We construct a Heisenberg-like algebra for the one dimensional quantum freeKlein-Gordon equation defined on the interval of the real line of length $L$.Using the realization of the ladder operators of this type Heisenberg algebrain terms of physical operators we build a 3+1 dimensional free quantum fieldtheory based on this algebra. We introduce fields written in terms of theladder operators of this type Heisenberg algebra and a free quantum Hamiltonianin terms of these fields. The mass spectrum of the physical excitations of thisquantum 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 infinitesquare-well potential of width $L$.
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机译：我们为长度为$ L $的实线的间隔定义的一维量子自由Klein-Gordon方程构造一个类似于Heisenberg的代数，利用这种Heisenberg代数算子的实现，根据物理算子，我们建立了一个3基于此代数的+1维自由量子场论。我们介绍用这种Heisenberg代数的梯形算子和这些场的自由量子哈密顿量写的场。该量子场论的物理激发的质谱由$ \ sqrt {n ^ 2 \ pi ^ 2 / L ^ 2 + m_q ^ 2} $给出，其中$ n = 1,2，... $表示质量为$ m_q $的粒子的水平，其宽度为$ L $的无限方阱势。
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