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Supersymmetry
Published in Harish Parthasarathy, Supersymmetry and Superstring Theory with Engineering Applications, 2023
[f] If an integral of the form ∫μ∧f(k,g)dk that represents a propagator correction or some scattering amplitude diverges as μ ↓ 0 (infrared divergence) of as ⋀ → ∞ (ultraviolet divergence) or both where ɡ is a coupling constant, or some parameter in the field theory Lagrangian like mass, charge or some parameter in the propagator, then we redefine a renormalized coupling constant ɡR= ɡR(μ, ⋀) so that this integral assumes a definite finite value say c and then we express all the ampltiudes etc in terms of this renormalized parameter ɡR:c=∫μΛf(k,gℛ)dk
Propagation and Energy Transfer
Published in James D. Taylor, Introduction to Ultra-Wideband Radar Systems, 2020
Robert Roussel-Dupré, Terence W. Barrett
The second example of power law behavior is the relaxation of a system close to a critical point predicted to have the form t−n, 0 < n < 1.33 It is well known that in the theory of critical pheomena the order parameter fluctuations are localized within a correlation length, which increases toward macroscopic size as a transition temperature is approached and as the order parameter fluctuations decrease. The equation of motion is nonlinear and generated from a thermodynamic force obtained from the free energy gradient. The mixing term is related to the intrinsic site probability density for the order parameter, permitting the order parameter to adopt a continuum of values at a site, even though only a restricted number are possible in the site coordinate system.35 As the fluctuation rate decreases and approaches a transition temperature, the mixing term ensures no gap opens between its time scale and that of the other modes. At the same time an infrared divergence in the self-energy occurs. There is thus a parallel with the Dissado-Hill picture, the major difference being that the correlation length is divergent only in the critical systems.
On self-energy contributions near Berezinskii–Kosterlitz–Thouless transition in interacting homogeneous 2D Bose system
Published in Philosophical Magazine, 2023
Pengtao Shen, Thomas Ainsworth, Benjamin M. Fregoso, Khandker F. Quader
With the inclusion of higher order self-energy terms, the spectrum near k = 0 ‘hardens’: and the infrared divergence of the total density of particle is cured. The second order self-energy diagrams are shown in Figure 2.