very_cryptic@hotmail.com
Sep14-04, 12:22 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I\'m kind of suspicious of the textbook derivation of the chiral anomaly\nusing Fujikawa\'s method. On the one hand, textbooks are claiming we\nshouldn\'t use the "direct" functional integral of the action (with the\nfull gauge invariance and without ghosts) because it wouldn\'t make\nsense because of all the divergences of the functional integral and we\nought to use a modified gauge fixed BRST version instead. But on the\nother hand, the same textbooks derive the formula for the chiral\nanomaly using the former functional integral which elsewhere, they\nargued doesn\'t make sense (and only formally agrees with the BRST gauge\nfixed version for the expectation value of gauge invariant quantities,\nand that, only formally!). But the whole point is, the chiral anomaly\nisn\'t a gauge invariant quantity which means we have no a priori reason\nto assume the former functional integral will give the same result as\nthe BRST functional integral. And just how can you perform a gauge\ntransformation upon the BRST gauge fixed version anyway?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I'm kind of suspicious of the textbook derivation of the chiral anomaly
using Fujikawa's method. On the one hand, textbooks are claiming we
shouldn't use the "direct" functional integral of the action (with the
full gauge invariance and without ghosts) because it wouldn't make
sense because of all the divergences of the functional integral and we
ought to use a modified gauge fixed BRST version instead. But on the
other hand, the same textbooks derive the formula for the chiral
anomaly using the former functional integral which elsewhere, they
argued doesn't make sense (and only formally agrees with the BRST gauge
fixed version for the expectation value of gauge invariant quantities,
and that, only formally!). But the whole point is, the chiral anomaly
isn't a gauge invariant quantity which means we have no a priori reason
to assume the former functional integral will give the same result as
the BRST functional integral. And just how can you perform a gauge
transformation upon the BRST gauge fixed version anyway?
using Fujikawa's method. On the one hand, textbooks are claiming we
shouldn't use the "direct" functional integral of the action (with the
full gauge invariance and without ghosts) because it wouldn't make
sense because of all the divergences of the functional integral and we
ought to use a modified gauge fixed BRST version instead. But on the
other hand, the same textbooks derive the formula for the chiral
anomaly using the former functional integral which elsewhere, they
argued doesn't make sense (and only formally agrees with the BRST gauge
fixed version for the expectation value of gauge invariant quantities,
and that, only formally!). But the whole point is, the chiral anomaly
isn't a gauge invariant quantity which means we have no a priori reason
to assume the former functional integral will give the same result as
the BRST functional integral. And just how can you perform a gauge
transformation upon the BRST gauge fixed version anyway?