Cinquero
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marcus said:do I need to be more rigorous and formal, and spell this out in more detail?
or is this OK?
No, it's ok. Thx!
marcus said:do I need to be more rigorous and formal, and spell this out in more detail?
or is this OK?
...
...this is part of an overview.
what I have to explain is how they set up one of these layered triangulated geometries----and how they then shuffle the cards so as to get a series of random geometries. this is the nutsandbolts part.
a 4-simplex is the 4D analog of a triangle and they build these appoximate piecewise flat geometries out of two TYPES of 4-simples, the
"level"-kind and the "tilt"-kind
they call them the (4,1) kind and the (3,2) kind. it is how the vertices are destributed between two causal layers
I have to balance giving an overview with giving some introductory nutsandbolts.
Is there a general theorem available for that purpose? I believe to remember that the mathematics behind that is usually quite non-obvious.marcus said:YOU CAN GET FROM ONE SET OF WEIGHTS TO THE OTHER SET OF WEIGHTS by the simple expedient of changing the eye into a minus sign, or the minus into an eye. this is called the WICK ROTATION, in honor of Joe Wick born in Torino around 1906.
So Wick rotation = analytic continuation?selfAdjoint said:It's a procedure in complex variables, called analytic continuation.
Cinquero said:So Wick rotation = analytic continuation?
selfAdjoint said:You have the integrals defined on the real axis, corresponding to Minkowski space, but they don't converge there, because they have factors like e^{ut}, which is unbounded as t goes to infinity. They are howeve analytic in the half plane above the real axis, and by continuation therefore on the imaginary axis, which correspond to i\tau = t, or euclidean four space. Then the integrals convege because the factors now read e^{ui\tau} which is bounded for all tau. Then after you evaluate the integrals (they mostly reduce to a gaussian quadrature) you can rotate back.
CarlB said:...
Stephen Hawking's latest paper uses "Euclidean Quantum Gravity":
http://arxiv.org/PS_cache/hep-th/pdf/0507/0507171.pdf
Does EQG have anything to do with LQG? My field is elementary particles, not gravitation. Sorry for the laziness. Hawking references a book I don't have immediate access to.
Carl
Cinquero said:Actually, mys request for hyperlinks was in regard to:
"Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity"
:)
For continuity I tried the same check today. This is now the papers November thru October, year by year, with any of the same keywords in the abstract.I'll be glad to try. The main thing is just to have a fixed set of keywords you can apply year by year, to get the trend in papers with those keywords.
In accordance with your suggestion, I checked how many papers were published each year (October thru September) with the words "brane" or "M-theory" or "AdS/CFT" or "superstring" or "heterotic" in the abstract.
Code:2001 1202 2002 1097 2003 970 2004 959
2001 1220
2002 1083
2003 972
2004 938
2001 98
2002 121
2003 140
2004 184
marcus said:...
Last month at selfAdjoint's suggestion I included "heterotic, superstring" in the list of keywords and did a search using the Harvard ADS abstract service engine.
https://www.physicsforums.com/showthread.php?p=789185#post789185
For continuity I tried the same check today. This is now the papers November thru October, year by year, with any of the same keywords in the abstract.
Code:2001 1220 2002 1083 2003 972 2004 938
... it NOT AS A SIGN THAT ONE THING IS RIGHT AND ANOTHER WRONG but that for whatever reason people are branching out in more directions, and trying non-string ones.
...
2001 1204
2002 1188
2003 1081
2004 1012
2005 843
marcus said:Early in 2005, Freidel and Livine posted
http://arxiv.org/abs/hep-th/0502106
Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
Laurent Freidel, Etera R. Livine
46 pages
"We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators"
...
Sauron said:Sorry by the slight off-topic.
I am currently reading the complete thread "intuitive content of loop..." that i had followed discontinously until now.
These one seems to be much of the same stuff ¿Why two duplicate threads?
¿Are topics covered here and uncovered in the other?