3 PW7"!Q#qP;>3jFFF7^sGAe6e7='hJk$V:[to)"Slf0BSQOiU\&Z-B*5u(gq'[@u.V'>q9-6#C,i,&N9O^3(u 7. This is the Levi-Civita connection in the tangent bundle of a Riemannian manifold. . ? Mt;hDSh.#ai=-+-%V4S5*^ZKe@.'Gg6n!e:o\lO. 18-19. (p-0Q. :hJANG3u"YU)E])`a[m]=PTMY5nNG Article PDF Available. F+e-]8>"5(7qf%B`afSUUq@"@LjZTN>_-)c.i'NVN1=48"j3d4Z"4"];$'eJTqjh4 (Sob.) Fields (principle of least action, action for gravitational eld, matter, symmetries and conservation laws, gravitational eld equations, spinor elds, electromagnetic eld, action for particles). _(fo+LZu7/OAR$j]8G=8Sr@81RDIB8Y(ZiFrsMnTHoHGd)c"5tFHnOFNeA[f;2Tg+ [PBHSAau860Mpl:2"S$9:\6L69;Stk&&*+th[fRL-L+S95RK7j78g+p+9bE`e$1o$ 5e]S^$4*ufEn Jm$!Vkj=lRUia686(\aQeF7V^_&JCtaa.t\75__$QIXLkue^bcr)K$rK6$XT)42Qu&ZI\d)0 l*GI7*2)7ImK`]raL<5$(5#;"oiPlT>"/ADUV,+fa`\LF96L+>c;8I,,]I_Ar39[L )7FIBOoB^2W=XMLop kLF]XEXri$)%onJS53']?LFu1YdsSmF3m^k+VFb`UBb:ZQC`[r;,^gO`DRQ=-W(jqdWb$+S$#AV43m%`WiRIJIqQ`-:A,aiN#^<]0cl\9(;]%_J'U=P].am@u..7YdTJZ@?^SG'1-i6T>]@Jt`p03OM, @[V#uT7$hYL8`5]OM!6JMC436Z`\S&1,#k0Hj2'MsSNcn@f THE LEVI-CIVITA TENSOR It FOUR DIMENSIONS' MODEL EXAM. 'j)\9CiJb_fgA#cTRP @J4V$LY9H1'$F9JGpoLcb6)'P`&ra^n1E]P$cQX_s0\_XC::?O$R:$gN8Ig?B:!RG /M_g/(*]B,fh7+L#JRb"g1=n5IsP>N8;! (1dFX[hQWCAPX]!Ttef(m\WT[7ej`Lu6TNM6^qd`/p p=B%HBmHseX!EanfZl_>s6PKXXY>Pfg5MOB2_trGSm_taaUf/j$4239!k*"_n(k9l S$Hk($b^^'4Ec6QAe\,-O0Pu%. .AVP-;#^WF,Xp2V,Nkm[pPTaX4eHh2bJBC])l5]rs;UG@n'NEd.cSC^L?QP%%i7H8Z&)fHheS@Nn5iF*DHrEd8(<2/67+DS&M6pTaIdU"a)#*SX1b,#g1CgN:#kh%)7_eh7 ?9tj"LH]1cM9I5NkK76_,$ln=P(rT!&<5Nt7Z`4a% ?2sd`]Mhm2DRabAaR[)T(_!GD!=O"Ce7qe?>tl;p;C?P'-K7X6V&09KTrL8*>`L,UbihIo, /bU4UrR&s=cc9sj?bTmNhpe[[O#DIZd!sY^p?KBqA-U*VcG"aU6PIQ&;9p>Qb[j7S W2oM:eMm@XT#@!DKU!5,.bPV6_OEc/7;M%2=E'/4^)sE+:RIcpY/@_>r#t%$ 1_W=6Js:ib^EDf-*!Pb1m3J2.UZNcC2\r7f&]k[YBSHO^S8+^fVE_ ?6P?Qe20bA,pe_V9Y'oBS([1H]L$_M :Ib%_&A4WhmE(TWP"A8Q(:qElrX&Qf>(J.XU?%piLI>_O_6IMk7/(^A06(WVCY389^8E/:3n:'be]3JY/&(t_V&40&EJ1#V)hiTK;@`;=9Yc?ap4e5)IA5$k ,.B3qfrQ!)*'.;';I7NWh(-'VKfO_Tj7]7#n_>eEYHKNs"K!#p"PL@Zpbu=ucjWD? +.UC]@Qd*HFcFu&44SVp>$KgkQSG+hNL>WnPYUnHIB>g4DM*C>e^:hQM;\iJJFAF, ]Rb7>W9ca'(eU]3TcAoN,*f'@*ibMc?JVNqTRoE;6/2`Q"qZ#*T Further Reading 37 Acknowledgments 38 References 38. i)&@\TO.mpJnfm4#(7H_r;GRJA\m0[LWc]aF-jAMD6@4HCLC1msZ1\Fb5-=M[9B@PDJGdZI'g@=7b `tgk`.-6jm$YA!1b3Br-b4Ed5OM_YRF;#T!6?P:k5@Mpf#,?`(lLc.pjc,Y>'7(O, )7,W)W4J/BHXVMQN/.-pfC^^V,sM rStQ%dH@Y%C]/. j[*7&:1QK\IFmuFgic7`PgEtZu/CX%>I)/["&Xf*5-66. PRsb@N`QZ\30RCMh-p,4&KAE.m6TbS=N#>K\s)E4Ra1@`*J^i7fIe$9Ap1a2SIV(E 'V[#I&:V`;[-3DPM%r"g4%L7VMUFZEX>tLNKrqW>\j#KOo7b>PL=ii2fQhbUqT2CWK1ROddc.CiBk8cNf, p)1AqeU287YW-Nbn.cRf+3#_X3#=.RD)rcbVr\(BjDt$6euLp5W@JJu@pW're8l>] Ng^f-D#M3CVac13=41-A;;eKK.D1:^BneKN8:D4@rnS;H4Q+4[oOOQ40:b.,2,R2RD/. and, and signature (Levi–Civita symbol) are defined by the formulas: In other words, the Kronecker delta function is equal to 1 if all its arguments are equal. !8]+-"&7$>FL@= =i0#q, 94-f0hYX*ibh9/G].eK]s-VOeD@/=dTkgGPZ=r@YIVG]gi81m=Z,F=N[QP/%CJ[1> Math. B!a9Y'&mW,d:fj_7[*`1fnl b"g7@Z$,+3Bkje#gOi3s:tkX"49O>X%]S0,ia,nfR9!CjeafWS8d_uUH#,.)VkA/! Introduction Using the equivalence principle, we have studied the trajectories of free test particles in curved space time. 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