Discrete and continue symmetries

[Yuri Danoyan]

my address yuri@danoyan.net

i can send you as attacment

Edited November 29, 2008 by Yuri Danoyan

[insane_alien]

again we do not have access to your harddrive. stop posting filepaths.

[Yuri Danoyan]

All essence this thread can read here:

C:\Documents and Settings\Yuri\My Documents\Time.htm

 

Sorry for the trouble. Here is the correct link :

http://www.danoyan.net/resultoftotaleffectfermi%26bosefields

[Yuri Danoyan]

The splitting into something discrete and something continuous seems to me to be a basic issue in all morphology. - Hermann Weyl

[ajb]

Everything of importance has been said before by somebody who did not discover it.

 

Alfred North Whitehead (1861 - 1947)

[swansont]

The splitting into something discrete and something continuous seems to me to be a basic issue in all morphology. - Hermann Weyl

 

Argument by quotation is really nothing more than argument from authority.

[Norman Albers]

To Swansont's statement, yes, but that does not take away from a good statement such as Weyl's.

[ajb]

I love quotations because it is a joy to find thoughts one might have, beautifully expressed with much authority by someone recognized wiser than oneself.

 

Marlene Dietrich (1901 - 1992)

[Yuri Danoyan]

Intersting quotation from from Freeman Dyson intersting new article:

http://www.ams.org/notices/200902/rtx090200212p.pdf

 

"Manin sees the future of mathematics

as an exploration of metaphors that are already

visible but not yet understood. The deepest such

metaphor is the similarity in structure between

number theory and physics. In both fields he sees

tantalizing glimpses of parallel concepts, symmetries

linking the continuous with the discrete. He

looks forward to a unification which he calls the

quantization of mathematics."

[Norman Albers]

Yuri, I love your motivating spirit. I suspect quantization stems from localization., and I remain to be convinced that current quantum probability theory says all we can know about IT ALL at the vacuum level. [[ ajb, once I ragged my friend 'solidspin' saying, "Jeez man, what do I have to do to satisfy you, integrate over just the irrational set?????"]]

Edited January 8, 2009 by Norman Albers

[Yuri Danoyan]

You can read also about Dyson attitude to string theorists today

p.221

[Yuri Danoyan]

What a pair of symmetries is primary?

Discrete & continuous;

Global & Local.

[ajb]

I think the biggest distinction is between global and local.

[Yuri Danoyan]

1.Continuous Symmetry can be both global and local.

2.Discrete symmetries can be both global and local.

3.Global symmetry can be both discrete and continuous.

4.Local symmetry can be both discrete and continuous

[ajb]

Discrete symmetries can be gauged (not all of them due to anomaly cancellation requirements). This is something I know very little about. This has been discussed in the literature in the early 90's.

 

See for example L. M. Krauss and F. Wilczek, Phys. Rev. Lett. 62 (1989) 1221

 

and subsequent publications by various people. As you know (classical) standard gauge theories form part of the connection theory on principle bundles. If we want to work in the category of smooth manifolds then the group in question must be a Lie group. Discrete groups can be Lie groups, i.e. they are manifolds with the discrete topology. So I guess one can still talk about connections etc.

 

I'd need to do some reading....

[Yuri Danoyan]

1.Continuous Symmetry[CS] can be both global and local.

2.Discrete Symmetries[DS] can be both global and local.

3.Global Symmetry[GS] can be both discrete and continuous.

4.Local Symmetry[LS] can be both discrete and continuous

 

Right answer: #1 and #3

 

[CS]---->split to [GS]&[LS]

[GS]---->split to [DS]&[CS]

[Yuri Danoyan]

"A global symmetry is one that holds at all points of spacetime, whereas a local symmetry is one that has a different symmetry transformation at different points of spacetime. Local symmetries play an important role in physics as they form the basis for gauge theories."(Wikipedia)

 

In the first case all points of spacetime mean homogeneity.

In the second case different points of spacetime mean heterogeneity.

 

Minimal homogeneity is the continuity (11).

Minimal heterogeneity is the discreteness(10 or 01).

[Yuri Danoyan]

Yuri:

"I want to clearly represent the relationship between these symmetries:

discrete &. continuous symmetries

global &. local symmetries

internal &. space-time symmetries"

 

Lubos:

"Sorry but there are almost no relationships between these 3 pairs of adjectives at all. Almost all 8 combinations exist, with an exception of "local spacetime" symmetries: local symmetries must be internal (but global symmetries may be both spacetime or internal). So 6 combinations exist. And even the local spacetime symmetries could be said to exist, with the diffeomorphisms being an example. So there's no diagram to draw."

 

http://motls.blogspot.com/2009/06/symmetry-and-beauty.html#comment-1471013257045861008

[Yuri Danoyan]

Today Nature Physics Portal Alert announced intersting letter about Platonic solids.

"Tetrahedron Dense packings of the Platonic and Archimedean solids"

S. Torquato & Y. Jiao

Nature

doi: 10.1038/nature08239, for detail see

http://www.princeton.edu/main/news/archive/S25/00/22A50/index.xml

Best model of Metasymmetry is Tetrahedron(first Platonic solid),which have 4 faces and each face is an triangle . This means there isn't a side that faces upward when it comes to rest on a flat surface Possible 4 Falls in Face.Every time, when we throw as dice, 3 Faces open, 1 Face closed. 3 vertices lie in one plane, while the fourth is not. Аny tetrahedrons can also be proof of the ratio of 3:1.I call it tetrahedron logic.

---

Merged post follows:

Consecutive posts merged

http://vixra.org/pdf/0907.0008v2.pdf

[Yuri Danoyan]

Strange idea of Dr. Achim Kempf

http://www.physorg.com/news180203376.html

 

Spacetime, which consists of three dimensions of space and one time dimension, is such a large, abstract concept that scientists have a very difficult time understanding and defining it. Moreover, different theories offer different, contradictory insights on spacetime’s structure. While general relativity describes spacetime as a continuous manifold, quantum field theories require spacetime to be made of discrete points. Unifying these two theories into one theory of quantum gravity is currently one of the biggest unsolved problems in physics.

[SES]

Strange idea of Dr. Achim Kempf

http://www.physorg.com/news180203376.html

 

Spacetime, which consists of three dimensions of space and one time dimension, is such a large, abstract concept that scientists have a very difficult time understanding and defining it. Moreover, different theories offer different, contradictory insights on spacetime’s structure. While general relativity describes spacetime as a continuous manifold, quantum field theories require spacetime to be made of discrete points. Unifying these two theories into one theory of quantum gravity is currently one of the biggest unsolved problems in physics.

 

I am afraid this isnt correct. The spacetime in QFT is also described by a manifold, usually plane and with a lorentzian metric. So in both cases the description of the spacetime is made with the same mathematical structure: a manifold. Anyway, a manifold is also a topological space, which is nothing but a set with a topology defined on it, so in this sense a manifold is a set of "discrete" points (although not countable) labelled locally with his coordinates in a chart and being the points the elements of the set. Of coruse, you have to add other mathematical structures to this set to obtain a manifold.

 

Changing the subject, do you realize what are you doing? You are taking the data that fits on your crazy idea and ignoring the rest of data that doesnt.

Edited January 3, 2010 by SES

[ajb]

I am afraid this isnt correct. The spacetime in QFT is also described by a manifold, usually plane and with a lorentzian metric. So in both cases the description of the spacetime is made with the same mathematical structure: a manifold.

 

OK. Depending on exactly what you are trying to do, considering manifolds with a Riemannian metric (maybe via a Wick rotation) is often useful or even necessary.

 

But certainly in standard approaches to QFT and classical gravity smooth manifolds play an important role.

 

Anyway, a manifold is also a topological space, which is nothing but a set with a topology defined on it, so in this sense a manifold is a set of "discrete" points (although not countable) labelled locally with his coordinates in a chart and being the points the elements of the set. Of coruse, you have to add other mathematical structures to this set to obtain a manifold.

 

In other words there is a forgetful functor from (the category of) manifolds to topological spaces.

 

I think what Yuri is confusing is the notion of quantum field theory on a space-time, which indeed uses classical manifolds (and fibre bundles etc.) and the ideas of applying quantum theory to the manifolds themselves.

 

Quantum gravity may well have a discrete or fuzzy nature in which the notion of points are lost.

 

One can then think about QFT on these "noncommutative" or "fuzzy" spaces.