markwh04@yahoo.com
Jun29-07, 05:04 AM
Part III: The Problem and its Resolution are Rooted in Classical
Physics
Continuing from the previous article:
On May 1, 9:40 pm, markw...@yahoo.com wrote:
> Part 2: The Generalized Principle of Relativity
> The upshot of what's to follow is that the solution to the ultraviolet
> divergence problem is that:
> * There are no quadratic couplings in the field Lagrangian at all.
> * Correspondingly, the field law is not linear, except asymptotically.
> * The couplings are all at least cubic and only asymptotically quadratic.
> * The free field propagators are therefore only valid as asymptotic approximations.
> * Combined with the generalized connection that mediates velocity-
> momenta relations, this produces a total space metric in the spirit of
> Kaluza-Klein.
An interesting result occurs when you actually carry out this
exercise: the qualitative features associated with the renormalized
couplings in gauge theory are reproduced at the classical level --
including the Landau pole, the screening/anti-screening modes, even a
confinement phase.
However at the classical level (within the particular model adopted
here) there is no restriction on which modes occur with which
Lagrangian theories. The modes investigated are those for
electromagnetism; and all 3 phases occur, including a confinement
mode.
What is interesting about the dynamics is that even though its
governing equations bear a superficial resemblance and behavior to
what you'd expect to see arising out of a quantum theory of gravity or
other quantum dynamics at the Planck scale, they are rooted firmly in
CLASSICAL physics!
The equation that emerges for the fine structure constant is the most
interesting one of all:
d^2(alpha)/du^2 = 3A alpha
for a point-like source, where A is the Planck area, and u = 1/r.
Despite appearances, this is NOT an equation of quantum gravity nor
(for that matter) even one residing in quantum physics! The
occurrences of Planck's constants cancel (alpha = e^2/(4 pi epsilon h-
bar c), A = (h-bar G/c^3).
Rather, what it is -- is a non-trivial feature of electro-
gravitational unification.
This article is not yet completely written out (particularly the
treatment of propagators, loop integrals and the renormalization group
equation), but I've included enough details to convey both the basic
idea and the broad generality of its range of application.
Curing the UV Divergence
http://federation.g3z.com/Physics/index.htm#CuringUV
Blurb:
In this article, the fundamental elements of a comprehensive
resolution to the ultraviolet divergence problem in both classical and
quantum field theory are presented. The central theme of this
resolution is that both the problem and its resolution are firmly
rooted in classical physics and do not involve the consideration of
any prospective theory of "quantum gravity".
Physics
Continuing from the previous article:
On May 1, 9:40 pm, markw...@yahoo.com wrote:
> Part 2: The Generalized Principle of Relativity
> The upshot of what's to follow is that the solution to the ultraviolet
> divergence problem is that:
> * There are no quadratic couplings in the field Lagrangian at all.
> * Correspondingly, the field law is not linear, except asymptotically.
> * The couplings are all at least cubic and only asymptotically quadratic.
> * The free field propagators are therefore only valid as asymptotic approximations.
> * Combined with the generalized connection that mediates velocity-
> momenta relations, this produces a total space metric in the spirit of
> Kaluza-Klein.
An interesting result occurs when you actually carry out this
exercise: the qualitative features associated with the renormalized
couplings in gauge theory are reproduced at the classical level --
including the Landau pole, the screening/anti-screening modes, even a
confinement phase.
However at the classical level (within the particular model adopted
here) there is no restriction on which modes occur with which
Lagrangian theories. The modes investigated are those for
electromagnetism; and all 3 phases occur, including a confinement
mode.
What is interesting about the dynamics is that even though its
governing equations bear a superficial resemblance and behavior to
what you'd expect to see arising out of a quantum theory of gravity or
other quantum dynamics at the Planck scale, they are rooted firmly in
CLASSICAL physics!
The equation that emerges for the fine structure constant is the most
interesting one of all:
d^2(alpha)/du^2 = 3A alpha
for a point-like source, where A is the Planck area, and u = 1/r.
Despite appearances, this is NOT an equation of quantum gravity nor
(for that matter) even one residing in quantum physics! The
occurrences of Planck's constants cancel (alpha = e^2/(4 pi epsilon h-
bar c), A = (h-bar G/c^3).
Rather, what it is -- is a non-trivial feature of electro-
gravitational unification.
This article is not yet completely written out (particularly the
treatment of propagators, loop integrals and the renormalization group
equation), but I've included enough details to convey both the basic
idea and the broad generality of its range of application.
Curing the UV Divergence
http://federation.g3z.com/Physics/index.htm#CuringUV
Blurb:
In this article, the fundamental elements of a comprehensive
resolution to the ultraviolet divergence problem in both classical and
quantum field theory are presented. The central theme of this
resolution is that both the problem and its resolution are firmly
rooted in classical physics and do not involve the consideration of
any prospective theory of "quantum gravity".