Galilean Conformal Algebra in Semi-Infinite Space

TL;DR

This paper studies Galilean conformal algebras in semi-infinite space, deriving correlation functions with boundary conditions, extending previous work on space-time correlations without boundaries.

Contribution

It introduces the calculation of two- and three-point correlation functions for Galilean conformal invariant fields in semi-infinite space with boundary conditions.

Findings

Derived correlation functions with boundary conditions at r=0.

Extended previous space-time correlation results to semi-infinite space.

Provided explicit formulas for fixed-time boundary conditions.

Abstract

In the present work we considered Galilean conformal algebras (GCA), which arises as a contraction relativistic conformal algebras ($x_i\rightarrow \epsilon x_i$, $t\rightarrow t$, $\epsilon \rightarrow 0$). We can use the Galilean conformal symmetry to constrain two-point and three-point functions. Correlation functions in space-time without boundary condition were found in \cite{1}. In real situations there are boundary conditions in space-time, so we have calculated correlation functions for Galilean confrormal invariant fields in semi-infinite space with boundary condition in $r=0$. We have calculated two-point and three-point functions with boundary condition in fixed time.