Dehn function: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
Newer edit →
en>Helpful Pixie Bot
m ISBNs (Build KE)
 
→Known results: Corrected a typo in Vogtmann's name.
Line 1: Line 1:
Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. You can either install Word - Press yourself or use free services offered on the web today. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. Hosted by Your Domain on Another Web Host - In this model, you first purchase multiple-domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage of the full power of Wordpress. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster. <br><br>
In physics, '''vector meson dominance''' (VMD) was a model developed by [[J. J. Sakurai]]<ref>Theory of strong interactions, [[J. J. Sakurai]], Ann. Phys., 11 (1960)</ref> in the 1960s before the introduction of [[quantum chromodynamics]] to describe interactions between energetic [[photon]]s and [[hadron]]ic matter.  


Any business enterprise that is certainly worth its name should really shell out a good deal in making sure that they have the most effective website that provides related info to its prospect. Best of all, you can still have all the functionality that you desire when you use the Word - Press platform. Well Managed Administration  The Word - Press can easily absorb the high numbers of traffic by controlling the server load to make sure that the site works properly. Apart from these, you are also required to give some backlinks on other sites as well. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. <br><br>The entrepreneurs can easily captivate their readers by using these versatile themes. As of now, Pin2Press is getting ready to hit the market. This platform can be customizedaccording to the requirements of the business. Newer programs allow website owners and internet marketers to automatically and dynamically change words in their content to match the keywords entered by their web visitors in their search queries'a feat that they cannot easily achieve with older software. After that the developer adds the unordered list for navigations. <br><br>The disadvantage is it requires a considerable amount of time to set every thing up. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. If you are looking for Hire Wordpress Developer then just get in touch with him. Look for experience: When you are searching for a Word - Press developer you should always look at their experience level. <br><br>Many developers design websites and give them to the clients, but still the client faces problems to handle the website. Here is more info about [http://snipitfor.me/wordpress_backup_plugin_5887430 wordpress backup plugin] check out our webpage. s ability to use different themes and skins known as Word - Press Templates or Themes. However, there are a few other Wordpress plugins also for its development which requires adding files in your Wordpress setup. Word - Press is an open source content management system which is easy to use and offers many user friendly features. Article Source: Hostgator discount coupons for your Wordpress site here.
In particular the hadronic components of the physical photon consist of the lightest vector mesons <math>\rho, \omega</math> and <math>\phi</math>. Therefore, interactions between photons and hadronic matter occur by the exchange of a hadron between the dressed photon and the hadronic target.
 
==Background==
Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons<ref>Bauer, T. H., Spital, R. D., Yennie, D. R. and Pipkin, F. M, The hadronic properties of the photon in high-energy interactions, Rev. Mod. Phys. 50, 261–436 (1978), pages 292-293</ref> in spite of the fact that the electric charge structures of protons and neutrons are substantially different.
 
According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.  
 
Just after 1970, when more accurate data on the above processes became available, some discrepancies with the VMD predictions appeared and new extensions of the model were published.<ref>Generalized vector dominance and inelastic electron nucleon scattering—the small <math>\omega</math>′ region, Sakurai J. J. and Schildknecht D., Phys. Lett., 40B (1972) 121</ref> These theories are known as Generalized Vector Meson Dominance theories (GVMD).
 
==VMD and Hidden Local Symmetry==
Whilst the ultraviolet description of the standard model is based on  QCD, work over many decades has involved writing a low energy effective description of QCD, and further, positing a possible ``dual`` description.   One such popular description is that of the hidden local symmetry.<ref>Nonlinear Realization and Hidden Local Symmetries, Bando, Masako and Kugo, Taichiro and Yamawaki, Koichi, DOI: 10.1016/0370-1573(88)90019-1</ref>  The dual description is based on the idea of emergence of gauge symmetries in the infrared of strongly coupled theories. Gauge symmetries are not really physical symmetries (only the global elements of the local gauge group are physical).  This emergent property of gauge symmetries was demonstrated in Seiberg duality  <ref>Electric - magnetic duality in supersymmetric nonAbelian gauge theories , Seiberg, N., hep-th/9411149</ref> and later in the development of the AdS/CFT correspondence.<ref>The Large N limit of superconformal field theories and
                        supergravity, Maldacena, Juan Martin, hep-th/9711200</ref> In its generalised form, Vector Meson Dominance appears in AdS/CFT, AdS/QCD , AdS/condensed matter  and some Seiberg dual constructions.  It is therefore a common place idea within the theoretical physics community.
 
==Attacks on VMD==
Measurements of the photon-hadron interactions in higher energy levels show that VMD cannot predict the interaction in such levels. In his Nobel lecture<ref>[[Jerome Isaac Friedman|J.I. Friedman]], Nobel Lecture, Deep Inelastic Scattering, Comparisons with the Quark Model, Rev. Mod. Phys. vol 63 3 1991</ref> [[Jerome Isaac Friedman|J.I. Friedman]] summarizes the situation of VMD as follows:
"...this eliminated the model [VMD] as a possible description of deep inelastic scattering... calculations of the generalized vector-dominance failed in general to describe the data over the full kinematic range..."
 
The theoretical basis of VMD raised doubts as well. According to VMD a photon is a superposition of pure electromagnetic photon which always moves in the speed of light and hadronic matter which always moves in lower speed. Therefore the VMD idea seems to contradict [[Special Relativity]].<ref>[[Eliyahu Comay|E. Comay]] Remarks on Photon-Hadron Interactions, Apeiron vol. 10,  87 (2003)</ref>
 
Today, VMD is not considered as part of the [[Standard Model]].<ref>H.B. O’Connell, B.C. Pearce, A.W. Thomas and A.G. Williams, Rho-omega mixing, vector meson dominance and the pion form-factor, Prog. Nucl. Part. Phys. 39 (1997) 201-252</ref>
 
[[Image:VMD1.png|thumb| Hadronic contribution to the photon propagator in the VMD model]]
 
==Notes==
<references/>
 
[[Category:Particle physics]]
[[Category:Nuclear physics]]

Revision as of 15:12, 28 August 2013

In physics, vector meson dominance (VMD) was a model developed by J. J. Sakurai[1] in the 1960s before the introduction of quantum chromodynamics to describe interactions between energetic photons and hadronic matter.

In particular the hadronic components of the physical photon consist of the lightest vector mesons ρ,ω and ϕ. Therefore, interactions between photons and hadronic matter occur by the exchange of a hadron between the dressed photon and the hadronic target.

Background

Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons[2] in spite of the fact that the electric charge structures of protons and neutrons are substantially different.

According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.

Just after 1970, when more accurate data on the above processes became available, some discrepancies with the VMD predictions appeared and new extensions of the model were published.[3] These theories are known as Generalized Vector Meson Dominance theories (GVMD).

VMD and Hidden Local Symmetry

Whilst the ultraviolet description of the standard model is based on QCD, work over many decades has involved writing a low energy effective description of QCD, and further, positing a possible ``dual`` description. One such popular description is that of the hidden local symmetry.[4] The dual description is based on the idea of emergence of gauge symmetries in the infrared of strongly coupled theories. Gauge symmetries are not really physical symmetries (only the global elements of the local gauge group are physical). This emergent property of gauge symmetries was demonstrated in Seiberg duality [5] and later in the development of the AdS/CFT correspondence.[6] In its generalised form, Vector Meson Dominance appears in AdS/CFT, AdS/QCD , AdS/condensed matter and some Seiberg dual constructions. It is therefore a common place idea within the theoretical physics community.

Attacks on VMD

Measurements of the photon-hadron interactions in higher energy levels show that VMD cannot predict the interaction in such levels. In his Nobel lecture[7] J.I. Friedman summarizes the situation of VMD as follows: "...this eliminated the model [VMD] as a possible description of deep inelastic scattering... calculations of the generalized vector-dominance failed in general to describe the data over the full kinematic range..."

The theoretical basis of VMD raised doubts as well. According to VMD a photon is a superposition of pure electromagnetic photon which always moves in the speed of light and hadronic matter which always moves in lower speed. Therefore the VMD idea seems to contradict Special Relativity.[8]

Today, VMD is not considered as part of the Standard Model.[9]

File:VMD1.png
Hadronic contribution to the photon propagator in the VMD model

Notes

  1. ↑ Theory of strong interactions, J. J. Sakurai, Ann. Phys., 11 (1960)
  2. ↑ Bauer, T. H., Spital, R. D., Yennie, D. R. and Pipkin, F. M, The hadronic properties of the photon in high-energy interactions, Rev. Mod. Phys. 50, 261–436 (1978), pages 292-293
  3. ↑ Generalized vector dominance and inelastic electron nucleon scattering—the small ω′ region, Sakurai J. J. and Schildknecht D., Phys. Lett., 40B (1972) 121
  4. ↑ Nonlinear Realization and Hidden Local Symmetries, Bando, Masako and Kugo, Taichiro and Yamawaki, Koichi, DOI: 10.1016/0370-1573(88)90019-1
  5. ↑ Electric - magnetic duality in supersymmetric nonAbelian gauge theories , Seiberg, N., hep-th/9411149
  6. ↑ The Large N limit of superconformal field theories and supergravity, Maldacena, Juan Martin, hep-th/9711200
  7. ↑ J.I. Friedman, Nobel Lecture, Deep Inelastic Scattering, Comparisons with the Quark Model, Rev. Mod. Phys. vol 63 3 1991
  8. ↑ E. Comay Remarks on Photon-Hadron Interactions, Apeiron vol. 10, 87 (2003)
  9. ↑ H.B. O’Connell, B.C. Pearce, A.W. Thomas and A.G. Williams, Rho-omega mixing, vector meson dominance and the pion form-factor, Prog. Nucl. Part. Phys. 39 (1997) 201-252
Retrieved from "https://en.formulasearchengine.com/index.php?title=Dehn_function&oldid=23171"