Construction of a non-standard quantum field theory through a generalized Heisenberg algebra

Abstract

We construct a Heisenberg-like algebra for the one dimensional quantum free Klein-Gordon equation defined on the interval of the real line of length $L$. Using the realization of the ladder operators of this type Heisenberg algebra in terms of physical operators we build a 3+1 dimensional free quantum field theory based on this algebra. We introduce fields written in terms of the ladder operators of this type Heisenberg algebra and a free quantum Hamiltonian in terms of these fields. The mass spectrum of the physical excitations of this quantum field theory are given by $\sqrt{n^2 \pi^2/L^2+m_q^2}$, where $n= 1,2,...$ denotes the level of the particle with mass $m_q$ in an infinite square-well potential of width $L$.