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!"#$%&'#()*+,&)-.+/$012$ - PowerPoint PPT Presentation

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  1. !"#$%&'#()*+,&)-.+/$012$ 34)&&5$4-$64(/#$54/+#-.)$ 7#6,$8(*5$"*6*/(4'"9 :4+;:4+$<&=$>*"4++4$?(,5#+/#(=$@./4#6$A-(9,*5=$>A$;$ -*$4''#4($%**+BBB

  2. !"#$%&#$"' ! ()*+'",-./0/1-2*+3"',-3#$%$#4/"5/6(7/%&3--8/ $'/9#+"':/8&:'*#$3/;*<,/=&+>$%?@AABC@ADDE? ! F)*/)"<":+&2)$3/3"-'#*+2&+#CCC ! G$',/<&##$3*/9"<-#$"'9/$'/&/)"<":+&2)$3/3"'#*H#/ I)$3)/3&'/.*/-9*,/5"+/3"',*'9*,/8&##*+/&',/ )*&%4/$"'/&22<$3&#$"'9

  3. !"#$%&'()%"'*'+,#-".%#**'/%0)%$'%)$0&.1 ! !(%2#3%*''4%#$%)$,'3+%2'0-*53+%-"(3'6(3#% 53%#%7)(658%2'3$,'**(&%/#.9 ! !(%"#:(%#%/(#4*.%2'0-*(&%&()2,5-$5'3 ! ;0$%/(%&'3<$%#*/#.)%43'/%/"#$%$"(% 03&(,*.53+%=(*&%$"(',.%5)%7$'->&'/3%:(,)0)% ?'$$'6>0-8 ! @'6($56()%$"5)%&'()3<$%6#$$(,%

  4. !"#$%&'(")*+"#,-.'/%"0%)$+$-*% 1$'+),2*,"-'%"0%+"-1$-'$1%#3**$)%2(4',+' ! 5)3-'63*,"-36%,-73),3-+$%%%,-8-,*$%+"-19+*,7,*4%3*%:$)"% #"#$-*9#% ;4$*%,'%-"*%3%'92$)+"-19+*")<%+0%=>?=@A <% ! B$%+3--"*%,#2"'$%*($%+"#26$C%63**,+$%'*)9+*9)$'%"0% )$36%#3*$),36'% ;*(9'%D$%#34%E$%#,'',-.%+)9+,36%2($-"#$-3A < ! B$%+3-%,#2"'$%',#26$%2$),"1,+%E"9-13)4%+"-1,*,"-'% ;F")"D,*:G%!3-*"'G%5"-.%/HI%J%7$)4%,-*$)$'*,-.%+"-19+*,7,*4%+0<%+92)3*$%'92$)+"-19+*")'A & ' " % & + )* � Σ � ,- � Σ � HIKL<KMHN % $ # $ ! ! ! " #! #" $! $" ! " #! #" $! $" Ω � ( Ω � (

  5. !"#$$$%&'()*'+,'-&##&.'#/)*'#/)# ! 0)#/&.'#/)*'-.&)12*3'#/&'4566&#.2&4'-5'/)*+'%&'()*' )74,'8*+'4"(/'4,7"#2,*4'+5*)62()775 ! 9/)#'(,*+2#2,*4'%277'()"4&'4"(/'4566&#.5'-.&)12*3:' ;</&.*=>26,*4'#&.64?'6)3*&#2('8&7+?'8*2#&'+&*42#5$$$@ ! >&&'%,.1',*'4A)#2)775'6,+"7)#&+'A/)4&4'2*'B+>C<DE' ;F,3".2'&#')7$?'G)"*#7&##'&#')7@

  6. !"#$%&'#()*+,&)-.+/$01234$56)&&7 ! 2"#(+*,&89$:;<;$=3>?>$ =3@&A6+*5.)9$>)".+,B#(9$?#/#B.69$ >)"#(#(C $7*,#BD#E-#+,#,$FGH$7*,#BC ! !"#$76%%$*I$-"#$("*$7#%*+$,#)(#6%#%$6%$J*&$.+)(#6%#$ -"#$76/+#-.)$K#B,$%-(#+/-"$6)(*%%$-"#$56)&&7 − 1 4 F 2 − 1 2 | D ρ | 2 + m 2 ρ ρ 2 L DSGS ∼ + ρ 0 contributions + nonminimal coupling ∼ F µ ν ρ µ ν

  7. !"#$%&'#()*+,&)-.+/$01234$56)&&7 8 9-$%*7#$)(.-.)6:$76/+#-.)$;#:,$%-(#+/-"$-"#$56)&&7$ ,#%-6<.:.%#%$6+,$)*+,#+%#% 8 !"#$("*$7#%*+$.%$)"6(/#,$6+,$-"&%$-"#$=>?@$.%$ %'*+-6+#*&%:A$<(*B#+ 8 C(*B#+$/6&/#,$=>?@$$$$%&'#()*+,&)-.5.-A 8 !"#$/(*&+,%-6-#$-&(+%$*&-$-*$<#$6+$9<(.B*%*5$:6--.)#

  8. !"#$%&$'&($()*+$),-,'."/)*0"--12 3 455,#6$7.85&#'&.6$9&.#&.6$:(.18,5$ !!"#$%&&! ; 3 <)&$*#+("=*-*(1$(,$"$+>/&.0,#8>0(*#'$+("(&$%"+$+),%#$),-,'."/)*0"--1 � 1 1 � � ! <)&$5,8&-; d 5 x √− g S = ( R − 2 Λ ) − + S bdy g 2 F a µ ν F aµ ν 2 κ 2 4ˆ 5 ! 48:?:0)%".@+0)*-8$*#$AB&$8*5&#+*,#+ ! :CDEF$G"#'HI*--+$A&-8$D/.,=&$"//.,J*5"(*,#F ! CDKF$0,5/,#&#($,L$+>='.,>/$(>.#&8$,#$D5"'#&(*0$A&-8F ! M#+("=*-*(1$,L$,#&$,L$()&$B&0(,.$5,8&+$"($"$0.*(*0"-$B"->&$,L$ ()&$5"'#&(*0$A&-8 <)*+$%*--$=.&"N$()&$CDKF$+155&(.1

  9. !"#$%&$'&($()*+$),-,'."/)*0"--12 Im w Re w � ! � " " ! � %$& ;+$()&$:"'#&(*0$ � "$% <&-=$*#0.&"+&+ � "$& � !$% � !$& � #$% >?"+*#,.:"-$:,=&+ 3345678839$%*()$/&.:*++*,#

  10. !"#$%&'('$)*$+'(%,)-./$,-$)-*%,0).)%/#$01%$ 2&,%$)*$%&'$3("1-4$*%,%'5 6 7,8)-3$9"1-4$%&,%$%&'$3("1-4$*%,%'$2)%&$-"$+"-4'-*,%'$ )*$1-*%,0.'#$2&,%$)*$%&'$%(1'$3("1-4$*%,%'5 6 :,-$2'$*&"2$%&,%$%&'$;0()<"*"8$.,%%)+'$&,*$,$."2'($ '-'(3/5 6 =&'('$,('$>,-/$4)99'('-%$.,%%)+'$+"-?31(,%)"-*@ 6 A'$+,-$*%14/$%&'$*)>B.'*%$9'2$,-4$?-4$%&'$."2'*%$ '-'(3/$"9$%&)*$*10*'%$C+9D$E)-F01(3GH,-4,1I 6 +9D$JKLJDMMNO#$P,'4,$'%$,.$G$QRL$4)>'-*)"-,.$SPR*+,.,(

  11. � � !"#$%#&'(')"#*+#,(*-."'(/(012-2'(,%+*'*3"' 4#-*-4(0'.(0+"'%$'*3"'&(5/"*-4'6"07 s E x,y = A 1 x,y + i A 2 x,y . orders. Our strategy is thus to solve for the fields in the following sequence al equations into three + O ( ε 5 ) ε 3 e x,y E x,y = ε E x,y + A 3 ε 2 a 3 + O ( ε 4 ) = + xB c y y + O ( ε 4 ) A 3 ε 2 a 3 = x x ! 8'4%+)0"7'"9+(*-%/2'$%#'*3"':'(7;%-/*' 4%&)%/"/*2'%$'<=>?@'-/'*3"'AB1'(/7'#(7-(0' 7-#"4*-%/2C

  12. � � !"#$%#&'(')"#*+#,(*-."'(/(012-2'(,%+*'*3"' 4#-*-4(0'.(0+"'%$'*3"'&(5/"*-4'6"07 s E x,y = A 1 x,y + i A 2 x,y . orders. Our strategy is thus to solve for the fields in the following sequence al equations into three + O ( ε 5 ) ε 3 e x,y E x,y = ε E x,y + A 3 ε 2 a 3 + O ( ε 4 ) = + xB c y y + O ( ε 4 ) A 3 ε 2 a 3 = x x ! 8'4%+)0"7'"9+(*-%/2'$%#'*3"':'(7;%-/*' 4%&)%/"/*2'%$'<=>?@'-/'*3"'AB1'(/7'#(7-(0' 7-#"4*-%/2C

  13. � � !"#$%#&'(')"#*+#,(*-."'(/(012-2'(,%+*'*3"' 4#-*-4(0'.(0+"'%$'*3"'&(5/"*-4'6"07 s E x,y = A 1 x,y + i A 2 x,y . orders. Our strategy is thus to solve for the fields in the following sequence al equations into three + O ( ε 5 ) ε 3 e x,y E x,y = ε E x,y + A 3 ε 2 a 3 + O ( ε 4 ) = + xB c y y + O ( ε 4 ) A 3 ε 2 a 3 = x x ! 8'4%+)0"7'"9+(*-%/2'$%#'*3"':'(7;%-/*' 4%&)%/"/*2'%$'<=>?@'-/'*3"'AB1'(/7'#(7-(0' 7-#"4*-%/2C

  14. !"#!$%&'()(*#+,--&./#&)#,#)(+0-&("#-(#-1/# /20,-&(")#(3#4(-&(" ∞ 2 2 B c ( x − nk Bc ) C n e − inky − 1 � = U ( u ) n = −∞ %,5&,+#5&%/.-&("#(3#!56 !-#/,.1#(%5/%#7/#1,*/#-(#.,+.0+,-/#-1/# %,5&,+#5/8/"5/"./ 9+()/#-(#-1/#.%&-&.,+#4,:"/-&.#;/+5#9#&)# )4,++#,"5#7/#8/%-0%$#&"#-1&)#8,%,4/-/%

  15. !"#$"%&'$()*#'+,"-."/#'#/#$#'0"(1+"2)++" +'+)0. � dudxdyf ( u ) A 2 + g ( u ) A 4 F ∼ � f ( u ) C 2 + ˜ dudxdy ˜ g ( u ) C 4 ∼ 3$"4+"/&5+" *4*."2)&/"(1+" %)#(#%*6"7+6, 8+)(9)-*(#5+"*'*6.$#$" &'6."5*6#,"%6&$+"(&"(1+" %)#(#%*6":&#'(

  16. ;'#-"/#$#)&+$"%3.$&#.$))+2'#,$4#),'#.0*'4)#<&''#'"'&%1# 5=1"$(+2$.#>&'$?+"%#@'&434#A0&0*+)B#')#$.C:# !"#$%&''('")#*+),#),'#-'./#),'0&1#2$.23.$)+0"4#5$"# '6)'"/'/#789#(0/'.:

  17. !"#$%&'()*%+),$- ! .#/&0/#$)%$1#+*2'1$%&')34&5)+$*%5+%$"5*% 6#&781'0+9: ! ;))%<"#$%21)95&$5'+*%&#+%6)%(#9)%3'1% ")#=>%5'+%2">*5&*: ! ?5+9%'0$%<")$")1%#%$15#+80/#1%/#$$5&)%5*% #/<#>*%3#='01)9%@%"'<%9')*%$")%4)/9%$")'1>% 5+%A0)*$5'+%#/$)1%$")%/#$$5&)- ! B22/>%$"5*%$'%&'+9)+*)9%(#$$)1%*>*$)(*:

  18. !"#$%&'()*

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