How do I visualize particles?
How do I visualize particles?
Insert: 06 Dec.2008,
08 Jan 2009, 11 April 09
25 May 2009
If you have been reading my blog then you have a pretty good idea.
Perfect Symmetry vs. broken symmetry (CPT)
1. First I realize that what we “see” is an interpretation of what is achieved by experiments
2. Experiments can only “see” a confined proton, neutron, size of approx. 10^-15. The interpretations are the QED of the Standard model .
3. At a smaller scale, QCD, inside the proton, models are still being developed, and tested against the results of experiments. If a physical minimum length, (ie. planck scale), is applied as a condition, then LQG, Lattice QCD etc. which all use a minimum length, would be a more accurate description and you can only get to a 4-Manifold, A3 lattice, a cube.
4. Experiments at high pressure and density have produced a liquid of quark gluon, which is not confined, which can be modeled as a perfect liquid and maybe as perfect symmetry.
For high school students, read my blog and see if there is anything there that you want to use.
======
http://en.wikipedia.org/wiki/Gauge_theory
=========
Read what John Baez has been presenting and see if what I have been saying “rings a bell”.
John Baez, at n-category café has started seminars/lessons on Lie Theory.
http://golem.ph.utexas.edu/category/...es_1.html#more
Lie Theory Through Examples 1
Posted by John Baez
http://golem.ph.utexas.edu/category/...es_2.html#more
Lie Theory Through Examples 2
Posted by John Baez
========
Question:
Could you give your definition of dimension and minimum length as it used for this subject.
Answer:
I’m using the usual definitions of ‘dimension’ and ‘length’ that apply to n-dimensional Euclidean space.
------
Note: That means he is not using minimum length, or Planck length.
------
http://en.wikipedia.org/wiki/Distance
Distance is a numerical description of how far apart objects are
http://en.wikipedia.org/wiki/Metric_(mathematics)
In mathematics, a metric or distance function is a function which defines a distance between elements of a set.
http://en.wikipedia.org/wiki/Dimension
dimension
http://en.wikipedia.org/wiki/Euclidean_space
n-dimensional Euclidean space
=======
Note: If you accept that particles are point like then you can get to E8.
If a physical minimum length, (planck scale), is applied as a condition, then LQG, Lattice QCD etc. which all use a minimum length, would be a more accurate description and you can only get to a 4-Manifold, A3 lattice, a cube.
=========
=====
http://math.ucr.edu/home/baez/qg-fall2008/lie3.pdf
Lie Theory Through Examples 3
========
http://golem.ph.utexas.edu/category/...es_4.html#more
Lie Theory Through Examples 4
========
The A3 lattice concept ....
12 points on those 12 edges of the cube.
By using the concept of minimum length and the definition of a dimension, you can squeeze 4 dimensions with a length of 4 into the same space occupied by 3 dimension.
Then using the concept of a vibrating string you obtain the concept of 12 energy nodes on those edges which produces the cubic lattice and perfect symmetry. Look at the attached picture. synchronization-2.GIF
I assume that before too long, John Baez’s lectures will show if there are errors in my assumptions/thinking that need corrections.
========
Here another interesting image to go with John Baez’ image
from FERMILAB
http://www.fnal.gov/pub/presspass/pr...ega-sub-b.html
Fermilab physicists discover "doubly strange" particle
=========
Another blog reference
http://www.math.columbia.edu/~woit/wordpress/
Not Even Wrong
Notes on BRST I: Representation Theory and Quantum Mechanics
November 5th, 2008
=======
I have been following the following to get a better understanding and to see if I got to change my mind.
http://www.sciencenews.org/view/gene...neutron_masses
Standard model gets right answer for proton, neutron masses
Correct calculation strengthens theory of quark-gluon interactions in nuclear particles
By Ron Cowen
December 20th, 2008; Vol.174 #13 (p. 13)
--------
http://arxiv.org/abs/0807.1610v1
Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
Authors: Reinhard Stock (Physics Department, University of Frankfurt)
(Submitted on 10 Jul 2008)
--------
The key tool enabling this advance is lattice gauge theory (5), a formulation of QCD and similar quantum field theories that replaces space-time with a four-dimensional lattice. To picture the lattice, think of a crystal with cubic symmetry evolving in discrete time steps.
To explore the predictions of QCD in this nonperturbative regime, the most systematic approach is to discretize (3) the above Lagrangian on a hypercubic space-time lattice with spacing a, to evaluate its Green's functions numerically and to extrapolate the resulting observables to the continuum (a0). A convenient way to carry out this discretization is to place the fermionic variables on the sites of the lattice, whereas the gauge fields are treated as 3 x 3 matrices connecting these sites. In this sense, lattice QCD is a classical four-dimensional statistical physics system.
In their calculations, Hoelbling and collaborators approximated the continuum of spacetime with a four-dimensional crystal lattice composed of discrete points spaced along columns and rows. The researchers solved the equations of QCD on finer and finer lattices, and then extrapolated the results to the continuum, painstakingly accounting and measuring every approximation and uncertainty along the way.
Confinement emerges naturally in lattice gauge theory at strong coupling (5). The lattice also reduces everything we would want to calculate to integrals that, in principle, can be evaluated numerically on a computer.
====== inserted 22 Dec
Here are two recent papers working on cubic packing/lattice symmetry. Heck! … Call it what you want.
http://arxiv.org/abs/0812.0713
The relation of a Unified Quantum Field Theory of Spinors to the structure of General Relativity
Authors: Martin Kober
(Submitted on 3 Dec 2008)
======
http://arxiv.org/abs/0812.1537
Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
Authors: C. Flori, T. Thiemann
(Submitted on 8 Dec 2008)
In other words, the semiclassical sector of LQG defined by those states is described by graphs with cubic topology! This has some bearing on current spin foam models which are all based on four valent boundary spin networks.
=====
Here are two more papers.
http://arxiv.org/abs/hep-th/0611042
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
Authors: Aristide Baratin, Laurent Freidel
(Submitted on 3 Nov 2006 (v1), last revised 28 Mar 2007
-------
http://arxiv.org/abs/0812.4055
The Holst Spin Foam Model via Cubulations
Authors: Aristide Baratin, Cecilia Flori, Thomas Thiemann
(Submitted on 21 Dec 2008)
------ 08 Jan 2009
Herbert W. Hamber considers a perfect fluid form. (perfect symmetry)
Note that a non-vanishing pressure contribution is generated in the effective field equations, even if one assumes initially a pressureless fluid, p(t) = 0
http://arxiv.org/abs/0901.0964
Quantum Gravity on the Lattice
Authors: Herbert W. Hamber
(Submitted on 8 Jan 2009)
I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton's costant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).
---------
insert 11 April09
If the following paper had been the first that I would have read about the Standard Model, it would have shortened my learning curve.
Getting an understand of perfect symmetry and the Standard model is well explained by the following:
http://arxiv.org/abs/0904.1556
The Algebra of Grand Unified Theories
Authors: John C. Baez, John Huerta
(Submitted on 9 Apr 2009)
In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations.
---------
I visualize a sphere containing a cube and a cube containing the double tetra.
--------
insert 25 May09
If you have not been reading my blog entries then look at Wiki for a good visual explanations of 4-simplex and tetrahedron before reading the next paper.
A picture tells a thousand words.
--------
Holomorphic Factorization for a Quantum Tetrahedron
Authors: Laurent Freidel, Kirill Krasnov, Etera R. Livine
(Submitted on 22 May 2009)
What has been worked out in the applications to AdS/CFT correspondence of string theory is the first few terms of the expansion (123) (in the case of four dimensions) for some simple integral conformal dimensions, and these have been shown to match the boundary CFT predictions.
=======
~~~ Since I am learning, I reserve the right to change my mind. ~~~~
Insert: 06 Dec.2008,
08 Jan 2009, 11 April 09
25 May 2009
If you have been reading my blog then you have a pretty good idea.
Perfect Symmetry vs. broken symmetry (CPT)
1. First I realize that what we “see” is an interpretation of what is achieved by experiments
2. Experiments can only “see” a confined proton, neutron, size of approx. 10^-15. The interpretations are the QED of the Standard model .
3. At a smaller scale, QCD, inside the proton, models are still being developed, and tested against the results of experiments. If a physical minimum length, (ie. planck scale), is applied as a condition, then LQG, Lattice QCD etc. which all use a minimum length, would be a more accurate description and you can only get to a 4-Manifold, A3 lattice, a cube.
4. Experiments at high pressure and density have produced a liquid of quark gluon, which is not confined, which can be modeled as a perfect liquid and maybe as perfect symmetry.
For high school students, read my blog and see if there is anything there that you want to use.
======
http://en.wikipedia.org/wiki/Gauge_theory
=========
Read what John Baez has been presenting and see if what I have been saying “rings a bell”.
John Baez, at n-category café has started seminars/lessons on Lie Theory.
http://golem.ph.utexas.edu/category/...es_1.html#more
Lie Theory Through Examples 1
Posted by John Baez
http://golem.ph.utexas.edu/category/...es_2.html#more
Lie Theory Through Examples 2
Posted by John Baez
========
Question:
Could you give your definition of dimension and minimum length as it used for this subject.
Answer:
I’m using the usual definitions of ‘dimension’ and ‘length’ that apply to n-dimensional Euclidean space.
------
Note: That means he is not using minimum length, or Planck length.
------
http://en.wikipedia.org/wiki/Distance
Distance is a numerical description of how far apart objects are
http://en.wikipedia.org/wiki/Metric_(mathematics)
In mathematics, a metric or distance function is a function which defines a distance between elements of a set.
http://en.wikipedia.org/wiki/Dimension
dimension
http://en.wikipedia.org/wiki/Euclidean_space
n-dimensional Euclidean space
=======
Note: If you accept that particles are point like then you can get to E8.
If a physical minimum length, (planck scale), is applied as a condition, then LQG, Lattice QCD etc. which all use a minimum length, would be a more accurate description and you can only get to a 4-Manifold, A3 lattice, a cube.
=========
=====
http://math.ucr.edu/home/baez/qg-fall2008/lie3.pdf
Lie Theory Through Examples 3
========
http://golem.ph.utexas.edu/category/...es_4.html#more
Lie Theory Through Examples 4
========
The A3 lattice concept ....
12 points on those 12 edges of the cube.
By using the concept of minimum length and the definition of a dimension, you can squeeze 4 dimensions with a length of 4 into the same space occupied by 3 dimension.
Then using the concept of a vibrating string you obtain the concept of 12 energy nodes on those edges which produces the cubic lattice and perfect symmetry. Look at the attached picture. synchronization-2.GIF
I assume that before too long, John Baez’s lectures will show if there are errors in my assumptions/thinking that need corrections.
========
Here another interesting image to go with John Baez’ image
from FERMILAB
http://www.fnal.gov/pub/presspass/pr...ega-sub-b.html
Fermilab physicists discover "doubly strange" particle
=========
Another blog reference
http://www.math.columbia.edu/~woit/wordpress/
Not Even Wrong
Notes on BRST I: Representation Theory and Quantum Mechanics
November 5th, 2008
=======
I have been following the following to get a better understanding and to see if I got to change my mind.
http://www.sciencenews.org/view/gene...neutron_masses
Standard model gets right answer for proton, neutron masses
Correct calculation strengthens theory of quark-gluon interactions in nuclear particles
By Ron Cowen
December 20th, 2008; Vol.174 #13 (p. 13)
--------
http://arxiv.org/abs/0807.1610v1
Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
Authors: Reinhard Stock (Physics Department, University of Frankfurt)
(Submitted on 10 Jul 2008)
--------
The key tool enabling this advance is lattice gauge theory (5), a formulation of QCD and similar quantum field theories that replaces space-time with a four-dimensional lattice. To picture the lattice, think of a crystal with cubic symmetry evolving in discrete time steps.
To explore the predictions of QCD in this nonperturbative regime, the most systematic approach is to discretize (3) the above Lagrangian on a hypercubic space-time lattice with spacing a, to evaluate its Green's functions numerically and to extrapolate the resulting observables to the continuum (a0). A convenient way to carry out this discretization is to place the fermionic variables on the sites of the lattice, whereas the gauge fields are treated as 3 x 3 matrices connecting these sites. In this sense, lattice QCD is a classical four-dimensional statistical physics system.
In their calculations, Hoelbling and collaborators approximated the continuum of spacetime with a four-dimensional crystal lattice composed of discrete points spaced along columns and rows. The researchers solved the equations of QCD on finer and finer lattices, and then extrapolated the results to the continuum, painstakingly accounting and measuring every approximation and uncertainty along the way.
Confinement emerges naturally in lattice gauge theory at strong coupling (5). The lattice also reduces everything we would want to calculate to integrals that, in principle, can be evaluated numerically on a computer.
====== inserted 22 Dec
Here are two recent papers working on cubic packing/lattice symmetry. Heck! … Call it what you want.
http://arxiv.org/abs/0812.0713
The relation of a Unified Quantum Field Theory of Spinors to the structure of General Relativity
Authors: Martin Kober
(Submitted on 3 Dec 2008)
======
http://arxiv.org/abs/0812.1537
Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
Authors: C. Flori, T. Thiemann
(Submitted on 8 Dec 2008)
In other words, the semiclassical sector of LQG defined by those states is described by graphs with cubic topology! This has some bearing on current spin foam models which are all based on four valent boundary spin networks.
=====
Here are two more papers.
http://arxiv.org/abs/hep-th/0611042
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
Authors: Aristide Baratin, Laurent Freidel
(Submitted on 3 Nov 2006 (v1), last revised 28 Mar 2007
-------
http://arxiv.org/abs/0812.4055
The Holst Spin Foam Model via Cubulations
Authors: Aristide Baratin, Cecilia Flori, Thomas Thiemann
(Submitted on 21 Dec 2008)
------ 08 Jan 2009
Herbert W. Hamber considers a perfect fluid form. (perfect symmetry)
Note that a non-vanishing pressure contribution is generated in the effective field equations, even if one assumes initially a pressureless fluid, p(t) = 0
http://arxiv.org/abs/0901.0964
Quantum Gravity on the Lattice
Authors: Herbert W. Hamber
(Submitted on 8 Jan 2009)
I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton's costant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).
---------
insert 11 April09
If the following paper had been the first that I would have read about the Standard Model, it would have shortened my learning curve.
Getting an understand of perfect symmetry and the Standard model is well explained by the following:
http://arxiv.org/abs/0904.1556
The Algebra of Grand Unified Theories
Authors: John C. Baez, John Huerta
(Submitted on 9 Apr 2009)
In this expository account for mathematicians, we explain only the portion of these theories that involves finite-dimensional group representations.
---------
I visualize a sphere containing a cube and a cube containing the double tetra.
--------
insert 25 May09
If you have not been reading my blog entries then look at Wiki for a good visual explanations of 4-simplex and tetrahedron before reading the next paper.
A picture tells a thousand words.
--------
Holomorphic Factorization for a Quantum Tetrahedron
Authors: Laurent Freidel, Kirill Krasnov, Etera R. Livine
(Submitted on 22 May 2009)
What has been worked out in the applications to AdS/CFT correspondence of string theory is the first few terms of the expansion (123) (in the case of four dimensions) for some simple integral conformal dimensions, and these have been shown to match the boundary CFT predictions.
=======
~~~ Since I am learning, I reserve the right to change my mind. ~~~~
Total Comments 5
Comments
-
Yahoo! has decided to close GeoCities
I have been using geocities as a web page to have links to pictures in my blog and in my postings.
Those links will no longer work.
Therefore, I will be doing some editing for my blog.
Unfortunately, I do not know what to do for the postings.
jalPosted May14-09 at 02:19 PM by jal 
-
Since the blog can only take 10,000 characters, I must make this link as a comment.
--------
The quest to understand symmetry and the confinement mechanisms from observations.
http://arxiv.org/abs/0906.0681
Lorentz Violation: Motivation and new constraints
Authors: Stefano Liberati (SISSA, Trieste and INFN, Trieste), Luca Maccione (DESY, Hamburg)
(Submitted on 3 Jun 2009)
In this review we focus upon the phenomenology of violations of fundamental symmetries, given that a convenient way to perform high-precision tests is to look for experimental deviations from symmetries that are believed to hold exactly in nature and that could be broken by QG.
An example of such a fundamental symmetry is CPT invariance, which requires that physics be unchanged under the combination of charge conjugation (C), parity inversion (P) and time reversal (T). C connects particles and antiparticles, P represents a spatial reflection of physical quantities with respect to the coordinate origin and T reverses a physics reaction in time.
jalPosted Jun4-09 at 06:22 PM by jal
-
I met Daniele Orit at the Emergent gravity conference in Vancouver and have been following his publications.
-----
http://arxiv.org/abs/0912.1546
Encoding simplicial quantum geometry in group field theories
Daniele Oriti, Tamer Tlas
(Submitted on 8 Dec 2009)
We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in it, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the GFT action.
-----
Maybe you will be able to see the two tetrahedra that I have been talking about. Check out wiki for an explanation and images.
http://en.wikipedia.org/wiki/Tetrahedron
jalPosted Dec8-09 at 10:48 PM by jal
-
If you have been following my blog then you will be glad to see the following mathematical presentation.
"We show the averaged size of 4-simplex, the element of the 4-simplices complex, has to be larger than the Planck length."
http://arxiv.org/abs/0912.2435
On Quantum Regge Calculus of Einstein-Cartan Theory
She-Sheng Xue
(Submitted on 12 Dec 2009)
This article presents detailed discussions and calculations of the recent letter "Quantum Regge Calculus of Einstein-Cartan theory" in Phys. Lett. B682 (2009) 300 [arXiv:0902.3407]. The Euclidean space-time is discretized by a 4-simplices complex. We adopt basic tetrad and spin-connection fields to describe the 4-simplices complex. Introducing diffeomorphism and local Lorentz invariant holonomy fields, we study a regularized Einstein-Cartan theory for the quantum dynamics of the 4-simplices complex and fermions. This regularized Einstein-Cartan action is shown to properly approaches to its continuum counterpart in the continuum limit. Based on the local Lorentz invariance, we derive the dynamical equations satisfied by invariant holonomy fields. In the mean-field approximation, we show the averaged size of 4-simplex, the element of the 4-simplices complex, has to be larger than the Planck length. This formulation provides a theoretical framework for analytical calculations and numerical simulations to study the quantum Einstein-Cartan theory.Posted Dec15-09 at 04:32 PM by jal
-
http://arxiv.org/abs/1101.1081
General Covariance in Gravity at a Lifshitz Point
Petr Horava
(Submitted on 5 Jan 2011)
It is natural to ask whether one can construct theories with anisotropic scaling and with propagating gravitons. Why? A consistent theory of gravity with anisotropic scaling can be potentially useful for a number of possible applications:
(i) Phenomenology of gravity in our Universe of 3 + 1 macroscopic dimensions.
(ii) New gravity duals for field theories in the context of the AdS/CFT correspondence; in
particular, duals for a broader class of nonrelativistic QFTs.
(iii) Gravity on worldsheets of strings and worldvolumes of branes.
(iv) Mathematical applications to the theory of the Ricci flow on Riemannian manifolds [1].
(v) IR fixed points in condensed matter systems, with emergent gravitons (new phases of
algebraic bose liquids) [5].
(vi) Relativistic gravity and string theory in asymptotically anisotropic spacetimes [6];
and possibly others.
Note that only application (i) is subjected to the standard observational tests of gravity, while the others are only constrained by their mathematical consistency.
How can the effective dimension of spacetime change continuously from four at long distances to two at short distances? An analytic explanation was offered in [3]: The spectral dimension is a precisely defined geometric quantity, and it can be calculated systematically in the contin-
uum approach to quantum gravity with anisotropic scaling. In the mean-field approximation
around the flat spacetime, the result is [3] ds = 1 + D z . (1.7)
Hence, if the gravity theory flows from a z = 3 UV fixed point to a z = 1 IR fixed point,
the qualitative crossover of ds observed in [19] is reproduced.
The topological dimension of spacetime is always four, but the spectral dimension changes because of the anisotropic scaling at short distances.Posted Jan7-11 at 10:18 AM by jal
