Abstract
In this article we extend a previous discussion about the influence of an external magnetic field on renormalons in a self interacting scalar theory by including now temperature effects, in the imaginary formalism, together with an external weak external magnetic field. We show that the location of poles in the Borel plane does not change, getting their residues, however, a dependence on temperature and on the magnetic field.The effects of temperature and the magnetic field strength on the residues turn out to be opposite. We present a detailed discussion about the evolution of these residues, showing technical details involved in the calculation.
Highlights
Since the paper by Dyson [1] on the convergence of perturbative series in quantum electrodynamics (QED), a seminal article based exclusively on physical arguments, we have learned that power series expansions in quantum field theory, in general, are divergent objects
In this article we extend a previous discussion about the influence of an external magnetic field on renormalons in a self-interacting scalar theory by including temperature effects, in the imaginary formalism, together with an external weak external magnetic field
For high orders of perturbation, the divergence grows like n!, where n is the order of the expansion, and this is essentially due to the multiplicity of diagrams that contribute to a certain Green function, or to a physical process, at such an expansion order
Summary
Since the paper by Dyson [1] on the convergence of perturbative series in quantum electrodynamics (QED), a seminal article based exclusively on physical arguments, we have learned that power series expansions in quantum field theory, in general, are divergent objects. In this article we analyze, in the frame of a self-interacting scalar λφ theory, the influence of the magnetic field and temperature on the position of the UV renormalons (the only ones relevant in λφ theory) and their residues in the Borel plane. Some extensions such as the q-Borel series have been proposed, allowing the discussion of series whose coefficients grow like ðk!Þq [34]. In the present article we extend previous discussions where the behavior of renormalons in λφ was analyzed, separately, for the case where thermal corrections appeared in the real time formalism, and for corrections due to the presence of a magnetic field.
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