Article View: fj.sci.math
Article #13602Re: infinite?
From: Masaki OSHIKAWA
Date: Tue, 13 Aug 1996 00:00
Date: Tue, 13 Aug 1996 00:00
134 lines
6326 bytes
6326 bytes
$B2!@n$G$9!#(B $BJ*M}$K$b4X78$7$^$9$N$G!"$=$C$A$K$b$U$j$^$9!#(B In article <4updsp$516@ns2.nisiq.net> pro00003@nisiq.net writes: $BD;1[(B@$BD;1[0e1!!'2,;38)0f86;T$G$9!#(B $B#H(B8/8/13$B$N(B fj.sci.math $B$XEj9F$7$?$b$N$G$9!#(B $BFbMF$N0lIt$O0J2<$NMM$G$9!#(B (1)$B!&!&!&L58BOB!a#1!\#2!\#3!\!&!&!&!a!]#1!?#1#2(B (2)$B!&!&!&L58B@Q!a#1!_#2!_#3!_!&!&!&!a%k!<%H#2&P(B $B$K$D$$$F!"$I$&$$$C$?463P$GM}2r$7$?$i$$$$$N$+!"C/$+J,$+$j$d$9$/65$($F!)(B $B$H$$$&Ej9F$N$D$b$j$G$7$?!#(B $B$H$$$&$3$H$@$C$?$N$G!"$"$i$?$a$F$b$&0lEYEj9FCW$7$^$9!#(B $BF|7P%5%$%(%s%9(B $B#1#9#9#4G/#67n9f!"?t$+$i8+$??t3X$NE83+!J9u@n=E?.!K$K%<!<%?(B $B4X?t$H$$$&$N$,=P$FMh$F!"$=$NCf$G(B $BL58B$N@Q$HOB!&%<!<%?@55,2=@Q$N#1#0#0G/!&!&!&2?$F!"=q$$$F$"$C$F(B $B>e$N!J(B1$B!K!&!J(B2$B!K$,=P$F$-$^$9!#(B $B>.@8$bEvA3L58B$KH/;6$9$k$N$,<+L@$H;W$&$N$G$9$,!&!&!&(B $B$b$A$m$s>e$NOB!?@Q$rIaDL$KDj5A$9$k$HH/;6$7$^$9!#(B $B?t3X<T$,$d$k$N$O!"Nc$($P(B(1)$B$K$D$$$F(B $B$^$:(B zeta $B4X?t$r(B zeta(s) = 1/1^s + 1/2^s + 1/3^s + 1/4^s + ...... $B$H$$$&L58BOB$GDj5A$7$^$9!#(B $B$9$k$H!"(Bzeta(s) $B$O(B s $B$N<BIt$,(B 1$B$h$jBg$-$$;~$K$O<}B+$7$F!"(B $B$"$k(B($BJ#AG2r@O(B)$B4X?t$rDj$a$^$9!#(B (1)$B$N5i?t$O7A<0E*$K(B zeta(-1) $B$H$J$j$^$9$,!"$b$A$m$s$3$N5i?t$OH/;6$7$F$$$k!#(B $B$?$@!"(Bzeta(s) $B$O(B s$B$N<BIt$,(B1 $B$h$jBg$-$$;~$K$O$-$A$s$H7h$^$C$F$$$k$N$G!"(B zeta(s)$B$,A4$F$NJ#AG?t(B s $B$K$D$$$F2r@OE*$K$J$k$h$&$K(B $B2r@O@\B3$H$$$&<jB3$-$G(B zeta(s)$B$r7h$a$k;v$,=PMh$^$9!#(B $B$=$&$d$C$F2r@O@\B3$G7h$a$?(B zeta(-1) $B$,(B -1/12 $B$K$J$k$H8@$&Lu$G$9!#(B $B$b$72r@O@\B3$J$I$4B8CN$G$J$1$l$P$=$l$r@bL@$7$J$$$H$$$1$J$$$N$G$9$,!"(B $B$A$g$C$H(B $BNL$,B?$/$J$j$^$9$N$GJ#AG2r@O$NK\$J$I$_$FD:$1$k$H9,$$$G$9!#(B $B<B$O>e$NH/;6$9$kL58BOB$N!VCM!W$OJ*M}E*$K$b=EMW$G$9!#(B $B!V%$%a!<%8!W$r$*5a$a$H$$$&$3$H$J$N$G!"$=$l$r>/$7@bL@$7$^$9!#(B $BNc$($P!"4JC1$N$?$a0l<!85$N6u4V$@$19M$($k;v$K$7$F!"(B $B4V3V(B L $B$G6bB0$rCV$$$?$H$7$^$7$g$&!#(B $B$=$&$9$k$H!"$=$N4V$KD9$5(B L $B$N??6u$,$"$j$^$9!#(B $B6bB0$N$H$3$m$GEE<'>l$K$D$$$F8GDjC<$N6-3&>r7o$,CV$+$l$^$9$N$G!"(B $BEE<'>l$K$D$$$F$O(B 1/L $B$N@0?tG\$N?6F0?t$7$+5v$5$l$^$;$s!#(B $BNL;RNO3X$K$h$k$H!"??6u(B($B%(%M%k%.!<$N:G$bDc$$>uBV(B)$B$G$b(B $B3F?6F0?t$N%b!<%I$O?6F0?t(B * Planck $BDj?t(B / 2 $B$N$$$o$f$k%<%mE@%(%M%k%.!<$r;}$A$^$9!#(B $BDj?t$r4JC1$N$?$aMn$7$^$9$H!"A4$F$N%b!<%I$N4sM?$+$iD9$5(BL $B$N??6u$O(B 1/L + 2/L + 3/L + 4/L + ....... $B$H$$$&%<%mE@%(%M%k%.!<$r;}$A$^$9!#(B $B$3$l$O(B $B>e$N(B(1)$B$N(B1/L$BG\$HF1$8$G$9$M!#(B $B$D$^$j!"??6u$OL58BBg$N%<%mE@%(%M%k%.!<$r;}$C$F$$$k;v$K$J$j$^$9!#(B $BDL>o!"$3$l$OL58BBg$@$1$I$$$D$bB8:_$9$k$N$G<N$F$F$7$^$&$N$G$9$,!"(B L $B$,JQ2=$7F@$k>l9g$K$OLdBj$K$J$j$^$9!#(B $B$=$3$G$b$&>/$7Cm0U?<$/$d$C$F$_$^$7$g$&!#(B $B:#$N$^$^$G$OH/;6$7$F$$$k$N$G$9$,!"2f!9$OL58B$K9b$$%(%M%k%.!<$N(B $B$H$3$m$^$GM}O@$r3N$+$a$?$o$1$G$O$J$$$N$G!"(B $B$I$3$+Hs>o$K9b$$%(%M%k%.!<(B C $B$NJU$j$G%<%mE@%(%M%k%.!<$,(B $B$J$/$J$k!"$H$7$^$7$g$&!#Nc$($P(B $B?6F0?t(B w $B$N%b!<%I$O(B w e^(-w/C) $B$N%<%mE@%(%M%k%.!<$r;}$D$H$7$^$9!#(B w << C $B$G$O(B $BA0$HF1$8!"(B w>>C $B$G$O%<%m$K$J$j$^$9!#(B $B!t$3$NJU$O0l8+$$$$2C8:$K7h$a$F$$$k$h$&$G$9$,!"B>$N$d$jJ}$r(B $B!t$7$F$b7k2L$OF1$8$K$J$j$^$9!#(B $B$9$k$H!"??6u$N%<%mE@%(%M%k%.!<$O(B 1/L e^(-1/(CL)) + 2/L e^(-2/(CL)) + ...... $B$H$$$&$3$H$K$J$j$^$9!#(B $B$3$NOB$O<}B+$7$F(B($B=iEyE*$K7W;;$G$-$k(B)$B!"(B1/C $B$GE83+$9$k$H(B L C^2 - 1/(12 L) + O(1/C) $B$H$J$j$^$9!#(B $B$3$3$G!"??6u$N%(%M%k%.!<L)EY$r9M$($k$H!"$3$l$r(B L $B$G3d$C$F(B C^2 - 1/(12 L^2) $B$H$J$j$^$9!#(B $BBh0l9`$O(B L $B$K$h$i$:!">!<j$KF3F~$7$?%Q%i%a!<%?(B C $B$@$1$K$h$C$F$$$^$9!#(B ($B$3$&$$$&$N$r2f!9$O%+%C%H%*%U$H8F$V(B) C $B$rL58BBg$K$9$k$H!"L58BBg$K$J$j$^$9$,$3$NItJ,$O(B L $B$rJQ$($F$b(B $B1F6A$5$l$J$$$N$G!"J*M}$K$O4X78$J$$$H$7$FK:$l$k;v$K$7$^$9!#(B $B!t=ENO$^$G9M$($k$HLdBj$K$J$j$^$9$,!"!"!"!"(B $B$7$+$7!"Bh#29`$O(B $B%+%C%H%*%U$KFHN)$G!"7O$N%5%$%:$K0MB8$9$k$N$G(B $BJ*M}E*$J8z2L$,$"$k$H9M$($i$l$^$9!#(B $B6qBNE*$K$O!"(BL $B$,>.$5$$Dx??6u$N%(%M%k%.!<$ODc2<$9$k!#(B $B!t(B $B$3$N$"$?$j!"$$$o$f$k7+$j9~$_$N9M$(J}$K$J$j$^$9(B $B$9$J$o$A!"(BL $B$,Dc2<$9$k$h$&$K(B $B6bB0$N4V$K$O0zNO$,F/$-$^$9!#(B $B$3$l$r(B Casimir$B8z2L$H8@$$!"<B:]$K4QB,$5$l$F$$$^$9!#(B ($B$D$^$j!"EE<'>l$N%<%mE@%(%M%k%.!<$O<B83E*$K4QB,$G$-$k(B) $B!t<B:]$N6bB0$N>l9g!"(B C $B$O6bB0$N@-<A$G7h$^$kM-8B$NCM$H(B $B!t9M$($k$Y$-$G$7$g$&$,!":#$OCV$$$F$*$-$^$9!#(B $B$5$F!":G=i$K(B zeta $B4X?t$N2r@O@\B3$G(B (1)$B$NL58BOB$r!VDj5A!W(B $B$9$k$H(B -1/12 $B$K$J$j$^$7$?$,!"$3$l$O:#$N%+%C%H%*%U$rF3F~$7$?(B $B7W;;$G(B $BJ*M}E*0UL#$N$"$kBh#29`$r<h$j=P$7$?;v$KAjEv$7$^$9!#(B ($BCM$bF1$8$K$J$k(B) $B$7$?$,$C$F!"(B(1)$B$N$h$&$J0l8+LGCc6lCc$JEy<0$b(B $BJ*M}E*$K$b(B $B0UL#$,$"$k$o$1$G$9!#(B $B>e$N$h$&$J4JC1$J>l9g$K$O%+%C%H%*%U$rF3F~$7$F7W;;$7$F$b(B $B$?$$$7$FLdBj$K$O$J$j$^$;$s$,!"$b$C$HJ#;($J>l9g$K$O(B $BBgJQ$K$J$k$N$G!"(Bzeta$B4X?t$N2r@O@\B3$rMxMQ$7$?(B ($BJ*M}E*0UL#$N$"$kM-8BItJ,$N(B)$B7W;;$,(B $B5;=QE*$KM-MQ$K$J$k$3$H$b$"$j$^$9!#(B $B$3$&$$$&$N$r(B zeta-function regularization$B$H2f!9$O8F$s$G$$$^$9!#(B ($B$b$A$m$s!"%+%C%H%*%U$rF3F~$7$F$b$A$c$s$H$d$l$P7k2L$O(B $BF1$8$K$J$k$O$:(B) -- Masaki OSHIKAWA < oshikawa@physics.ubc.ca > -------------------------------------------------------------------- Dept. of Physics & Astronomy | Phone: (604)822-1383 University of British Columbia | FAX : (604)822-5324 6224 Agricultural Road, |----------------------------------- Vancouver BC V6T 1Z1 CANADA |
Technical Details
Message-ID:
<OSHIKAWA.96Aug14070016@appi.mmm.t.u-tokyo.ac.jp>Path:
arc1-ca.pugleaf.net!unknown!not-for-mailReferences:
<4updsp$516@ns2.nisiq.net>Show Full Headers
Complete Article Headers
X-Google-Language: Japanese,JIS X-Google-Thread: f4956,d027b47b210a68a1,start X-Google-Attributes: gidf4956,public X-Google-Thread: 114713,d027b47b210a68a1,start X-Google-Attributes: gid114713,public From: oshikawa@mmm.t.u-tokyo.ac.jp (Masaki OSHIKAWA) Subject: Re: infinite? Date: 1996/08/13 Message-ID: <OSHIKAWA.96Aug14070016@appi.mmm.t.u-tokyo.ac.jp> X-Deja-AN: 173996428 references: <4updsp$516@ns2.nisiq.net> organization: Dept. of Applied Physics, University of Tokyo newsgroups: fj.sci.math,fj.sci.physics