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Upper and Lower Bound States for Zero Dimensional Space in Scalar Quantum Field Theory

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Abstract

The varational method with the Hamiltonian formalism of quantum field theory (QFT) is used to study the bound state for scalar particle and antiparticle (bosons with spin 0) in a reformulated model. We first recall some points about the two-body ground state energy solutions in 3 + 1 dimensions. In this case, some approximations are needed to obtain numerical solutions. Then, we study the upper and lower bound states in zero dimensional space for the two-body problem using simple trial states. It is shown that when the dimension of space is zero some analytical (exact) solutions can be obtained when the interactions are small.

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  1. Department of Physics, Faculty of Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Mohsen Emami-Razavi

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  1. Mohsen Emami-Razavi
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Correspondence to Mohsen Emami-Razavi.

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Emami-Razavi, M. Upper and Lower Bound States for Zero Dimensional Space in Scalar Quantum Field Theory. Int J Theor Phys 60, 3128–3142 (2021). https://doi.org/10.1007/s10773-021-04897-8

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