Questions about Path Intergral for Lagrangian Density = 0
- From: "Jay R. Yablon" <jyablon@xxxxxxxxxxxx>
- Date: Fri, 29 Feb 2008 08:58:43 -0500
I have a question: Consider the path integral:
Z = DA exp[-iS(A)] = C exp [iW(J)]
where S(A) = $d^4x L.
Above, the field variable is A, the source of the field is J, the
amplitude is W(J), the action is S(A), the Lagrangian density is L, and
C is an overall product factor independent of J and often containing a
product of inverse determinants.
Let's posit that L=0, everywhere. We take that as a supposition.
Perhaps 0 = some other expression involving the sources and fields, but
nonetheless, this expression L is always = 0.
Would the following deductions be true / permissible?
1) S(A) = 0, because the integral over a volume of anything which is
zero, is itself zero. No constants of integration come into play. For
example, thinking about Maxwell's equations in integral form, if there
is a three volume within which the charge is zero everywhere, then the
total enclosed charge is zero.
if 1) is true, then:
2) Z = DA, because exp[-iS(A)] = 1
if 2) is true, then:
3) given Z=DA, we can select C such that DA = C. Then, exp [iW(J)] =1.
if 3) is true, then
4) W(J) = 2pi n and so is quantized.
Please evaluate and advise if there is any flaw in this logic.
Thanks,
Jay.
____________________________
Jay R. Yablon
Email: jyablon@xxxxxxxxxxxx
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm
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