Search Results for « Infrared divergences »

The infrared divergences of quantum electrodynamics are eliminated to all orders of perturbation theory in the matrix elements by an appropriate choice of initial and final soft photon states. The condition for this cancellation restricts these states to representations of the canonical commutation rules which are unitarily inequivalent to the usual Fock representation.

It has been found recently that the vacuum state of quantum electrodynamics (QED) is infinitely degenerate. The authors exploit this fact and show that any non-trivial scattering process in QED is necessarily accompanied by a transition among the degenerate vacua, making the scattering amplitude finite at low energy scales (infrared finite).

The aim of this article is to explore the interplay between the eikonal resummation in impact-parameter space and the exponentiation of infrared divergences in momentum space for gravity amplitudes describing collisions of massive objects. The eikonal governs the classical dynamics relevant to the two-body problem, and its infrared properties are directly linked to the zero-frequency limit of the gravitational wave emission spectrum and to radiation-reaction effects. Combining eikonal and infrared exponentiations it is possible to derive these properties at a given loop order starting from lower-loop data. This is illustrated explicitly in $\mathcal{N}=8$ supergravity and in general relativity by deriving the divergent part of the two-loop eikonal from tree-level and one-loop elastic amplitudes.

The Higgs effective potential in the Standard Model (SM), calculated perturbatively, generically suffers from infrared (IR) divergences when the (field-dependent) tree-level mass of the Goldstone bosons goes to zero. Such divergences can affect both the potential and its first derivative and become worse with increasing loop order. In this paper we show that these IR divergences are spurious, we perform a simple resummation of all IR-problematic terms known (up to three loops) and explain how to extend the resummation to cure all such divergences to any order. The method is of general applicability and would work in scenarios other than the SM. Our discussion has some bearing on a scenario recently proposed as a mechanism for gauge mediation of scale breaking in the ultraviolet, in which it is claimed that the low-energy Higgs potential is non-standard. We argue that all non-decoupling effects from the heavy sector can be absorbed in the renormalization of low-energy parameters leading to a SM-like effective theory.

We show that the emission of soft photons via nonlinear Compton scattering in a pulsed plane wave (laser field) is in general infrared divergent. We give examples of both soft and soft-collinear divergences, and we pay particular attention to the case of crossed fields in both classical and quantum theories.

Inflationary correlation functions are potentially affected by infrared divergences. For example, the two-point correlator of curvature perturbation at momentum k receives corrections ∼ ln ( kL ), where L is the size of the region in which the measurement is performed. We define infrared-safe correlation functions which have no sensitivity to the size L of the box used for the observation. The conventional correlators with their familiar log-enhanced corrections (both from scalar and tensor long-wavelength modes) are easily recovered from our IR-safe correlation functions. Among other examples, we illustrate this by calculating the corrections to the non-Gaussianity parameter f NL coming from long-wavelength tensor modes. In our approach, the IR corrections automatically emerge in a resummed, all-orders form. For the scalar corrections, the resulting all-orders expression can be evaluated explicitly.

Measurements of the luminosity distance have played a key role in discovering the late-time cosmic acceleration. However, when accounting for inhomogeneities in the Universe, its interpretation has been plagued with infrared divergences in its theoretical predictions, which are in some cases used to explain the cosmic acceleration without dark energy. The infrared divergences in most calculations are artificially removed by imposing an infrared cut-off scale. We show that a gauge-invariant calculation of the luminosity distance is devoid of such divergences and consistent with the equivalence principle, eliminating the need to impose a cut-off scale. We present proper numerical calculations of the luminosity distance using the gauge-invariant expression and demonstrate that the numerical results with an ad hoc cut-off scale in previous calculations have negligible systematic errors as long as the cut-off scale is larger than the horizon scale. We discuss the origin of infrared divergences and their cancellation in the luminosity distance.

Continuous and discrete superselection rules induced by the interaction with the environment are investigated for a class of exactly soluble Hamiltonian models. The environment is given by a boson field. Stable superselection sectors can only emerge if the low frequences dominate and the ground state of the boson field disappears due to infrared divergence. The models allow uniform estimates of all transition matrix elements between different superselection sectors.