Faddeev–Popov ghost

From formulasearchengine
Revision as of 06:31, 26 April 2013 by en>Srich32977 (Cleaned up using AutoEd | Assisted by Citation bot r419)
Jump to navigation Jump to search

Template:Multiple issues

In mathematics and physics, in particular differential geometry and general relativity, a warped geometry is a Riemannian or Lorentzian manifold whose metric tensor can be written in form

ds2=gab(y)dyadyb+f(y)gij(x)dxidxj.

Note that the geometry almost decomposes into a Cartesian product of the y geometry and the x geometry – except that the x-part is warped, i.e. it is rescaled by a scalar function of the other coordinates y. For this reason, the metric of a warped geometry is often called a warped product metric.[1][2]

Warped geometries are useful in that separation of variables can be used when solving partial differential equations over them.

Examples

Warped geometries acquire their full meaning when we substitute the variable y for t, time and x, for s, space. Then the d(y) factor of the spatial dimension becomes the effect of time that in words of Einstein 'curves space'. How it curves space will define one or other solution to a space-time world. For that reason different models of space-time use warped geometries. Many basic solutions of the Einstein field equations are warped geometries, for example the Schwarzschild solution and the Friedmann–Lemaitre–Robertson–Walker models.

Also, warped geometries are the key building block of Randall–Sundrum models in particle physics.

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.


Template:Differential-geometry-stub Travel Agency Manager Alfonzo from Manotick, has numerous hobbies including comics, commercial property developers in singapore developers in singapore and creating a house. Recollects what an incredible area it was having traveled to Tubbataha Reefs Natural Park.

  1. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  2. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534