'LIGHT-CONE-GAUGE'

                                                      'LIGHT-CONE-GAUGE'

Contents:-

Ø  Light Cone Gauge

Ø  World-Sheet

Ø  Lorentz Symmetry

Ø  Gauge Symmetry

Ø  Yang-Mills Theory

Ø  Faddeev Popov Ghost

Light Cone Gauge:-

When light propagates  in the world Sheet , it remains invariants but it does not remain invariants at infinity-like. So , here it is presenting that such a equation which eliminates the 'Ghosts ' and other unphysical degree of freedom . Light-Cone-Gauge fixes the reparameterization   invariance on the 'World-Sheet' by :-

where P+   is a constant and T  is the worldsheet time.

Though this equation is able to show out the fix reparameterization , it is unable to tell about 'Lorentz Symmetry'.

'Light-Cone-Gauge' through String Theory is approachable a little bit to 'Yang-Mills –Symmetry' but more work has to be performed out for 'Yang-Mills-Symmetry:-

Light-cone gauge refers to the condition A+=0  where

                                                                                                                                                                                                                                          

So, Light-Cone-Gauge is applicable to manifest  Guage-Theory in terms of Strings.

Gauge Symmetry:-Gauge theory is a type of field theory in which the 'Lagrangian' is invariant under a continuous group of local transformations. Gauge theory successfully tells us about the dynamics of Elementary Particles. Quantum Electrodynamics is an Abelian gauge theory .Abelian Gauge Theory deals with U(1) and has one gauge field , the electro-magnetic four-potential , with the photon being the Gauge-Boson. The standard model is a Non-Abelian Gauge Theory.  Non-Abelian Gauge Theory deals with symmetry Group U(1)×SU(2)×SU(3) and has  a total of 12 Gauge Bosons: the Photon , three weak Bosons and Eight Gluons.

Yang-Mills Theory – Yang Mills Theory is a Gauge Theory based on the SU(N) group  which is given by the Compactness in Semi-Simple Lie Group. Yang Mills Theory also deals with the unification of the Electro-Magnetic and Weak Forces and Strong Force through U(1) ×SU(2) ×SU(3).

Faddeev –Popov Ghost:- In the Path Integral Formulation , the Gauge Symmetry is breakable by adding some additional fields. Ghost particles appear as Virtual Particles in the interactive Particles'Path Integral formulation. In 'Feynmann –'t-Hooft Gauge , it is encompassed  widely the Popov Ghost.

Lorentz Symmetry:-  In Lorentz Symmetry , six dimensional non-compact non-Abelian  real Lie Group , are not connected . The restricted Lorentz group consists of those Lorentz transformations that preserve the orientation of Space and direction of Time in  SO⁺(1,3) .  Mathematically, the Lorentz group of n+1-dimensional Minkowski space is the group O(n,1) (or O(1,n)) of linear transformations of Rⁿ⁺¹ . The low-dimensional cases n = 1 and n = 2 are often useful as "toy models" for the physical case n = 3, while higher-dimensional Lorentz groups are used in physical theories such as 'string theory' that posit the existence of hidden dimensions. The Lorentz group O(n,1) is also the isometry group of n-dimensional de Sitter space dS_n, which may be realized as the homogeneous space O(n,1)/O(n−1,1). In particular O(4,1) is the isometry group of the de Sitter universe dS₄, a cosmological model.

World Sheet:- Around 1967 , famous physicist 'Leonard Susskind' coined the World-Sheet to describe the embedding of a string of a two dimensional manifold in 'Space-Time'. In 'Bosonic String World-Sheet ' , there consists of  26 dimensions in Minkowski space which has 26 free 'Scalars- Field' . In Superstring, World-Sheet, there consists of 10 dimensions in Minkwoski Space which has 10 free 'Scalars-Field'.

Ø  References:- https://en.wikipedia.org/wiki/Light_cone_gauge

Writer- Jayaram Bista