Towards perturbative renormalization of 𝜙2(𝑖𝜙)ɛ quantum field theory
In a previous paper it was shown how to calculate the ground-state energy density E and the p-point Green’s functions Gp(x1,x2,…,xp) for the PT-symmetric quantum field theory defined by the Hamiltonian density H=12(∇ϕ)2+12ϕ2(iϕ)ϵ in D-dimensional Euclidean spacetime, where ϕ is a pseudoscalar field....
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
7 October 2021
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| In: |
Physical review
Year: 2021, Volume: 104, Issue: 8, Pages: 1-17 |
| ISSN: | 2470-0029 |
| DOI: | 10.1103/PhysRevD.104.085011 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1103/PhysRevD.104.085011 Verlag, lizenzpflichtig, Volltext: https://link.aps.org/doi/10.1103/PhysRevD.104.085011 
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| Author Notes: | Alexander Felski, Carl M. Bender, S.P. Klevansky, and Sarben Sarkar |
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| 520 | |a In a previous paper it was shown how to calculate the ground-state energy density E and the p-point Green’s functions Gp(x1,x2,…,xp) for the PT-symmetric quantum field theory defined by the Hamiltonian density H=12(∇ϕ)2+12ϕ2(iϕ)ϵ in D-dimensional Euclidean spacetime, where ϕ is a pseudoscalar field. In this earlier paper E and Gp(x1,x2,…,xp) were expressed as perturbation series in powers of ϵ and were calculated to first order in ϵ. (The parameter ϵ is a measure of the nonlinearity of the interaction rather than a coupling constant.) This paper extends these perturbative calculations to the Euclidean Lagrangian L=12(∇ϕ)2+12μ2ϕ2+12gμ20ϕ2(iμ1−D/20ϕ)ϵ−ivϕ, which now includes renormalization counterterms that are linear and quadratic in the field ϕ. The parameter g is a dimensionless coupling strength and μ0 is a scaling factor having dimensions of mass. Expressions are given for the one-, two-, and three-point Green’s functions, and the renormalized mass, to higher order in powers of ϵ in D dimensions (0≤D≤2). Renormalization is performed perturbatively to second order in ϵ and the structure of the Green’s functions is analyzed in the limit D→2. A sum of the most divergent terms is performed to all orders in ϵ. Like the Cheng-Wu summation of leading logarithms in electrodynamics, it is found here that leading logarithmic divergences combine to become mildly algebraic in form. Future work that must be done to complete the perturbative renormalization procedure is discussed. | ||
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