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By Brookes S.D.

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This also provides us quantitative measures on the strengths and weaknesses of numerical procedures in handling singular interactions (in the context of lightfront field theory) on the computer. It is crucial to have such quantitative measures in order to study the effects of similarity cutoff factors on the nature of the spectrum. Just as the Tamm-Dancoff or the Bloch-Horowitz formalism, Bloch effective Hamiltonian of QCD in the first non-trivial order also does not exhibit confinement in (3+1) dimensions.

3) ¯ ν T a ψ = 0. 4) Because we are in (2+1) dimensions, we immediately face an ambiguity since there are no γ matrices in (2+1) dimensions. In the literature both two component [18] and four component representation [19] have been in use. For simplicity, we pick the two component representation. Explicitly, γ 0 = σ2 = 0 i −i , γ 1 = iσ3 = 0 i 0 24 0 , γ 2 = iσ1 = −i 0 i . 5) 0 2i γ ± = γ 0 ± γ 2, γ + = 1 Λ± = γ ∓ γ ± , Λ+ = 4 0 , γ− = 0 1 0 0 −2i . 0 0 0 , Λ− = 0 0 0 0 . 7) Fermion field operator ψ ± = Λ± ψ .

In the Wilsonian approach the cutoff on energy is lowered and the number of degrees of freedom is reduced in an iterative way and in each step one has to construct the effective interactions for the effective degrees of freedom. , only nearby degrees of freedom are directly coupled by the interactions which holds true for original local theories we normally deal with [5]. Construction of nondiagrammatic RG transformations enables one to solve them numerically in a computer and hence the problems which cannot be solved by Feynman diagrams can be solved by using RG.

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A Model for Communicating Sequential Processes [PhD Thesis] by Brookes S.D.

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