q-deformed conformal and Poincar{\'e} algebras on quantum 4-spinors

TL;DR

This paper constructs and analyzes q-deformed conformal and Poincaré algebras using quantum 4-spinors, providing a framework for quantum symmetry in four-dimensional spacetime.

Contribution

It introduces a quantum space for $sl_q(4,C)$, derives deformed $su(4)$ and $su(2,2)$ algebras, and constructs the q-deformed Poincaré algebra from quantum 4-spinors.

Findings

Quantum space for $sl_q(4,C)$ constructed.

Deformed $su(4)$ and $su(2,2)$ algebras derived.

Q-deformed Poincaré algebra identified as a subalgebra.

Abstract

We investigate quantum deformation of conformal algebras by constructing the quantum space for $sl_q(4,C)$. The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed $su(4)$ and $su(2,2)$ algebras from the deformed $sl(4)$ algebra using the quantum 4-spinor and its conjugate spinor. The 6-vector in $so_q(4,2)$ is constructed as a tensor product of two sets of 4-spinors. The reality condition for the 6-vector and that for the generators are found. The q-deformed Poincar{\'e} algebra is extracted as a closed subalgebra.