## Why doesn't statistical mechanics apply for the quantum field

<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>In the standard big bang model we calculate the energy densities due to\nthe standard model fields - photons, electrons, W\'s, Z\'s, quarks, et al\n- with statistical mechanics (from the Bose and Fermi distributions)\nand put our Hubble parameter proportional to the square root of their\nsum.\n\nWhy is it when we do inflation driven by some hypothetical quantum\nfield (i.e. some yet to be observed particle in nature) - aka the\n"inflaton" - we don\'t do the same? It seems that if we do apply stat\nmech then no quantum field can be responsible for inflation?\n\nA slightly more general question is: when should one use statistical\nmechanics for quantum fields (or classical fields)? Does the magnetic\nfield around a very strong magnet (say in that of an MRI machine) have\nsome sort of potential in its lagrangian associated with it? If so does\nthat mean it creates negative pressure too, just like the inflaton\ndoes?\n\nThanks!\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>In the standard big bang model we calculate the energy densities due to
the standard model fields - photons, electrons, W's, Z's, quarks, et al
- with statistical mechanics (from the Bose and Fermi distributions)
and put our Hubble parameter proportional to the square root of their
sum.

Why is it when we do inflation driven by some hypothetical quantum
field (i.e. some yet to be observed particle in nature) - aka the
"inflaton$" - we$ don't do the same? It seems that if we do apply stat
mech then no quantum field can be responsible for inflation?

A slightly more general question is: when should one use statistical
mechanics for quantum fields (or classical fields)? Does the magnetic
field around a very strong magnet (say in that of an MRI machine) have
some sort of potential in its lagrangian associated with it? If so does
that mean it creates negative pressure too, just like the inflaton
does?

Thanks!

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