chapter2 - Fkdswhu 5 WKH IRUPDOLVP RI TXDQWXP PHFKDQLFV Wkh...

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Fkdswhu 5 WKH IRUPDOLVP RI TXDQWXP PHFKDQLFV Wkh sxusrvh ri wklv vhfwlrq lv wzrirog= +4, wr hqxphudwh wkh edvlf srvwxodwhv ri txdqwxp phfkdqlfv lq d irup zklfk lv pdqlihvwo| uhsuhvhqwdwlrq lqghshqghqw/ dqg zklfk lv srwhq0 wldoo| dssolfdeoh wr jhqhudo txdqwxp phfkdqlfdo v|vwhpv ri rqh ru pruh sduwlfohv> dqg +5, wr surylgh wkh pdwkhpdwlfdo iudphzrun qhfhvvdu| wr xqghuvwdqg wkh frqwhqwv ri wkhvh srvwxodwhv1 Wr wklv hqg lw lv xvhixo wr dgrsw dq dssurdfk zklfk pl{hv wkhvh wzr wdvnv1 Wkxv/ zh vwduw rxw e| vlpso| vwdwlqj wkh ±uvw srvwxodwh/ iroorzhg e| d jhqhudo glvfxvvlrq ri lwv pdwkhpdwlfdo lpsolfdwlrqv1 Wklv surfhgxuh zloo eh uhshdwhg iru wkh uhpdlqlqj srv0 wxodwhv1 Iroorzlqj wkh jhqhudo vwuxfwxuh lqwurgxfhg hduolhu/ zh ehjlq wkh srvwxodwhv e| ghvfulelqj wkh phdqv e| zklfk dq duelwudu| g|qdplfdo vwdwh ri d txdqwxp phfkdqlfdo v|vwhp lv vshfl±hg1 514 Srvwxodwh L= Vshfl±fdwlrq ri wkh G|qdplfdo Vwdwh Wkh g|qdplfdo vwdwh ri d txdqwxp phfkdqlfdo v|vwhp lv dw hdfk lqvwdqw ri wlph dvvrfldwhg zlwk d vwdwh yhfwru m # l 1 Srvvleoh vwdwh yhfwruv duh hohphqwv ri d frpsoh{ olqhdu yhfwru vsdfh V / uhihuuhg wr dv wkh vwdwh vsdfh ru Kloehuw vsdfh ri wkh v|vwhp1 Reylrxvo|/ d suhuhtxlvlwh wr rxu xqghuvwdqglqj ri wklv srvwxodwh dqg lwv lpsolfdwlrqv lv d nqrzohgjh ri olqhdu yhfwru vsdfhv1 51414 Surshuwlhv ri Olqhdu Yhfwru Vsdfhv Dvhw V ri remhfwv im # l > m ± l > m ² l >=== j irupv d olqhdu yhfwru vsdfh +OYV, li lw lv forvhg xqghu wzr pxwxdoo| glvwulexwlyh rshudwlrqv= +4, dq dvvrfldwlyh dqg frppxwdwlyh odz ri yhf0 wru dgglwlrq / dqg +5, pxowlsolfdwlrq e| hohphqwv ri dq dvvrfldwhg ±hog I ri vfdoduv i ³>´>µ>=== j 1 Wklv rshudwlrq ri yhfwru dgglwlrq lv dvvxphg wr vdwlvi| wkh surshuwlhv hqx0 phudwhg ehorz1 41 Iru doo yhfwruv m # l dqg m ² l lq V wkhuh h{lvwv d yhfwru m " l lq V vxfk wkdw m " l @ m # l . m ² l 1 +Forvxuh, 51 m # l . m ² l @ m ² l . m # l 1 +Frppxwlylw|, 61 m # l .+ m ² l . m " l ,@+ m # l . m ² l ,. m " l 1 +Dvvrfldwlylw|, 71 Wkhuh h{lvwv d xqltxh qxoo yhfwru 3 lq V vxfk wkdw 3. m ² l @ m ² l 1 81 Iru hdfk m ² l lq V wkhuh h{lvwv dq hohphqw ±m ² l /vxfkwkdw m ² l ±m ² l ,@ m ² l±m ² l @3 1 +Dgglwlyh lqyhuvh, Wkh ±hog zlwk uhvshfw wr zklfk wkh vsdfh lv gh±qhg lv dq dvvrfldwhg vhw I ri qxpehuv +xvxdoo| wkh vhw U ri uhdo qxpehuv ru wkh vhw F ri frpsoh{ qxpehuv, zklfk zh pd| xvh wr pxowlso| wkh hohphqwv ri wkh vsdfh lwvhoi1 Wklv rshudwlrq lqyroylqj pxowlsolfdwlrq ri hohphqwv ri V e| hohphqwv ri I lv dvvxphg wr kdyh wkh iroorzlqj surshuwlhv=
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63 Wkh Irupdolvp ri Txdqwxp Phfkdqlfv 41 Iru doo yhfwruv m # l lq V dqg vfdoduv ± lq I wkhuh h{lvwv d yhfwru m " l lq V vxfk wkdw m " l @ ± m ² l 1 +Forvxuh,1 51 ± ^ m # l . m ² l `@ ± m ² l . ± m # l +Glvwulexwlrq ri vfdodu pxowlsolfdwlrq ryhu yhfwru dgglwlrq, 61 ± 4 m # l . ± 5 m # l @+ ± 4 . ± 5 , m # l +Glvwulexwlrq ri vfdodu dgglwlrq ryhu pxowlsolfdwlrq ri yhfwruv e| vfdoduv1, 71 ± 4 + ± 5 m # l ,@+ ± 4 ± 5 , m # l +Dvvrfldwlylw| ri vfdodu pxowlsolfdwlrq1, 81 Wkhuh h{lvwv dq lghqwlw| hohphqw 4 lq I vxfk wkdw 4 m ² l @ m ² l iru hdfk m ² l lq V 1 Vrph ri wkhvh surshuwlhv duh dfwxdoo| dvvrfldwhg zlwk gh±qlwlrqv ri wkh whup ±hog 1W k h
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chapter2 - Fkdswhu 5 WKH IRUPDOLVP RI TXDQWXP PHFKDQLFV Wkh...

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