Point groups in two dimensions - Revision history

en>Yobot: WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T11:59:23Z

WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 13:59, 5 May 2014
Line 1:		Line 1:
	~~{{Unreferenced\|date=January 2010}}~~		Hello and welcome. My title is Numbers Wunder. For years he's been operating as a receptionist. Her family life in Minnesota. Doing ceramics is what adore performing.<br><br>Here is my blog post :: at home std testing, [http://simple-crafts.com/groups/best-techniques-for-keeping-yeast-infections-under-control/ please click the following webpage],
	~~In [[theoretical physics]],~~ '~~''massive gravity''' is~~ a ~~particular generalization of [[general relativity]] studied by [[Hendrik van Dam]], [[Martinus J~~. G. ~~Veltman]] (1)~~
	~~, and [[Vladimir E~~. ~~Zakharov]].(2)~~

	~~One assumes that physics takes place in [[Minkowski space]] and gravity is caused by a massive [[spin (physics)\|spin]]-2 field h that couples to matter like the [[graviton]], namely by the term~~
	:<~~math~~>~~h^{\mu\nu}T_{\mu\nu}~~<~~/math~~>
	~~where T~~ is ~~the~~ [~~[stress~~-~~energy tensor]]~~.

	~~The adjective "massive" means that there are also mass terms in the Lagrangian proportional to~~
	~~:<math>h^{\mu\nu}h_{\mu\nu}<~~/~~math> .~~
	At distances shorter than the corresponding [[Compton wavelength]], one recovers the [[Newton's gravitational law]]. In the same limit, however, the bending of light is only three quarters of the result [[Albert Einstein]] obtained in general relativity. This is known as the '''vDVZ discontinuity'''.

	~~More technically stated by E. Babichev, ''et al.'' (3), "The (quadratic) Pauli~~-Fierz theory is known to suffer from the van Dam-Veltman-Zakharov (vDVZ) discontinuity,i.e. the fact that when one lets the mass m of the graviton vanish, one does not recover predictions of general relativity. E.g., if one adjusts the parameters (namely the Planck scale) such that the [[Newton constant]] agrees with the one measured by some type of [[Cavendish experiment]], then the light bending as predicted by [[Pauli-~~Fierz theory]] (and~~ for ~~a vanishingly small graviton mass) will be 3/4 of the one obtained by linearizing GR."~~

	~~The fact that it is smaller is easy to understand: the essential difference between Pauli~~-Fierz theory and linearized GR comes from an extra propagating scalar mode present in the massive theory. This mode exerts an extra attraction in the massive case compared to the massless case. Hence, if one wants measurements of the force exerted between non relativistic masses to agree, the coupling constant of the massive theory should be smaller than that of the massless theory. But light bending is blind to the scalar sector - because the light energy momentum tensor is traceless. Hence, provided the two theories agree on the force between non relativistic probes, the massive theory would predict a smaller light bending than the massless one.

	It has been recently argued{{By whom\|date=July 2009}} that although this discontinuity survives in many particular realizations of the situation, it may disappear if the theory becomes fully covariant. More precisely, this discontinuity states that in the limit as the mass goes to zero, we get a spin-~~2 graviton ''and'' a scalar [[boson]] which couples to the stress~~-~~energy tensor. This scalar boson has not been observed experimentally.~~

	~~{{Theories of gravitation}}~~

	~~==References==~~
	~~1. H. van Dam and M. G. Veltman, “Massive and massless Yang~~-~~Mills and gravitational field,”~~
	~~Nucl. Phys. B 22, 397 (1970)~~

	~~2. V. I. Zakharov, “Linearized gravitation theory and~~ the ~~graviton mass,” JETP Lett. 12, 312~~
	~~(1970) [Pisma Zh. Eksp. Teor. Fiz. 12, 447 (1970)~~]

	~~3. E. Babichev, C. Deffayet, and R. Ziour~~, ~~“ The recovery of general relativity in massive gravity~~
	~~via the Vainshtein mechanism,” [http://arxiv.org/abs/1007.4506 arXiv:1007.4506] [gr-qc] (2010)~~

	~~{{DEFAULTSORT:Massive Gravity}}~~
	~~[[Category:Theories of gravitation]]~~

en>Tomruen: /* Discrete groups */

2014-01-01T23:29:52Z

Discrete groups

← Older revision		Revision as of 01:29, 2 January 2014
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	Hi there. ~~Allow me start~~ by ~~introducing~~ the ~~writer~~, ~~her title~~ is ~~Myrtle Cleary~~. ~~South Dakota~~ is ~~her birth location but she needs~~ to ~~transfer simply~~ because ~~of her family members~~. ~~I am~~ a ~~meter reader but I strategy on changing~~ it. ~~What I adore doing is doing ceramics but I haven~~'~~t produced~~ a ~~dime with it~~.~~<br><br>Here is my blog: home std test kit~~ ([http://~~www~~.~~ninfeta.tv~~/~~blog~~/~~99493 click through the following web page~~])		{{Unreferenced\|date=January 2010}}
			In [[theoretical physics]], '''massive gravity''' is a particular generalization of [[general relativity]] studied by [[Hendrik van Dam]], [[Martinus J. G. Veltman]] (1)
			, and [[Vladimir E. Zakharov]].(2)

			One assumes that physics takes place in [[Minkowski space]] and gravity is caused by a massive [[spin (physics)\|spin]]-2 field h that couples to matter like the [[graviton]], namely by the term
			:<math>h^{\mu\nu}T_{\mu\nu}</math>
			where T is the [[stress-energy tensor]].

			The adjective "massive" means that there are also mass terms in the Lagrangian proportional to
			:<math>h^{\mu\nu}h_{\mu\nu}</math> .
			At distances shorter than the corresponding [[Compton wavelength]], one recovers the [[Newton's gravitational law]]. In the same limit, however, the bending of light is only three quarters of the result [[Albert Einstein]] obtained in general relativity. This is known as the '''vDVZ discontinuity'''.

			More technically stated by E. Babichev, ''et al.'' (3), "The (quadratic) Pauli-Fierz theory is known to suffer from the van Dam-Veltman-Zakharov (vDVZ) discontinuity,i.e. the fact that when one lets the mass m of the graviton vanish, one does not recover predictions of general relativity. E.g., if one adjusts the parameters (namely the Planck scale) such that the [[Newton constant]] agrees with the one measured by some type of [[Cavendish experiment]], then the light bending as predicted by [[Pauli-Fierz theory]] (and for a vanishingly small graviton mass) will be 3/4 of the one obtained by linearizing GR."

			The fact that it is smaller is easy to understand: the essential difference between Pauli-Fierz theory and linearized GR comes from an extra propagating scalar mode present in the massive theory. This mode exerts an extra attraction in the massive case compared to the massless case. Hence, if one wants measurements of the force exerted between non relativistic masses to agree, the coupling constant of the massive theory should be smaller than that of the massless theory. But light bending is blind to the scalar sector - because the light energy momentum tensor is traceless. Hence, provided the two theories agree on the force between non relativistic probes, the massive theory would predict a smaller light bending than the massless one.

			It has been recently argued{{By whom\|date=July 2009}} that although this discontinuity survives in many particular realizations of the situation, it may disappear if the theory becomes fully covariant. More precisely, this discontinuity states that in the limit as the mass goes to zero, we get a spin-2 graviton ''and'' a scalar [[boson]] which couples to the stress-energy tensor. This scalar boson has not been observed experimentally.

			{{Theories of gravitation}}

			==References==
			1. H. van Dam and M. G. Veltman, “Massive and massless Yang-Mills and gravitational field,”
			Nucl. Phys. B 22, 397 (1970)

			2. V. I. Zakharov, “Linearized gravitation theory and the graviton mass,” JETP Lett. 12, 312
			(1970) [Pisma Zh. Eksp. Teor. Fiz. 12, 447 (1970)]

			3. E. Babichev, C. Deffayet, and R. Ziour, “ The recovery of general relativity in massive gravity
			via the Vainshtein mechanism,” [http://arxiv.org/abs/1007.4506 arXiv:1007.4506] [gr-qc] (2010)

			{{DEFAULTSORT:Massive Gravity}}
			[[Category:Theories of gravitation]]

en>Brad7777: /* External links */ removed geometry

2011-11-16T19:03:50Z

External links: removed geometry

New page

Hi there. Allow me start by introducing the writer, her title is Myrtle Cleary. South Dakota is her birth location but she needs to transfer simply because of her family members. I am a meter reader but I strategy on changing it. What I adore doing is doing ceramics but I haven't produced a dime with it.<br><br>Here is my blog: home std test kit ([http://www.ninfeta.tv/blog/99493 click through the following web page])