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

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

2001-05-14

arxiv.org/abs/hep-th/0105130v1

Int.J.Mod.Phys. A17 (2002) 661-674

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 16 pages

Scientific paper

10.1142/S0217751X0200959X

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 $L$.

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