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63 pages
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Rayleigh scattering, asymptotic completeness, quantized radiation field, 
radiative decay, atoms and photons, nonrelativistic QED,  
Pauli-Fierz Hamiltonian
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%%Page: 16 16
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%%Page: 17 17
17 16 bop 120 -200 a Fs(F)n(GSc)n(h,)24 b(30/Mar/01|Asymptotic)h
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2909 y(+)22 b(\()p Fr(D)1458 2924 y Fq(v)1499 2909 y
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4082 123 4 v 1918 4173 a(@)g(t)2057 4105 y Fw(+)23 b
Fr(r)2249 4037 y Ft(@)5 b(S)p 2249 4082 V 2264 4173 a(@)g(t)2403
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5219 y(+)22 b Fr(D)952 5178 y Fp(2)949 5244 y Fq(v)991
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y Fq(v)1334 5219 y Ft(v)t Fw(\))g Fr(\001)g(r)p Ft(S)3667
5147 y Fw(\(57\))120 5407 y(the)33 b(lemma)d(follo)m(ws.)p
3769 5407 4 66 v 3773 5345 59 4 v 3773 5407 V 3831 5407
4 66 v eop
%%Page: 21 21
21 20 bop 120 -200 a Fs(F)n(GSc)n(h,)24 b(30/Mar/01|Asymptotic)h
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1148 a Ft(t)1276 1080 y Fr(h)p Ft(\037 )1439 1095 y Fq(t)1469
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1080 y Fw(\))p Ft(\037 )2562 1095 y Fq(t)2592 1080 y
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b(propagation)e(estimate)h(equally)g(holds)g(on)2682
1496 y(~)2653 1521 y Fr(H)i Fw(and)f(with)f Ft(H)53 b
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1642 y Ft(H)40 b Fw(and)33 b(d\000\()p Ft(v)1155 1606
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Fr(\012)i Fw(d\000\()p Ft(v)1896 1606 y Fp(2)1935 1642
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1924 y(~)3023 1951 y Ft(h)p Fw(\()p Ft(s)p Fw(\))28 b(=)3332
1871 y Fm(R)3399 1897 y Fq(s)3380 1985 y Fp(0)3452 1951
y Ft(ds)3549 1915 y Fn(0)3572 1951 y Ft(h)3628 1915 y
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y Ft(h)p Fw(\()p Ft(s)p Fw(\))c(=)885 2060 y(~)884 2086
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2086 y Ft(h)p Fw(\()p Ft(s)p Fw(\))23 b Fr(\000)2460
2060 y Fw(~)2459 2086 y Ft(h)p Fw(\(3\))34 b(for)f Ft(s)d
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3200 y(\037:)964 b Fw(\(58\))120 3390 y(Next)851 3510
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%%Page: 22 22
22 21 bop 120 -200 a Fw(22)120 107 y(Since)33 b([)p Ft(\037;)17
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638 V 3831 638 4 66 v 120 852 a Fg(Prop)s(osition)40
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%%Page: 35 35
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%%Page: 37 37
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eop
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y Fw(=)i Ft(H)1354 1442 y Fq(i)1385 1427 y Fr(\012)s
Fw(1)s(+)s(1)s Fr(\012)s Fw(d\000\()p Fr(j)p Ft(k)s Fr(j)p
Fw(\))21 b(on)2205 1402 y(~)2176 1427 y Fr(H)2260 1442
y Fq(i)2316 1427 y Fw(=)28 b Fr(H)2504 1442 y Fq(i)2534
1427 y Fr(\012)s(F)2686 1442 y Fq(i)2714 1427 y Fw(,)d(and)e(Ran)17
b Ft(U)10 b Fw(\012)3284 1442 y Fp(+)3344 1427 y Fw(\()p
Ft(U)3458 1391 y Fn(\003)3501 1427 y Fr(\012)s Ft(U)3657
1391 y Fn(\003)3697 1427 y Fw(\))28 b Fr(\033)120 1547
y Ft(U)10 b(\037)p Fw(\()p Ft(H)376 1562 y Fp(mo)r(d)544
1547 y Fr(\024)28 b Ft(\026)p Fw(\))p Fr(H)g(\033)g Ft(\037)p
Fw(\()p Ft(H)1143 1562 y Fq(i)1199 1547 y Fr(\024)g Ft(\026)p
Fw(\))p Fr(H)1485 1562 y Fq(i)1535 1547 y Fr(\012)23
b Fw(\012)1705 1562 y Fq(s)1742 1547 y Fw(.)44 b(F)-8
b(urthermore)1051 1753 y Ft(U)10 b Fw(\012)1197 1768
y Fp(+)1257 1753 y Fw(\()p Ft(U)1371 1711 y Fn(\003)1433
1753 y Fr(\012)23 b Ft(U)1609 1711 y Fn(\003)1649 1753
y Fw(\))k(=)h(\012)1888 1768 y Fq(i)1939 1753 y Fr(\012)22
b Fw(\()p Ft(I)2119 1768 y Fq(s)2156 1753 y Fw(\()p Ft(\037)p
Fw(\()p Ft(N)2371 1768 y Fq(s)2436 1753 y Fw(=)27 b(0\))22
b Fr(\012)h Fw(1)2797 1768 y Fq(s)2833 1753 y Fw(\)\))120
1968 y(where)41 b(\012)479 1983 y Fq(i)547 1968 y Fw(=)e
Ft(s)27 b Fr(\000)h Fw(lim)975 1983 y Fq(t)p Fn(!1)1163
1968 y Ft(e)1208 1932 y Fq(iH)1290 1942 y Fj(i)1316 1932
y Fq(t)1346 1968 y Ft(I)1389 1983 y Fq(i)1417 1968 y
Ft(e)1462 1932 y Fn(\000)p Fq(i)1559 1915 y Fp(~)1541
1932 y Fq(H)1599 1942 y Fj(i)1625 1932 y Fq(t)1655 1968
y Fw(\()p Ft(P)1756 1983 y Fq(B)1817 1968 y Fw(\()p Ft(H)1936
1983 y Fq(i)1963 1968 y Fw(\))f Fr(\012)h Fw(1\).)64
b(In)40 b(fact)f Ft(U)10 b(I)e Fw(\()p Ft(U)2880 1932
y Fn(\003)2948 1968 y Fr(\012)27 b Ft(U)3128 1932 y Fn(\003)3168
1968 y Fw(\))40 b(=)f Ft(I)3404 1983 y Fq(i)3459 1968
y Fr(\012)28 b Ft(I)3607 1983 y Fq(s)3683 1968 y Fw(and)120
2089 y Ft(U)10 b(P)259 2104 y Fq(B)320 2089 y Fw(\()p
Ft(H)e Fw(\))p Ft(U)561 2052 y Fn(\003)641 2089 y Fw(=)40
b Ft(P)820 2104 y Fq(B)881 2089 y Fw(\()p Ft(H)1000 2104
y Fq(i)1028 2089 y Fw(\))27 b Fr(\012)h Ft(\037)p Fw(\()p
Ft(N)1375 2104 y Fq(s)1452 2089 y Fw(=)41 b(0\).)65 b(It)40
b(follo)m(ws)f(that)h Ft(U)10 b Fw(\012)2554 2104 y Fp(+)2614
2089 y Fw(\()p Ft(U)2728 2052 y Fn(\003)2795 2089 y Fr(\012)28
b Ft(U)2976 2052 y Fn(\003)3016 2089 y Fw(\))40 b(exists)h(on)f
Ft(\037)p Fw(\()3638 2063 y(~)3613 2089 y Ft(H)3694 2104
y Fq(i)3763 2089 y Fr(\024)120 2209 y Ft(\026)p Fw(\))246
2184 y(~)217 2209 y Fr(H)301 2224 y Fq(i)348 2209 y Fr(\012)19
b(F)516 2224 y Fq(s)571 2209 y Fr(\012)g(F)739 2224 y
Fq(s)803 2209 y Fr(\033)28 b Fw(\()p Ft(U)h Fr(\012)20
b Ft(U)10 b Fw(\))p Ft(\037)p Fw(\()1376 2184 y(~)1351
2209 y Ft(H)35 b Fr(\024)29 b Ft(\026)p Fw(\))1698 2184
y(~)1670 2209 y Fr(H)i Fw(and)g(that)g(its)f(range)h(con)m(tains)g
Ft(\037)p Fw(\()p Ft(H)3142 2224 y Fq(i)3198 2209 y Fr(\024)d
Ft(\026)p Fw(\))p Fr(H)3484 2224 y Fq(i)3530 2209 y Fr(\012)19
b(F)3698 2224 y Fq(s)3763 2209 y Fr(\033)120 2329 y Ft(U)10
b(\037)p Fw(\()p Ft(H)36 b Fr(\024)28 b Ft(\026)p Fw(\))p
Fr(H)q Fw(.)43 b(Hence)31 b(\012)1126 2344 y Fp(+)1216
2329 y Fw(exists)g(on)g Ft(\037)p Fw(\()1741 2304 y(~)1716
2329 y Ft(H)k Fr(\024)28 b Ft(\026)p Fw(\))2063 2304
y(~)2034 2329 y Fr(H)j Fw(and)g(b)m(y)g(the)g(in)m(tert)m(wining)e
(relation)g(for)g(\012)3753 2344 y Fp(+)3813 2329 y Fw(,)120
2450 y(the)37 b(range)g(of)f(\012)747 2465 y Fp(+)807
2450 y Fr(j)-24 b Fw(\022)-8 b Ft(\037)p Fw(\()976 2425
y(~)951 2450 y Ft(H)42 b Fr(\024)35 b Ft(\026)p Fw(\))1312
2425 y(~)1283 2450 y Fr(H)j Fw(con)m(tains)e Ft(\037)p
Fw(\()p Ft(H)43 b Fr(\024)35 b Ft(\026)p Fw(\))p Fr(H)q
Fw(.)56 b(The)38 b(theorem)f(no)m(w)g(follo)m(ws)f(b)s(ecause)120
2570 y Ft(\026)27 b(<)h Fw(\006)33 b(w)m(as)g(arbitrary)f(and)h
Fr(k)p Fw(\012)1325 2585 y Fp(+)1384 2570 y Fr(k)27 b
Fw(=)h(1.)p 3769 2570 4 66 v 3773 2508 59 4 v 3773 2570
V 3831 2570 4 66 v 120 2857 a Fh(10.2)136 b(Relaxation)47
b(to)e(the)g(Ground)f(State)120 3042 y Fw(With)g(the)g(help)g(of)g(A)m
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y(Consider)j(the)g(Hamilton)d(op)s(erator)1238 3969 y
Ft(H)1319 3984 y Fq(g)1386 3969 y Fw(=)e Ft(K)h Fr(\012)23
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b(e)33 b(assume)g(that)1260 4568 y(sup)1314 4647 y Fq(x)1424
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4568 y Fw(\()p Ft(k)s Fw(\))p Fr(j)1847 4527 y Fp(2)1902
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Fp(2)1964 4933 y Fm(Z)2080 5068 y Ft(dk)2211 5001 y Fr(j)p
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39 38 bop 120 -200 a Fs(F)n(GSc)n(h,)24 b(30/Mar/01|Asymptotic)h
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%%Page: 40 40
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%%Page: 41 41
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4190 y(\014)1304 4214 y Fw(=)1408 4070 y Fm(\014)1408
4130 y(\014)1408 4190 y(\014)1408 4249 y(\014)1441 4079
y(Z)1557 4214 y Ft(dk)p 1662 4124 217 4 v 3 w(f)1721
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Fw(\))p Ft(e)2148 4173 y Fq(i)p Fn(j)p Fq(k)r Fn(j)p
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%%Page: 43 43
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%%Page: 46 46
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%%Page: 50 50
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%%Page: 51 51
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b(completeness)i(for)f(Ra)m(yleigh)f(scattering.)42 b
Fu(J.)34 b(Math.)h(Phys.)p Fw(,)562 875 y(38\(5\):2281{2296,)30
b(1997.)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF
---------------0103301635364--
