Strong interaction model in DFR noncommutative space–time

Abstract

The Doplicher-Fredenhagen-Roberts (DFR) framework for noncommutative (NC) space-times is considered as an alternative approach to describe the physics of quantum gravity. In this formalism, the NC parameter, i.e. θ µν , is promoted to a coordinate of a new extended space-time.Consequently, we can construct a Field Theory in a space-time with spatial extra-dimensions.This new coordinate has a canonical momentum associated, where the effects of a new physics point of view can emerge in the fields propagation along the extra-dimension. In this paper we have introduced the gauge invariance in the DFR NC space-time by the composite symmetry U ⋆ (N ) × U ⋆ (N ). We have constructed the non-Abelian gauge symmetry based on DFR formalism, and we analyzed the consequences of this symmetry in the presence of such extradimensions. The gauge symmetry in this DFR scenario can reveal new gauge fields attached to θ-extra-dimension. As an application, we have accomplished the unification of Strong Interaction with the electromagnetism and a Higgs model to give masses to the NC bosons. We have estimated their masses by using some experimental constraints of QCD.

Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence

“…Here we see that when the weight function reduces to unity, the above equation, Eq. (5.12), becomes the plane wave solution in d = 7 as shown in [18,32] for a 0 = 1 and for arbitrary a 1 . Taking this as a criterion, set a 0 = 1 (see the discussion after Eq.…”

“…Here we observe that the Lagrangian contains a λ 2 dependent term signifying the θ contribution of the DFRA action. We get the commutative action corresponding to the scalar field in the limit λ → 0 and using the result lim λ→0 e [32]. The equations of motion corresponding to the scalar field in DFR space-time, by varying the action given in Eq.…”

“…The above equation reduces to the commutative scalar field EOM in the lim λ → 0 with θ = 0. It is to be noted that the first three terms on the LHS of the above equation correspond to the EOM obtained from the Casimir of the DFRA algebra [15,32]. The dynamics and the canonical quantisation of the DFRA scalar field obeying that equation of motion has been studied in detail in [18], starting from Lagrangian.…”

A general relativity formulation for the Doplicher-Fredenhagen-Roberts noncommutative space-time

“…Using the coordinate representation, the operators P μ and Ki can be written in terms of the derivatives Pμ −→ i∂ μ and Ki −→ i∂ θ . Thereby, the first Casimir operator on-shell result leads us to the field equations of scalar and fermions fields [52]. From now on, the notation θ means the θ i -coordinates θ = (θ 1 , θ 2 , θ 3 ) and…”

“…Note that the coordinates of θ in X A are defined as being dimensionless due to the length scale λ. The components of the metric Ξ AB (θ) are elements of the 7 × 7 diagonal matrix [52] Ξ…”