SLIDE 1
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:4+;:4+$<&=$>*"4++4$?(,5#+/#(=$@./4#6$A-(9,*5=$>A$;$
- *$4''#4($%**+BBB
!"#$%&'#()*+,&)-.+/$012$ - - PowerPoint PPT Presentation
!"#$%&'#()*+,&)-.+/$012$ - - PowerPoint PPT Presentation
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SLIDE 2
SLIDE 3
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! !(%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)% ?'$$'6>0-8
! @'6($56()%$"5)%&'()3<$%6#$$(,%
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#"#$-*9#%;4$*%,'%-"*%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,*,"-'%
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! " #! #" $! $" ! $ % & ' Ω( )*Σ ! " #! #" $! $" ! # $ + % " & Ω( ,-Σ
HIKL<KMHN
SLIDE 5
!"#$$$%&'()*'+,'-&##&.'#/)*'#/)#
! 0)#/&.'#/)*'-.&)12*3'#/&'4566&#.2&4'-5'/)*+'%&'()*'
)74,'8*+'4"(/'4,7"#2,*4'+5*)62()775
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;F,3".2'&#')7$?'G)"*#7&##'&#')7@
SLIDE 6
LDSGS ∼ −1 4F 2 − 1 2 |Dρ|2 + m2
ρρ2
+ρ0 contributions + nonminimal coupling ∼ F µνρµν
!"#$%&'#()*+,&)-.+/$01234$56)&&7
! 2"#(+*,&89$:;<;$=3>?>$=3@&A6+*5.)9$>)".+,B#(9$?#/#B.69$
>)"#(#(C$7*,#BD#E-#+,#,$FGH$7*,#BC
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- "#$76/+#-.)$K#B,$%-(#+/-"$6)(*%%$-"#$56)&&7
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8 9-$%*7#$)(.-.)6:$76/+#-.)$;#:,$%-(#+/-"$-"#$56)&&7$
,#%-6<.:.%#%$6+,$)*+,#+%#%
8 !"#$("*$7#%*+$.%$)"6(/#,$6+,$-"&%$-"#$=>?@$.%$
%'*+-6+#*&%:A$<(*B#+
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SLIDE 8
!"#$%&$'&($()*+$),-,'."/)*0"--12
3
455,#6$7.85&#'&.6$9&.#&.6$:(.18,5$!!"#$%&&!;
3
<)&$*#+("=*-*(1$(,$"$+>/&.0,#8>0(*#'$+("(&$%"+$+),%#$),-,'."/)*0"--1
! <)&$5,8&-; ! 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
S =
- d5x√−g
1 2κ2
5
(R − 2Λ) − 1 4ˆ g2 F a
µνF aµν
- + Sbdy
<)*+$%*--$=.&"N$()&$CDKF$+155&(.1
SLIDE 9
!"#$%&$'&($()*+$),-,'."/)*0"--12
! " " ! #$% !$& !$% "$& "$% %$&
Im w Re w
3345678839$%*()$/&.:*++*,# ;+$()&$:"'#&(*0$ <&-=$*#0.&"+&+
>?"+*#,.:"-$:,=&+
SLIDE 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*+,.,(
SLIDE 11
!"#$%#&'(')"#*+#,(*-."'(/(012-2'(,%+*'*3"' 4#-*-4(0'.(0+"'%$'*3"'&(5/"*-4'6"07
! 8'4%+)0"7'"9+(*-%/2'$%#'*3"':'(7;%-/*'
4%&)%/"/*2'%$'<=>?@'-/'*3"'AB1'(/7'#(7-(0' 7-#"4*-%/2C
- rders. Our strategy is thus to solve for the fields in the following sequence
Ex,y = εEx,y
- +
ε3ex,y + O(ε5) A3
y
A3
x
= = xBc + ε2a3
y
ε2a3
x
- + O(ε4)
+ O(ε4)
s Ex,y = A1
x,y + iA2 x,y.
al equations into three
SLIDE 12
!"#$%#&'(')"#*+#,(*-."'(/(012-2'(,%+*'*3"' 4#-*-4(0'.(0+"'%$'*3"'&(5/"*-4'6"07
! 8'4%+)0"7'"9+(*-%/2'$%#'*3"':'(7;%-/*'
4%&)%/"/*2'%$'<=>?@'-/'*3"'AB1'(/7'#(7-(0' 7-#"4*-%/2C
- rders. Our strategy is thus to solve for the fields in the following sequence
Ex,y = εEx,y
- +
ε3ex,y + O(ε5) A3
y
A3
x
= = xBc + ε2a3
y
ε2a3
x
- + O(ε4)
+ O(ε4)
s Ex,y = A1
x,y + iA2 x,y.
al equations into three
SLIDE 13
!"#$%#&'(')"#*+#,(*-."'(/(012-2'(,%+*'*3"' 4#-*-4(0'.(0+"'%$'*3"'&(5/"*-4'6"07
! 8'4%+)0"7'"9+(*-%/2'$%#'*3"':'(7;%-/*'
4%&)%/"/*2'%$'<=>?@'-/'*3"'AB1'(/7'#(7-(0' 7-#"4*-%/2C
- rders. Our strategy is thus to solve for the fields in the following sequence
Ex,y = εEx,y
- +
ε3ex,y + O(ε5) A3
y
A3
x
= = xBc + ε2a3
y
ε2a3
x
- + O(ε4)
+ O(ε4)
s Ex,y = A1
x,y + iA2 x,y.
al equations into three
SLIDE 14
!"#!$%&'()(*#+,--&./#&)#,#)(+0-&("#-(#-1/# /20,-&(")#(3#4(-&("
%,5&,+#5&%/.-&("#(3#!56
=
∞
- n=−∞
Cne−inky− 1
2 Bc(x− nk Bc ) 2
U(u)
!-#/,.1#(%5/%#7/#1,*/#-(#.,+.0+,-/#-1/# %,5&,+#5/8/"5/"./ 9+()/#-(#-1/#.%&-&.,+#4,:"/-&.#;/+5#9#&)# )4,++#,"5#7/#8/%-0%$#&"#-1&)#8,%,4/-/%
SLIDE 15
!"#$"%&'$()*#'+,"-."/#'#/#$#'0"(1+"2)++" +'+)0.
F ∼
- dudxdyf(u)A2 + g(u)A4
∼
- dudxdy ˜
f(u)C2 + ˜ g(u)C4
3$"4+"/&5+" *4*."2)&/"(1+" %)#(#%*6"7+6, 8+)(9)-*(#5+"*'*6.$#$" &'6."5*6#,"%6&$+"(&"(1+" %)#(#%*6":&#'(
SLIDE 16
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5=1"$(+2$.#>&'$?+"%#@'&434#A0&0*+)B#')#$.C:#
SLIDE 17
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! .#/&0/#$)%$1#+*2'1$%&')34&5)+$*%5+%$"5*%
6#&781'0+9:
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")#=>%5'+%2">*5&*:
! ?5+9%'0$%<")$")1%#%$15#+80/#1%/#$$5&)%5*%
#/<#>*%3#='01)9%@%"'<%9')*%$")%4)/9%$")'1>% 5+%A0)*$5'+%#/$)1%$")%/#$$5&)-
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SLIDE 18
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