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

M. A. Rego-Monteiro·E. M. F. Curado
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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 $\sqrt{n^2 π^2/L^2+m_q^2}$, where $n= 1,2,...$ denotes the level of the particle with mass $m_q$ in an infinite square-well potential of width $L$.

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M. A. Rego-Monteiro, E. M. F. Curado. 2001-05-14. Construction of a non-standard quantum field theory through a generalized Heisenberg algebra. https://doi.org/10.1142/s0217751x0200959x

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