```
----------------------------------------------------------------------------
Six fundamental paramters:  h (action quantum)
c ("coupling" of space to time & mass to energy)
k (coupling of geometry to stress-E-p,
field to mass)
e (electron charge)

n (size)
N (Max. particle number)

NB: While GR is metrical, EM is topological; both are "gauge fields"

a (fine structure) = (e^2 c)/(4 pi h) = 1/137.036
----------------------------------------------------------------------------
I Single Particle (N = 1)

RELATIVISTIC - NONGRAVITATIONAL (k=0)
|------------------------------------------------------------|
Q | RFCCR(n)           | RQM                | SR               | N
U | k=0                | k=0                | h=0, k=0         | E
A | high temp.         |                    |                  | W
N |                    |                    |                  | T
T |                    |                    |                  | O
U |                    |                    | ISO(3,1)         | N
M |------------------------------------------------------------| I
| FCCR(n)            | QM                 | CM               | A
| low temp.          |    1/c=0, k=0      | h=0, 1/c=0, k=0  | N
|                    |                    |                  |
|                1/n -> 0               h -> 0               |
| G(n)<->SU(n-1, 1)  |                    |                  |
| SU(n+1)/SU(n)=P(n) |                    |                  |
--------------------------------------------------------------
[SU(n-1, 1)/S(U(n) X U(1)) = H(n-1) : complex hyperbolic space]
[SU(n)/SU(n-1) = P(n-1) : complex projective space]

RELATIVISTIC - GRAVITATIONAL (k!=0)
|------------------------------------------------------------|
Q | RFCCRG(n): QG(n)   | GQM                | GR               | N
U | high temp.         |                    | h=0              | E
A | Big Bang           |                    |                  | W
N |                    |                    |                  | T
T |                    |                    |                  | O
U |                    |                    |                  | N
M |------------------------------------------------------------| I
| FCCRG(n) : QG(n)   | QMG                | CMG              | A
| low temp.          |    1/c=0,          | h=0, 1/c=0,      | N
|                    |                    |                  |
|                1/n -> 0               h -> 0               |
| G(n)<->SU(n-1, 1)  |                    |                  |
| SU(n+1)/SU(n)=P(n) |                    |                  |
--------------------------------------------------------------
[SU(n-1, 1)/S(U(n) X U(1)) = H(n-1) : complex hyperbolic space]
[SU(n)/SU(n-1) = P(n-1) : complex projective space]

II Many Particles (N)

RELATIVISTIC - NONGRAVITATIONAL (k=0)
|------------------------------------------------------------|
Q | RFCCR(n)           | RQM                | SR w/ Bernoulli? | N
U | k=0                | k=0                | h=0, k=0         | E
A | high temp.         |                    |                  | W
N |                    |                    |                  | T
T |                    |                    |                  | O
U |                    |                    |                  | N
M |------------------------------------------------------------| I
| FCCR(n)            | QM                 | CM w/ Bernoulli? | A
| low temp.          |    1/c=0, k=0      | h=0, 1/c=0, k=0  | N
|                    |                    |                  |
|                1/n -> 0               h -> 0               |
|                    |                    |                  |
|                    |                    |                  |
--------------------------------------------------------------

RELATIVISTIC - GRAVITATIONAL (k!=0)
|------------------------------------------------------------|
Q | RFCCRG(n): QG(n)   | GQM                | GR               | N
U | high temp.         |                    | h=0              | E
A | Big Bang           |                    |                  | W
N |                    |                    |                  | T
T |                    |                    |                  | O
U |                    |                    |                  | N
M |------------------------------------------------------------| I
| FCCRG(n)           | QMG                | CMG              | A
| low temp.          |    1/c=0,          | h=0, 1/c=0,      | N
|                    |                    |                  |
|                1/n -> 0               h -> 0               |
|                    |                    |                  |
|                    |                    |                  |
--------------------------------------------------------------

III Infinite Particles (1/N = 0) Approximation by continuum
NB: limits of full finite theories may not exist, as they are unphysical
E.g., FCCR phase operator has no operator limit.

RELATIVISTIC - NONGRAVITATIONAL (k=0)
|------------------------------------------------------------|
Q | RFCCR(n)           | RQM                | SR w/ Boltzman   | N
U | k=0                | k=0                | h=0, k=0         | E
A | high temp.         |                    |                  | W
N |                    |                    |                  | T
T |                    |                    |                  | O
U |                    |                    |                  | N
M |------------------------------------------------------------| I
| FCCR(n)            | QM                 | CM w/ Boltzman   | A
| low temp.          |    1/c=0, k=0      | h=0, 1/c=0, k=0  | N
|                    |                    |                  |
|                1/n -> 0               h -> 0               |
|                    |                    |                  |
| "vacuum"           |                    |                  |
--------------------------------------------------------------

RELATIVISTIC - GRAVITATIONAL (k!=0)
|------------------------------------------------------------|
Q | RFCCRG(n): QG(n)   | GQM                | GR               | N
U | high temp.         |                    | h=0              | E
A | Big Bang -PhotNeuto|                    |                  | W
N | particle phase 'e' |                    |                  | T
T | atomic phase       |                    |                  | O
U | molec. phase       |                    |                  | N
M |------------------------------------------------------------| I
| FCCRG(n)           | QMG                | CMG              | A
| low temp.          |    1/c=0,          | h=0, 1/c=0,      | N
|                    |                    |                  |
|                1/n -> 0               h -> 0               |
|                    |                    |                  |
| "vacuum" (flat)    |                    |                  |
--------------------------------------------------------------

TOC

Footnotes

1.

2.

3.

Physics Pages

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Email me, Bill Hammel at

bhammel@graham.main.nc.us

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Created: December 9, 2004

Last Updated:

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