Renormalization of the Vector Current in QED

It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the four-divergence of the electromagnetic field-strength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the MSbar-renormalized current by a definite finite renormalization. This happens in such a way that Gauss's law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory.Comment: 9 pages. Corresponds to published version (Phys. Rev. D), including appendix about Weeks's parado

Global Color is not Always Defined

Far away from a fundamental magnetic monopole of the SU(5) grand unified theory, the full theory reduces to one whose gauge group is unbroken SU(3) ⊗ U(1). The algebra of generators of smooth gauge transformations in this unbroken theory, however, will not in general contain any subalgebra isomorphic to su(3). This means that global color rotations are not always defined. The resulting inability to classify semiclassical dyon states by their color climinates an apparent paradox related to the vacuum angle θ

A Comment on Sigma Model Anomalies

Some non-linear sigma models with fermions are known to be ill-defined because of a global obstruction to any consistent quantization. Sigma models relevant to phenomenological theories of dynamical symmetry breaking must satisfy the additional constraint of appropriately realizing the flavor symmetries of the underlying theory at the one-loop level. This is possible if and only if \u27t Hooft\u27s anomaly condition is satisfied. In particular, we show that there always exists a Wess-Zumino term which correctly reproduces the flavor anomalies, and the global obstruction vanishes, whenever \u27t Hooft\u27s condition is satisfied

The impossibility of low rank representations for triangle-rich complex networks

The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact human behavior via social networks, search engines, and recommender systems to name a few. A widely used algorithmic technique for modeling such complex networks is to construct a low-dimensional Euclidean embedding of the vertices of the network, where proximity of vertices is interpreted as the likelihood of an edge. Contrary to the common view, we argue that such graph embeddings do not}capture salient properties of complex networks. The two properties we focus on are low degree and large clustering coefficients, which have been widely established to be empirically true for real-world networks. We mathematically prove that any embedding (that uses dot products to measure similarity) that can successfully create these two properties must have rank nearly linear in the number of vertices. Among other implications, this establishes that popular embedding techniques such as Singular Value Decomposition and node2vec fail to capture significant structural aspects of real-world complex networks. Furthermore, we empirically study a number of different embedding techniques based on dot product, and show that they all fail to capture the triangle structure

The Zero-Bin and Mode Factorization in Quantum Field Theory

We study a Lagrangian formalism that avoids double counting in effective field theories where distinct fields are used to describe different infrared momentum regions for the same particle. The formalism leads to extra subtractions in certain diagrams and to a new way of thinking about factorization of modes in quantum field theory. In non-relativistic field theories, the subtractions remove unphysical pinch singularities in box type diagrams, and give a derivation of the known pull-up mechanism between soft and ultrasoft fields which is required by the renormalization group evolution. In a field theory for energetic particles, the soft-collinear effective theory (SCET), the subtractions allow the theory to be defined with different infrared and ultraviolet regulators, remove double counting between soft, ultrasoft, and collinear modes, and give results which reproduce the infrared divergences of the full theory. Our analysis shows that convolution divergences in factorization formul\ae occur due to an overlap of momentum regions. We propose a method that avoids this double counting, which helps to resolve a long standing puzzle with singularities in collinear factorization in QCD. The analysis gives evidence for a factorization in rapidity space in exclusive decays.Comment: 92 pages, v4- Journal version. Some improvements to language in sections I, IIA, VI

Enhanced nonperturbative effects in jet distributions

We consider the triple differential distribution d\Gamma/(dE_J)(dm_J^2)(d\Omega_J) for two-jet events at center of mass energy M, smeared over the endpoint region m_J^2 << M^2, |2 E_J -M| ~ \Delta, \lqcd << \Delta << M. The leading nonperturbative correction, suppressed by \lqcd/\Delta, is given by the matrix element of a single operator. A similar analysis is performed for three jet events, and the generalization to any number of jets is discussed. At order \lqcd/\Delta, non-perturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two and three jet events.Comment: Significant changes made. The first moment does not vanish--the paper has been modified to reflect this. Relations between different numbers of jets still hol

Coupled impacts of the diurnal cycle of sea surface temperature on the Madden–Julian oscillation

Author Posting. © American Meteorological Society, 2014. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 27 (2014): 8422–8443, doi:10.1175/JCLI-D-14-00141.1.This study quantifies, from a systematic set of regional ocean–atmosphere coupled model simulations employing various coupling intervals, the effect of subdaily sea surface temperature (SST) variability on the onset and intensity of Madden–Julian oscillation (MJO) convection in the Indian Ocean. The primary effect of diurnal SST variation (dSST) is to raise time-mean SST and latent heat flux (LH) prior to deep convection. Diurnal SST variation also strengthens the diurnal moistening of the troposphere by collocating the diurnal peak in LH with those of SST. Both effects enhance the convection such that the total precipitation amount scales quasi-linearly with preconvection dSST and time-mean SST. A column-integrated moist static energy (MSE) budget analysis confirms the critical role of diurnal SST variability in the buildup of column MSE and the strength of MJO convection via stronger time-mean LH and diurnal moistening. Two complementary atmosphere-only simulations further elucidate the role of SST conditions in the predictive skill of MJO. The atmospheric model forced with the persistent initial SST, lacking enhanced preconvection warming and moistening, produces a weaker and delayed convection than the diurnally coupled run. The atmospheric model with prescribed daily-mean SST from the coupled run, while eliminating the delayed peak, continues to exhibit weaker convection due to the lack of strong moistening on a diurnal basis. The fact that time-evolving SST with a diurnal cycle strongly influences the onset and intensity of MJO convection is consistent with previous studies that identified an improved representation of diurnal SST as a potential source of MJO predictability.The authors gratefully acknowledge support from the Office of Naval Research (N00014-13-1-0133 and N00014-13-1-0139) and National Science Foundation EaSM-3 (OCE-1419235). HS especially thanks the Penzance Endowed Fund for their support of Assistant Scientists at WHOI.2015-05-1

Soft-Collinear Factorization and Zero-Bin Subtractions

We study the Sudakov form factor for a spontaneously broken gauge theory using a (new) Delta -regulator. To be well-defined, the effective theory requires zero-bin subtractions for the collinear sectors. The zero-bin subtractions depend on the gauge boson mass M and are not scaleless. They have both finite and 1/epsilon contributions, and are needed to give the correct anomalous dimension and low-scale matching contributions. We also demonstrate the necessity of zero-bin subtractions for soft-collinear factorization. We find that after zero-bin subtractions the form factor is the sum of the collinear contributions 'minus' a soft mass-mode contribution, in agreement with a previous result of Idilbi and Mehen in QCD. This appears to conflict with the method-of-regions approach, where one gets the sum of contributions from different regions.Comment: 9 pages, 5 figures. V2:ref adde