Re: Questions about Path Intergral for Lagrangian Density = 0

On Feb 29, 8:58 am, "Jay R. Yablon" <jyab...@xxxxxxxxxxxx> wrote:
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.

What is the gradient of a volume that has no charge at
any point within the volume?

http://personal.ee.surrey.ac.uk/Personal/D.Jefferies/emant.html

Sue...



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: jyab...@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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