Natural Science Forum / Physics / Research / June 2007

Dear SPR friends:
I am writing to clarify my understanding of what is meant when people
talk about "virtual particles" and their related propagators.
Insofar as I understand the use of this term, it refers to a particle

Can someone please straighten me out on the meaning of C^(infinity)
functions, as applied in describing maps among subsets of R^n?
Specifically, on pg. 12 of Wald's "General Relativity" (1984), and on
pgs. 49-52 of Flanders' "Differential Forms with Applications to the

I am interest to study how the exciton being created inside the
material, such as organic semiconductor. Could anyone explain this to
me? Or do you have any idea that which subjects should be looking at,
to comprehend the knowledge more efficiently?

Using $ to designate "integral from -infinity to + infinity," the
Gaussian integral:
$dx e^(-.5Ax^2)  (1)
is of course central to Quantum Field Theory, Fourier transforms, etc.

Symplectic structure vs. metric structure
A question about the relationship between the phase space of the  
Hamiltonian formulation of classical mechanics and of the Lagrangian  
formulation; that is, between the cotangent bundle of configuration  

I am looking for a value and a reference for the energy of the
chemical bonds in sapphire (alpha-Al2O3).  Apparently, the bond is a
mix of ionic and covalent, and there is data on bonding things to
sapphire, but I can't find anything for bonds in the sapphire itself.

I have a question about Gaussian integrals and path integrals.  In the
below, I use $ to designate "integral from negative infinity to positive
infinity."  I am concerned here only with J=0.
The basic Gaussian integral used in QFT, for J=0, is:

Rovelli made a big deal about the hole paradox in his 2004 quantum
gravity book. He insisted on taking the tack that this leads
invariably to the notion that after you take out gravity, there's

On Jun 9, 5:58 pm, Jack Sarfatti <sarfa...@pacbell.net> wrote:

Newtonian Physics; Galilei group -- 11 parameters.

Penrose's treatment (through null tetrads) leads to an explicit set of
equations useful for calculations. The one thing, however, that has
put me (and undoubtedly a large number of other people) is its seeming
arcane nature. Over time, it's almost certain that the coefficients

In classical EM theory if a plane EM wave moves in direction (+x) E,M
are perpendicular to x.
Let's have an electron in x1. The force would be eE and the electron
moves (becomes an impulse) preferably perpendicular to x. Preferably

There is controversy as to whether depleted uranium is a health risk.
Am I correct in thinking that with a half life of 4.5 billion years
that depleted uranium would not be radioactive enough to be a
radiation risk?   If so, then perhaps the effects are due to heavy

Writing the Legendre polynomials as P(n,x)
with n a non-negative integer and x ranging from
-1 to 1,  and a prime, ', denoting differentiation with
respect to x, I have four integrals involving the P(n,x).

Been doing some reading on permeability lately... My question is would
the permeability of free space (u0) be related in any way to the
vacuum
energy density or would it remain the same regardless (4PIx10-7)?

What is the current thinking as to the value of the cosmological constant
given the most recent observations of the universe expansion?