Mike Vaughn
Apr7-04, 09:06 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resize=yes,status=no,wi dth=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>In article <c4dtbf$nl1$1\\@glue.ucr.edu>, baez\\@galaxy.ucr.edu (John Baez) wrote:\n\n> In article <c3r931$2b12u1$1\\@ID-193047.news.uni-berlin.de>,\n> Rene Meyer <meyr2\\@web.de> wrote:\n>\n> >I got puzzled about this: Why does one use a Wick-Rotation tau -> itau\n> >in string theory, rather than tau -> -itau? For example, Richard Szabo\n> >does this in his lecture notes.\n>\n> All this stuff is a matter of convention. However, when you make a bunch\n> of interlocking conventions, you can\'t change some without changing others.\n>\n> There\'s a completely arbitrary choice about whether energies should\n> be positive or negative. Most physicists like energies to be positive,\n> for the fairly obvious reason: positive numbers are just simpler.\n\nAlso, having started with kinetic energy = (1/2) mv^2 , we would like to\nhave positive mass everywhere. Simpler? Natural?\n\n> There\'s also an independent completely arbitrary choice about whether\n> time evolution goes like exp(-itH) or exp(itH). For some reason that\'s\n> not so obvious - but is amusing to figure out - most physicists use\n> exp(-itH).\n\nHow do you figure it out? It _is_ convenient in relativistic quantum\nmechanics, having chosen \\exp(ip.x) as the representation for a pane\nwave. but the \\exp(-iHt) may have come before that. (?)\n\n> Having made both of these choices, I\'m pretty sure you\'re locked into\n> a specific convention regarding Wick rotations.\n\nExactly. It is the sign of the \\epsilon ( > 0) in writing a Green function as\n\n(E - H + i\\epsilon)^(-1)\n\nwhich constrains the Wick rotation -- the +i\\epsilon fixes singularities\nin the complex E plane and the Wick rotation of the contour should\nnot move the contour across these singularities.\n\n> So, maybe Szabo changed one of these two choices. I\'d be happy if\n> he did time evolution via exp(itH), since the usual minus sign is a\n> bit of a drag.\n\nThen pretend to be an electrical engineer and call it \\exp(jHt) ;-)\n\n> Or maybe there are some other arbitrary conventions floating around\n> this vicinity, which I\'m forgetting, and he changed one of those.\n> I don\'t know.\n>\n> Someday someone will make a hypercube of all 2^n consistent sign\n> conventions for doing physics, and authors of textbooks will just\n> tell us which one they\'re using. But unfortunately, n is fairly large.\n\n--\nMike Vaughn\n\n"A ship is safe in a harbor --\nBut that is not what ships are built for."\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>In article <c4dtbf$nl1$1@glue.ucr.edu>, baez@galaxy.ucr.edu (John Baez) wrote:
> In article <c3r931$2b12u1$1@ID-193047.news.uni-berlin.de>,
> Rene Meyer <meyr2@web.de> wrote:
>
> >I got puzzled about this: Why does one use a Wick-Rotation \tau -> itau
> >in string theory, rather than \tau -> -itau? For example, Richard Szabo
> >does this in his lecture notes.
>
> All this stuff is a matter of convention. However, when you make a bunch
> of interlocking conventions, you can't change some without changing others.
>
> There's a completely arbitrary choice about whether energies should
> be positive or negative. Most physicists like energies to be positive,
> for the fairly obvious reason: positive numbers are just simpler.
Also, having started with kinetic energy = (1/2) mv^2 , we would like to
have positive mass everywhere. Simpler? Natural?
> There's also an independent completely arbitrary choice about whether
> time evolution goes like \exp(-itH) or \exp(itH). For some reason that's
> not so obvious - but is amusing to figure out - most physicists use
> \exp(-itH).
How do you figure it out? It _is_ convenient in relativistic quantum
mechanics, having chosen \exp(ip.x) as the representation for a pane
wave. but the \exp(-iHt) may have come before that. (?)
> Having made both of these choices, I'm pretty sure you're locked into
> a specific convention regarding Wick rotations.
Exactly. It is the sign of the \epsilon ( > 0) in writing a Green function as
(E - H + i\epsilon)^(-1)
which constrains the Wick rotation -- the +i\epsilon fixes singularities
in the complex E plane and the Wick rotation of the contour should
not move the contour across these singularities.
> So, maybe Szabo changed one of these two choices. I'd be happy if
> he did time evolution via \exp(itH), since the usual minus sign is a
> bit of a drag.
Then pretend to be an electrical engineer and call it \exp(jHt) ;-)
> Or maybe there are some other arbitrary conventions floating around
> this vicinity, which I'm forgetting, and he changed one of those.
> I don't know.
>
> Someday someone will make a hypercube of all 2^n consistent sign
> conventions for doing physics, and authors of textbooks will just
> tell us which one they're using. But unfortunately, n is fairly large.
--
Mike Vaughn
"A ship is safe in a harbor --
But that is not what ships are built for."
> In article <c3r931$2b12u1$1@ID-193047.news.uni-berlin.de>,
> Rene Meyer <meyr2@web.de> wrote:
>
> >I got puzzled about this: Why does one use a Wick-Rotation \tau -> itau
> >in string theory, rather than \tau -> -itau? For example, Richard Szabo
> >does this in his lecture notes.
>
> All this stuff is a matter of convention. However, when you make a bunch
> of interlocking conventions, you can't change some without changing others.
>
> There's a completely arbitrary choice about whether energies should
> be positive or negative. Most physicists like energies to be positive,
> for the fairly obvious reason: positive numbers are just simpler.
Also, having started with kinetic energy = (1/2) mv^2 , we would like to
have positive mass everywhere. Simpler? Natural?
> There's also an independent completely arbitrary choice about whether
> time evolution goes like \exp(-itH) or \exp(itH). For some reason that's
> not so obvious - but is amusing to figure out - most physicists use
> \exp(-itH).
How do you figure it out? It _is_ convenient in relativistic quantum
mechanics, having chosen \exp(ip.x) as the representation for a pane
wave. but the \exp(-iHt) may have come before that. (?)
> Having made both of these choices, I'm pretty sure you're locked into
> a specific convention regarding Wick rotations.
Exactly. It is the sign of the \epsilon ( > 0) in writing a Green function as
(E - H + i\epsilon)^(-1)
which constrains the Wick rotation -- the +i\epsilon fixes singularities
in the complex E plane and the Wick rotation of the contour should
not move the contour across these singularities.
> So, maybe Szabo changed one of these two choices. I'd be happy if
> he did time evolution via \exp(itH), since the usual minus sign is a
> bit of a drag.
Then pretend to be an electrical engineer and call it \exp(jHt) ;-)
> Or maybe there are some other arbitrary conventions floating around
> this vicinity, which I'm forgetting, and he changed one of those.
> I don't know.
>
> Someday someone will make a hypercube of all 2^n consistent sign
> conventions for doing physics, and authors of textbooks will just
> tell us which one they're using. But unfortunately, n is fairly large.
--
Mike Vaughn
"A ship is safe in a harbor --
But that is not what ships are built for."