Alfred Einstead
May11-04, 05:09 AM
<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>"Hatim Hegab" <htm_00@hotmail.com> wrote:\n> Can someone here give me a good idea about Higgs theory?, or provide me with\n> some sites that can help?\n\nIt\'s a way of explaining away mass dynamically. So the "m"\'s\nin the Lagrangian are then not constants but actually fields --\nin fact, the same field multiplied by different coupling constants\nfor each type of particle. The field is permanently turned on by\na negative potential energy (negative, that is, relative to the\npotential when the field is turned off). So, if H is the magnitude\nof the field, the potential would be something like:\nk (H^2 - v^2)^2.\n\nRelative to the condition where H is turned off, H = 0, in which\nthe potential is\nk v^4,\nthe potential of the field in the on state will be:\nk (H^2 - v^2)^2 - k v^4\n= k H^4 - 2kv^2 H^2.\n\nThe minimum value, of course, is given by H^2 = v^2. So, it\nfluctuates around the value v, taking on the form\nH = v U chi\nwhere U is a unitary matrix and chi a (arbitrarily chosen) unit\nvector.\n\nAll of this should bother people, because General Relativity says\nthat mass is gravitational charge. If the Higgs is producing mass,\nthen isn\'t it also directly linked to the gravitational field?\n\nIn fact, you can answer this in part, by looking at how the Higgs\nwould act if the world were classical instead of quantum theoretic.\n\nMore interesting is what the Higgs mechanism would look like for\nclassical point particles. In this case, the Lagrangian has the\nform:\nL = m/2 v^2 = m/2 sum (g_{ij} u^i u^j\nwhere\nu^i = d(x^i)/dt\ni = 0,1,2,3\nt = proper time\ng_{ij} = spacetime metric.\n(Which, in fact, yields the geodesic law of motion in a\ngeneral relativistic context).\n\nInterestingly, also, this Lagrangian breaks down when the particle\nis massless -- even though its equations of motion reduce to those\nfor a massless particle, when the limit m -> 0 is taken of them.\n\nBut if one starts out assuming, as above, that mass is dynamically\ngenerated by the Higgs, you\'re starting with massless particles.\n\nUsing the prescription outlined above, the mass is treated as\nthe field, itself, up to a coupling constant. So, it is replaced\nby a coupling constant g = (m/v) multiplied by the field H:\nL = 1/2 g sum (H g_{ij} u^i u^j)\n= 1/2 g sum (H_{ij} u^i u^j)\nwhere\nH_{ij}(x) = H(x) g_{ij}(x).\n\nBasically, what this does is introduce an extra degree of symmetry:\nscale symmetry. So, the Higgs field can be thought of as the\nscale part of a scale-invariant metric, the metric g_{ij} being\nthe rest of the metric, and the potential k(H^2 - v^2)^2 forcing\nH to remain in a permanently turned on state around the value\nH = v; thus breaking scale symmetry.\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>"Hatim Hegab" <htm_00@hotmail.com> wrote:
> Can someone here give me a good idea about Higgs theory?, or provide me with
> some sites that can help?
It's a way of explaining away mass dynamically. So the "m"'s
in the Lagrangian are then not constants but actually fields --
in fact, the same field multiplied by different coupling constants
for each type of particle. The field is permanently turned on by
a negative potential energy (negative, that is, relative to the
potential when the field is turned off). So, if H is the magnitude
of the field, the potential would be something like:
k (H^2 - v^2)^2.
Relative to the condition where H is turned off, H = 0, in which
the potential is
k v^4,
the potential of the field in the on state will be:
k (H^2 - v^2)^2 - k v^4= k H^4 - 2kv^2 H^2.
The minimum value, of course, is given by H^2 = v^2. So, it
fluctuates around the value v, taking on the form
H = v U \chi
where U is a unitary matrix and \chi a (arbitrarily chosen) unit
vector.
All of this should bother people, because General Relativity says
that mass is gravitational charge. If the Higgs is producing mass,
then isn't it also directly linked to the gravitational field?
In fact, you can answer this in part, by looking at how the Higgs
would act if the world were classical instead of quantum theoretic.
More interesting is what the Higgs mechanism would look like for
classical point particles. In this case, the Lagrangian has the
form:
L = m/2 v^2 = m/2 sum (g_{ij} u^i u^j
where
u^i = d(x^i)/dti = 0,1,2,3
t = proper time
g_{ij} = spacetime metric.
(Which, in fact, yields the geodesic law of motion in a
general relativistic context).
Interestingly, also, this Lagrangian breaks down when the particle
is massless -- even though its equations of motion reduce to those
for a massless particle, when the limit m -> is taken of them.
But if one starts out assuming, as above, that mass is dynamically
generated by the Higgs, you're starting with massless particles.
Using the prescription outlined above, the mass is treated as
the field, itself, up to a coupling constant. So, it is replaced
by a coupling constant g = (m/v) multiplied by the field H:
L = 1/2 g sum (H g_{ij} u^i u^j)= 1/2 g sum (H_{ij} u^i u^j)
where
H_{ij}(x) = H(x) g_{ij}(x).
Basically, what this does is introduce an extra degree of symmetry:
scale symmetry. So, the Higgs field can be thought of as the
scale part of a scale-invariant metric, the metric g_{ij} being
the rest of the metric, and the potential k(H^2 - v^2)^2 forcing
H to remain in a permanently turned on state around the value
H = v; thus breaking scale symmetry.
> Can someone here give me a good idea about Higgs theory?, or provide me with
> some sites that can help?
It's a way of explaining away mass dynamically. So the "m"'s
in the Lagrangian are then not constants but actually fields --
in fact, the same field multiplied by different coupling constants
for each type of particle. The field is permanently turned on by
a negative potential energy (negative, that is, relative to the
potential when the field is turned off). So, if H is the magnitude
of the field, the potential would be something like:
k (H^2 - v^2)^2.
Relative to the condition where H is turned off, H = 0, in which
the potential is
k v^4,
the potential of the field in the on state will be:
k (H^2 - v^2)^2 - k v^4= k H^4 - 2kv^2 H^2.
The minimum value, of course, is given by H^2 = v^2. So, it
fluctuates around the value v, taking on the form
H = v U \chi
where U is a unitary matrix and \chi a (arbitrarily chosen) unit
vector.
All of this should bother people, because General Relativity says
that mass is gravitational charge. If the Higgs is producing mass,
then isn't it also directly linked to the gravitational field?
In fact, you can answer this in part, by looking at how the Higgs
would act if the world were classical instead of quantum theoretic.
More interesting is what the Higgs mechanism would look like for
classical point particles. In this case, the Lagrangian has the
form:
L = m/2 v^2 = m/2 sum (g_{ij} u^i u^j
where
u^i = d(x^i)/dti = 0,1,2,3
t = proper time
g_{ij} = spacetime metric.
(Which, in fact, yields the geodesic law of motion in a
general relativistic context).
Interestingly, also, this Lagrangian breaks down when the particle
is massless -- even though its equations of motion reduce to those
for a massless particle, when the limit m -> is taken of them.
But if one starts out assuming, as above, that mass is dynamically
generated by the Higgs, you're starting with massless particles.
Using the prescription outlined above, the mass is treated as
the field, itself, up to a coupling constant. So, it is replaced
by a coupling constant g = (m/v) multiplied by the field H:
L = 1/2 g sum (H g_{ij} u^i u^j)= 1/2 g sum (H_{ij} u^i u^j)
where
H_{ij}(x) = H(x) g_{ij}(x).
Basically, what this does is introduce an extra degree of symmetry:
scale symmetry. So, the Higgs field can be thought of as the
scale part of a scale-invariant metric, the metric g_{ij} being
the rest of the metric, and the potential k(H^2 - v^2)^2 forcing
H to remain in a permanently turned on state around the value
H = v; thus breaking scale symmetry.