On bound states in Quantum Field Theory

Abstract

In this paper, a new method to describe the energy spectrums of bound states in Quantum Field Theory is presented. We point out that the fundamental field and its dual soliton combine together to form bound states and the soliton corresponds to the ghost particle in our regularization scheme which takes advantage of dimensional regularization and Pauli-Villars regularization. Based on this point of view, we discuss the bound states of massive Thirring model, the positronium ($e^{+}{e}^{-}$) in QED and the vector meson in QCD. We also give a new way to obtain the mass of soliton (quantum soliton) from the stationary condition (gap equation). Our results agree with experimental data to high precision. We argue that the hypothetic $X_{17}$ particle in decay of ${}^8\mathrm{Be}$ and ${}^4\mathrm{He}$ is a soliton. For vector meson, we find the squared masses of $\rho$ resonances are $m^2(n)\sim (a{n}^{1/3}-b{)}^2$ which coincide well with experiments.

arXiv comment18 pages, 11 figures

References in corpus (14)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• Observation of Anomalous Internal Pair Creation in ${}^8$Be: A Possible Signature of a Light, Neutral Boson
• New evidence supporting the existence of the hypothetic X17 particle
• A note on the boundary contribution with bad deformation in gauge theory
• Toward precision holography with supersymmetric Wilson loops
• Baryons in Massive Gross-Neveu Models
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• On 1/2-BPS Wilson-'t Hooft loops
• Fermion Bags in the Massive Gross-Neveu Model
• Vortex mass in the three-dimensional $O(2)$ scalar theory
• Mesons and Nucleons in Soft-Wall AdS/QCD
• Quantum Solitons in any Dimension: Derrick's Theorem v. AQFT

Cited by in corpus (1)

• On positronium states in $\mathrm{QE}{\mathrm{D}}_3$