• Keine Ergebnisse gefunden

erste Weyl- kammer Weyl-

N/A
N/A
Protected

Academic year: 2021

Aktie "erste Weyl- kammer Weyl-"

Copied!
38
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Volltext

(1)

! #" %$'&(*) +,.-0/1! #" 3254 .6*

78 9 :" %$<; " /=/ >?$A@ 4BDC E F-

G -%H 4 & /:- <I J

KML0L>NPO QR 4S-

TVUXWZY[UX\^]%_M`(UXWbacUedgfh\gWi]

j kmlon n prqts'uvp wexgy kmlzn n prqts'uvp^{hs#p^|}wXx8~mj

 -M/€/ ‚ƒ;ƒ …MEo†‚K0K‚K

(2)

\gdY UedEY€U U ]U a W'f \ d UXd

u?|^}(qt} p s'uvp^x

! €Uef"W$#% Y'&( ) Y* U+ ],[U - [U#mWa U

U.€Uef"W$#X]/ & Uha d0XUeW1ƒ_32 YcY _") # U

]4EYrW'fBU 5 \hYgd6RUXd W$# #78gd Y9 a f

: WZY ;Xa<EYMa=# d ! a d^]4RUha d^]/8U - [U#mWa U

) a d f># ] fƒa@? A B! W UhaC dXa=] DFEHGJILK

MON P D

MRQN P M

S u?xg|UT8s p V sWTexYXLZ[ s#n T qtu+gx p^x(\

M Q ]9^

MR_

Q P `

Qba

M a c d Q I e

MR_

Q P `

Qfa e M a

g Q a e MR_

Q e

Mh_

a P g Q a e M Q e M a P i

`kjlgY` P g I D g Q a N P

za Y%D/mI

]

mI

]

mhI

] m N

n _ :

W<Yza Ued

o Q P D mE

oUp

Irq

N i o _

Q P D ` s J N a Q o a P ` a

Q o a

t e

MhQ

f# dW<Y ; YhWa Y d

t o Q

f>#; YrWa Ygd6

t u

Qv

Q P g Q a u Q v a w

#W UXd6yxra d ; YhWa Y d&

(3)

"!#%$ '&)(+*,$ -.*

w

_M` \ dgf Ma # d / P e O M 0 I 0 P 0

D"17I

o Q 1 N

2 YrWa YMa=# d^]43hWba dxra53 D76

w

#W UXd6yxra d ; YhWa Y d83W UU.+

N

9 6 P : I 6 P e G;/

P e N M 0 <

= U UL \gde]/%€Uha \gd UXd

o Q D o 0

o D o Q 1 N N ] o 0

o 1 P :

>

p^u X@?zuvp,Avp

CB\ W w

Y WZYgd U0_ED a RUed

t F

€Uha d _ : #mW1 # d `oU 0 P D o Q 1

NHG

o Q 1 ] I † 1 G 1

P i

DKJ

c I † N 1 P :

t D a W<YM_M`oU 0 P L

M DONQP

Q o Q ] I N M I L

M P M G P K

P i

DON

oR ] I N M P :

(4)

w B

# ] \gd UXd

^ w B

#X]P\gd Ued.8 6 a d; YrWa Ygd6

t

#za d8YrW U0_d; YrWa Ygdx9

1 _ D

Mh_ N P

1lD

MN

I M _ D

Mh_ N P 6 M D

MN

M _ P M c d P i 9 1 P d Q o Q 1

t : #%0 Y€U D/m

N _ ! aCXa d; YrWa YgdhYLx9

1 _ D

MN P

1lD

MN

I M _ D

MN P M D

MN

P m c

N

P i 9 1 P

N 1

&E . ! O*! $

= U UL \gde]/%€Uha \gd UXd

i

9 0 P o 0

o D o Q 1 N o Q D 9 1 N c o 0

o 1 9 1 P o Q D o 0

o D o Q 1 N 9 1 N

bdgd[UXW U 2%8 U Wa UXd

9 0 P : i

Q P 9 0

9 D o Q 1 N 9 1%I

o Q Q P : <

! W Y9 RUed8U # U [UXW Y \ d Ued

P : I P e O M K P e O M 9 1 D

MN

(5)

23f‚YcYrW Q P N D o Q 1 G 1 ] 1 G o Q 1 N I P N D 1 G 1 ] 1 G 1 N

D a WZY Q P L

M P Q M I P M G M

f‚YgdY# dea], f># dE\oacUeW[RU W 3g\91]/za RU

P o 0

o

1 I 1 D

MON I

D

N P 9 D K

M ] K N i

@1 D

MN

I P e O

1 D

MN I

D

N 9 1 D

N P 9 1 D

MON

I

p^s p8w ~ q

G

wex.TX{ }

u?|^}(qtsWTXxLXLZ hs'n Tmqtu x p x

- WZY d ]UcY6Ma # d8Ued 6 a d ; YhWba Y d8

0

deaC a d ; YhWa Y d

9 0 P o a 0 P o Q D 9 0

9 D o Q 1 N o a 1 N i o Q Q P :

# U [UXW ]4W$#

P ! d8UeW1za U0_W 3g\91] - Ued ],#mW

Qa P Qa I Q a P o 0

o D o Q 1 N o a 1 ] g Q a 0 <

# U [UXW Y \ d

P ! d8UeW1za U0_W 3g\91]

Q P e O M K Q I K P e O M D

1 ] 0 N

(6)

( ! (+&

} n r~ p x p T p,A+A~ Avp u?|}wXx8~ p^x

q K

v P : I q K

c mE o K

v

o G P : i

K

v P q K

u I K

P ] mE o K

u

o G ] q <

! aCW<Ygd #W Y6Ma # d8Ued a< P

%DWGJILK

MN

K

u _ P K

u ] q (I

_ P c mE o

o G I D K

I K

v N ^ D K

I K

v N

D@I

K

u N

D

_ I K u _ N

Uha

B

Y \Xa ; Y9€UXd6RU

#RUedMa Y€U

W U. & `(#mW \ a UXW#\gd n _ 2 UXf #W 3.#RUedMa Y

D u Q N P D u K I u J I u † I u O N P

D I K

u N

D u Q N P D u K I u J I u † I u O N P

D I ] K

u N@<

u |}oqts TXxYXZ hs'n T qtu x p^x(\

u Q ]^

u _Q P u Q ] o Q

(7)

o Q u Q P : P i J u Q P Q I D

Q N P

DI

K

N <

^ w a UXdhYhW$r_ a UL8UeW[8

<K< <

! .7()' & ( -' D L P E P m N

t ) UhYgdea f.

]^

] I K

] ^ K

P K

] K

u

P m

I K

†

]9^

P m

I D K

] K

u N † c

^ w

#W Uedyxv]/8Ued = U U \ dX],%€U a g\ d Ued

CB

\ W( U0_

cY Ued8U

\gd f" RUha 8Ued

t 5 \ Y dRUed UL Y dXa f

hs's#pX@? x y p^x s p0~ p A?x

]9^

N o p

\gd K

]9^

mN q

^ 2 gW B#za d UXW5_ 8 F

=Uha dP_ : #W$9# d _ \gd D a W<Y %€U a:_

g\ d a d B

Yg\^]R]UeW Ued U+ &V`(U. UXW'd&

t ! Wi]U yx \gdr_ \ d

F

#mW'W U ]43.# d UXdx D

Q P D IRK

N N

Q ]9^

Q ] u Q ] ^ N D o Q c N u Q N

N

Q <

(8)

Q P o Q N u Q

TbT A

! #"$% &(')*

,+

.-/- 0

1$23 465 7 891 : ;=<>3 41 7 8?1 : ;=<?23 1 @ 891BAC5

7 <!DFEG

2 8 1 : ;=<>3 1 5

<.HIDFEJG

1$23 4K5 7 L 1$23 5ML

HONQP

LC2SRI5 7 <

DFEGT*UWV X Y

2[Z5

\

"]% % ^?_`a"$

b 1 P c_de7 ;=<

2

8913 c @ 8cf3 1 5 g

;=<ihj1?c P

2[Z5

jkmlonjp p qkmlQrst uvwyxlBz- ql

+

h1`c 7 {||||} ~  N  €  

@  N ~ @ ‚  ‚ €

@  € ‚  ~ @ ‚ N

@   @ ‚ € ‚ N ~

ƒ„

„„„

…

† 8 1 h

1`c

7 ‡ c P h 1`c

'B&‰ˆ)Š)&‹,ŒB#&/Ž`

0

;=<ih 1`c 23 465 7 b 1 23 465

P c 23 465od

7 b L 1$23 5ML HN P L c23 5ML HN d

7 ;=<L‘hj1?c23 5ML HON 7 ;=<ih1`c23 5

(9)

! #"$% &(')* Ž')Ž^i" &('

3 41 7 3 1 @ 8 1 A P 4 7 L 7 †

2 123 5 5 4 g 1I23 4 5 )4 7 L 1$23 5 P

l 2 P 8 5

yf-/- j w +

)- w

r,sjk - l

+

p -Ck

+

Ž

L x -) l,

2 P 5

.-

- )j w

+

- w

r,sj -l

+

p -C

+

Ž

2SRI5

LC2SRI5 2SRI5

P 3 1I2SR$5

3 1C2SRI5@ 891qA 2SRI5

!

p p -)w "

+# $

8?1 @ 1 7 8?1 : ;=<>3 1

% 'B& '& &(')( ' 'B&‰ˆ)Š)&‹,ŒB#&/Ž`a' +*^Ž , - .Ž'0/21 &‰ˆ Š`a')

\ ( 'B&‹'/43 "I65Ž"] 7'(85

:9

7 2 1 5<;

1 @ = € ;

7 † 2 1 1 : = € 5 7 ~

1 & ˆ2/27j')(85

?>

7 @A 2;CB

1 1 @ = 5 A

7 †

2; ED @ = 5 A 7 ~ P FD 7 B 1 1

(10)

z

‘

, *" 9^.Ž') 5Ž') ( '&‹'/

3 "I65Ž"] 1 ‘ˆ ( 'B&‰ˆ)ŠŽ^. '&!Ž' 5I

2 4 P 3 41 5

2 A 4 P 3 41 5 P A 4 7 L A

2

LC2SR$5 7 '& 2;=<[A 2SRI5

5 ' ' ` ( ( , *"9^.Ž'

& '#&‹% 'a' Ž^! 5Ž' 5Ž' >" ( ( ' &‰ˆ Š" 5 ^=ˆ)Š

# Š$i'*-5t'^-t' Š)&%a' 5Ž')% & '(-5 )!)$* "+ ^,

) 5 ) - Š ) '. */) 0' ( ( * ,Œ1$ * " ^" ) 2^3 ")$* /

Š*-

* ) #

Š1

)

425 6'.73 "

*

'8

) 3 *

L:9SR.;

)1*

7'. 5 ) ^. 5 )

w=<

?>

w=@

rs

>

A>

B* ˆ Š'/

&'C

)

"

*

$(

9 ^D3 3 )

Š$.E

\

'(

)F

* '(

;

G & * ~ P N

€IH

B* ˆ Š$&J * K* & )$* .5 ) ^" * ) ) (L3 NM M

O PRQTS"UQWV7XDS"V7PZY [

A F

'8\]

H^

_ ; A P

^a`

_ ~ † ^

cb

_ ~

de ‡ e _ ~ P ‡ e _ ;=<,f

d b

d 9 e ; @ g ih kj

(11)

b 9 P ;

cb

9 P ;

‡ e 9 P d ; ‡ e 9 P ;

‡ e

)1* ˆ Š * ,Œ1J * " ) Š$$( )

z

)$* ) 5

‡ e _ @

^

b

^a`

e _ @ d b

^a`

e

1 ^=ˆ Š )

&$(

* J*

) )

ˆ)Š^- +*^

)$*

) ( -5

) )

G F $( J ) (85E( +*^ ) ( ˆ Š )

‡ e _ @ ;=<,f9 e ; ; @ ; e j

1 ^=ˆ Š ^^" ^- ŒK'(

b

9k<

D G P ` e @ ;

de

A:;

_ b 9 P ` e ;

z

)$*

) 5 4*^

)$*

1 *

2ˆ4

)

(85

‡ e _ < @

A B e A

V S=PXV

^

_ ~ † d e h e c _ ‡ c P )

Q^ˆ Š"

_ R P

(12)

( '.

)

"

J*

,Œ1J

*

"

)$*

ˆ)Š

*

,Œ1$

*

"

9 ` ;

^ h e c _ ^ 9 d e ` c @ d c ` e ; _ d e

^D`

c @ d c

^D`

e _ †

^

Rth

e

cWh

e c _ R 9 ^ h e c ; h e c

_ @ R

^D`

c d e h e c

_ @ N

R h e

ch

e c P

^

^D`

c _ d e h e c

,Œ1$ * " ) ,W-W2. ) 5 * ˆ)Š ) M * F ^.

_ @ N

h e c h e c : b 9 P ; P _

: b

^

_ ~ † 7 ) ( 5 (

)$*

ˆ Š^-

)

‡ e

)1* ˆ Š * ,Œ1J * " ) Š$$( )

( )F 4 ' 513 * F _ Y 9[ZK; / B* ˆ Š"Š ) '. */)

d?e

e _ † 1 13

* F

3 ) '(3 ) 4 * */) J^- 5 ) M M 9 7( ) *^-5 ) ( ;

F *'8 ) F '8 * ) ^1" * */) ) 5 )

^"

) *

) \]^$(

*

ˆ)Š

) *

)

)$*

\

* 3 3 ^- 3 *

&

) * 3 )

"

)

(13)

) ( -5 ) ) 7 ) (85 )

@ Y 9 L1;

P Y 9 L1; _ 5 *

. 9 < DFE

l G P P < DFE G ;

1 $ \

) ( (y^. ŒK'(

Y 9[ZK; _ f L L _ )

&

;=<[A j H

Y 9[ZK; _ P Y 9 LLJ; _ Y 9 L1; Y 9L$;

,W-5 ^- < X † * 7 ) 5 1 J \ ) ( (y^-

& )

"

)

73

= € ` e ` e * Œ )

'C

)

^$" * */) ^.

^1 ) ( )F 4 ' 513 * F

* ˆ Š * ,Œ1J * * ]$ * * 5 ) 1

! " #$ " " % &'" (

Y

9[ZK; / G

:3 3 ) 4 */) @ * ˆ Š" / ) ([ˆ Š ) G

:3 3 ) 4 */)

)+*

Y Y QS"VLQ,V 8Q - U8V7Q . LQ0/21 348Q65V7Q

9 G &

)"J*/)

( ( ;

^

* *

) 3 ^ &$&

) H

Y 987 ; _ faL X 9 : 9<; ;= L ; L _ j`P

5 * 3 _ 7 €

Y 987 ; _ faL X Y 987 ;= 5 ) L _ Z j?P 5 * 3 _ 7 € @ Z

(14)

@ w @

_ f_; L _ < D : ; j

X _ † N : € P b N P € d X ;

( * ) J

)

^3 3 * b P d

1 F '

*

/ 5 )

*

*"

b P

b

_

G & )"J*/) ( ( H

! 987 ; H _ "$#

"%&#

' ( ) 9* ( ; ;

! 987 ; H + _ 5 ) 9 " # ; _ )

&

9,) G & ;

1 3 *

-/.

987 ; _

f0 1

; G & _ .j

%

* f/2

j G

4,3

F

43

F

'(\]"

) 5 6

87 9 : H

2 2 7 _ ) 5 6

87 2 6

; >=<

> H 3 "

* 3 @?

) G

F

'83 3 3"

*/)

) BA

) 2

fDC E

8 8

C F j G fH2 j I J >BKML >N<PORQ <SL

@

K6>NT

@VU K6>

W@XZY(9

! 987 ; ; _ 7 ( +

(15)

@

!

(

+

-8.

2 E

!

"$#

2%02

7 E

&

7

"('*)

3%+

' 3 )

+-, X/.

' W X '0

X

2

2 7 )21

7 6 2 6 3 5 6

7 1 7 6

L K

54

K

6 ! 7

2 +

98

+

8

: C E 2;

C 2<

= 0 ? ?>-? W X@X @ W

'*)BADCE0

X

FHG I JLK M K

M K K

K K KON

FQPRI J%K SUT K

T K K

K K KVN

FXWRI JYM K K

K SZM K

K K KON

F\[ I J K K M

K K K

M K K N

FQ]RI J K K SUT

K K K

T K K N

F_^/I J K K K

K K M

K M K N

FQ` I J K K K

K K SUT

K T K N

FQaRI

M

b c J M K K

K M K

K K Sed N f

"$#

2R2

7 E

&

7

2

2 7 ) 5 6

7 2 6

(16)

Mhd M

[

M g d

[

dg

[ g [ g

M G

P S G

P G

P G

P G

P S G

P W

P W

P

"!$#%&!

! (' ) ( I ! Z

9 *

+ -, 3 X A '/.

W ) ,

! 10 ! Z ! 0 -, ! "

3 ! % E ! % E Z ! 2 Z

3 A 0 ) A

054

X A 0 ) 0 X A 0 3 X A W

A76D3 XZY

A 0 ) '0 8 W ) .

'0

? ? 3 XBY

A

094

X A 0 ) 0 X A 0 8 W ) .

'0

? ? 3 XZY

( I ! Z 9 *

: ;

+-, ? # ?

09<

+ , X 6 3 Y A 0 ) '0 8 W ) .

'0

? ? 3

XZY

( I ! Z

9 *

: ;

W

A76D3 XZY

A 0 ) '0 8 W ) .

'0

? ? 3

XBY

( I = > Z-, = > Z@? /? % E , + ACB

D

Q U N<

4FEHG 0ZA

Y

0JI

A

WLK = >

0ZA

X 0 8 W ) .

'0

? ? 3 XZY

A . ' 3 X A

A WJK = >

6NM

6FO

7

(17)

X

A

W . ? ?

XZY

M I

M

M B

M

? M ? M

M

/?

E M Z

M

? M Z

E

M

? , ! M ? -,

M !

" . # ,%$ Y '

M

'& -,

M

'&)( !9 *,+ -

( M

'&

-

-B

"

A/.

3 ' 3 0 ,

)BA 0 X I X10 W

)hA

W@X '0

X

#

X32W

? 0 X ' W $ 0 8 W ) .

'0

$4$4

XBY + : ;

" + W $ W

)X# ) , 2

%+

' 65 ,87Z 9 ;:

5 7

; M

< 3 5 ,h=7 65 ,7Z

> ? 2 6@)A3B

A 0 ) '0 8 ? ) .

'0

$4$4CADB + A

" + ? $ ? )X#

, 2 +

' ? ,

"$#

?

= > Z@? , = > ZE

"$#

/? : ? ,

FHG

) 0 3 0 A ' F 2 0 ) ? 2

6@)A3B

A 0 ) '0

A 8 ? ) .

'0

$$4)A3B

= > Z = > 0ZJI /? : 0/? 0 : K ?

Referenzen

ÄHNLICHE DOKUMENTE

und auch in diesem Jahr hoffen wir auf tolle Oldtimer-Raritäten und natürlich besondere Young- timer.“ Häufig stießen sogar noch im letzten Moment frisch restaurierte

After we got the Clebsch-Gordan coefficients of the highest weight state, we can calculate the coefficients of all other states in the dominant Weyl chamber.. Since the action of

As each of these layers exhibits surface states Fermi arcs emerge, which are surface states connecting the surface projection of both WP and merge into the bulk by reaching

Alexis Goldstein / Louis Lazaris / Estelle Weyl.. Mit

Sakhnovich, Skew-selfadjoint Dirac systems with rational rectangular Weyl func- tions: explicit solutions of direct and inverse problems and integrable wave equations, Math..

[14] Fritzsche B, Kirstein B, Roitberg I Ya and Sakhnovich A L 2011 Weyl theory and explicit solutions of direct and inverse problems for a Dirac system with rectangular

[r]

Deppert, W., „Kritik des Kosmisierungsprogramms“, in: Hans Lenk, (Hrsg.), Zur Kritik der wissen- schaftlichen Rationalität, Festschrift für Kurt Hübner, Freiburg 1986.. Deppert,