Abstract
We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg–Schweber model. The method is based on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually used in nonperturbative light-front Hamiltonian methods and, therefore, does not suffer from the spectator dependence, Fock-sector dependence, and uncanceled divergences caused by such truncations.
Highlights
The central problem of a quantum field theory is to compute its mass spectrum and the corresponding eigenstates
If the theory is quantized in terms of light-front coordinates [1], this spectral problem can be written as a Hamiltonian eigenvalue problem [2], Pμ|ψ(P ) = P μ|ψ(P ), where P− ≡ P0 − Pz is the light-front energy operator, P ≡ (P+ = P0 + Pz, P⊥ = (Px, Py)) is the light-front momentum operator, and P μ are the corresponding eigenvalues
The coefficients in the expansion are the light-front momentum-space wave functions. This takes advantage of two important aspects of light-front coordinates [2]: the relative-momentum coordinates separate from the external momentum, so that the wave functions depend only on the relative momenta, and the positivity of P + = (P )2 + M2 + P z excludes vacuum contributions to the expansion, so that the wave functions represent the properties of the eigenstate only
Summary
The central problem of a quantum field theory is to compute its mass spectrum and the corresponding eigenstates. The truncation causes self-energy contributions and vertex functions to be dependent on the momenta of Fock-state constituents that are only spectators to the process in question. Wave-function renormalization is broken for interactions internal to a bound-state problem This is what drives the renormalization of the charge in a sector-dependent parameterization of the theory [5, 6], but this is clearly unphysical and has nothing to do with ordinary charge renormalization.. The analog of these difficulties with truncation can be induced in Feynman perturbation theory by separating covariant diagrams into time-ordered diagrams and discarding those time orderings that include intermediate states with more particles than some finite limit This destroys covariance, disrupts regularization, and induces spectator dependence for subdiagrams. This happens not just to some finite order in the coupling but to all orders
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