Return to Question

Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific function $F(x^\mu)$?

Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific function $F(x^\mu)$?

Edit 1: We know that a subgroup of Poincare group $P(1,3)$ leaves the hypersurface $\Sigma: x^+ = 0$ invariant where $x^+ \equiv x^0 + x^3$. To show this a formula is needed.

Let $F(x^\mu)$ is a scalar function. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific function $F(x^\mu)$?

Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific function $F(x^\mu)$?