and in general mathematicians tend to behave like "fermions" i.e. avoid working in areas which are too trendy whereas physicists behave a lot more like "bosons" which coalesce in large packs and are often "overselling" their doings, an attitude which mathematicians despise."
I have to disagree with Connes on this.His statement does not do justice to at least one physicist. Hartland Snyder (Phys.Rev.1947) introduced the idea of non-commutative geometry 50 years before A. Connes. Even before Connes was born, Weyl,,Hiesengerg and Paule spoke about non-commutative spacetime.
By the way, human beings (mathematicians included) behave like bosons with respect to any "profitable" activities. Nothing wrong with this.
As a physicist, I would say to Connes:
Human beings are bosons. They are a classical system.Therefore, they can not behave like fermions.Fermions have no classical limit
Any way, let us move on,this is hardly an issue in this thread.
There are two stages of resummation between the velocity eigenstates and standard physics. Feynman's comments cover one of those two stages, and I'll restrict my comments to that one. Let me quote directly from his popular book:
Carl, Feynman was explaining,to school kids, the first three terms of the perturbation series for the 2-point Green's function.
So, tell me and
show me the math
What is the connection between Feynman's statements(
perturbation theory) and your statements about
defining particles and their
mass?
If you,as you say,
educated in mathematics, then show us:
1) How do you define particles in terms of their position and velocity eigenstates?
2) How can you get mass from your undefined interaction?
I want to see your math.
if you want hints on how to do it with left and right handed (massless) chiral electron states to form them into a single massive electron propagator, just ask and I'll point you in the right direction.
No, I don't want "hints", Prove your claims.
Let me tell you something about propagators.Have you herd about the integral representation of Huygen's principle? Well, it is:
w(c) = Integ.[K(c,a).
w(a)] da.
In QM, we write this as:
<c|
w> = Integ.[<c|a><a|
w>] da.
The Huygen's kernel K(.,.), the transition amplitude from a to c (<c|a>), The Green's function G(x,y), and the matrix element of the time evolution operator(<x|U(t,T)|y>) are names for propagator:
Propagator<x,t|y,T>=G(x,t;y,T)=<x|G(t,T)|y>=<x|exp[iH(T-t)]|y>.
In field theory, the propagator in p-space can be obtained by inverting the Fourier-transformed differential operator contained in the
action integral:
S~
w(x).D(x).
w(x).
Propagator=1/D(k),
or, equivalently, the Fourier-transformed vacuum expectation value of the time-ordered product of fields(2-point Green's function):
<0|:{
w(x)
w(x)}:|0> = G(x,y).
In Feynman diagrams,we assign a propagator to internal lines=virtual particles.
For photons(in Feynman gauge), It is ~1/k^2
For (massless) electrons: ~p/p^2.
***
If you remember, this thread was about the importance of symmetries in physics,your example of symmetry(the Mendeleev table!) made me laugh, then,you made a very strange claim about particles and mass.I had to ask you to prove your claim.You said it is easy! Yet you proved nothing.You didn't write a single equation to support your claim
To make matter worst, you brought about Feynman and his propagator "hint" story,
If I recall correctly, the method is to use propagators of 1/v (in Dirac algebra notation), and vertices of E. The resummation turns this set of Feynman diagrams into a propagator of 1/p.
and,now you say this
Is this meant to be a statement about physics?
Do you,seriously believe, that you could sell such a mumbo-jumbo garbage to me?
Carl, your "physics" painted,for me,the following pictures about you:
1) You didn't understand Feynman.
2) You don't understand propagators.
So, I suggest you leave physics for the professionals.
cheers
sam
