----------------------------------------------------------------------------
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.
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Created: December 9, 2004
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