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It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
We introduce N-parameter perturbation theory as a new tool for the study of non-linear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to…
The gauge parameter dependence of QED in the covariant gauge can be determined explicitly by introducing a Stueckelberg field, which is a non-interacting fictitious Goldstone boson field. Examples of QED with electrons or charged scalars…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
We state the implications on the properties of vector mesons due to gauge invariance. In particular, we find that polarized vector mesons exhibit a property in the radiation distribution of order $\omega^{-1}$ in the photon energy, namely…
We argue that a spontaneous breakdown of local Weyl invariance offers a mechanism in which gravitational interactions contribute to the generation of particle masses and their electric charge. The theory is formulated in terms of a…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
We obtain, for the first time, an analytic theory of the forward stimulated Brillouin scattering instability of a spatially and temporally incoherent laser beam, that controls the transition between statistical equilibrium and…
Full waveform inversion is an ill-posed inverse problem whose solution non-uniqueness -- i.e., arising from band-limited, finite-aperture, noisy data -- calls for uncertainty quantification to avoid overconfident geological interpretations.…
We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian…
We describe the gauge-invariant treatment of the finite-width effects of W and Z bosons in the fermion-loop scheme and its application to the six-fermion (LEP2) processes e^- e^+ -> four fermions, with massless external fermions. The…
We discuss both theoretical tools to verify gauge invariance in numerical calculations of cross sections and the consistency of approximation schemes used in realistic calculations. A finite set of Ward Identities for 4 point scattering…
Irreducible gauge theories in both the Lagrangian and Hamiltonian versions of the Sp(2)-covariant quantization method are studied. Solutions to generating equations are obtained in the form of expansions in power series of ghost and…
We show that the naively expected large virtual heavy fermion effects in low energy processes may be screened if the process under consideration contains external gauge bosons constrained by gauge invariance. We illustrate this by a typical…
We investigate SU(2) gauge theory in a constant chromomagnetic field in three dimensions both in the continuum and on the lattice. Using a variational method to stabilize the unstable modes, we evaluate the vacuum energy density in the…
Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…
We calculate the perturbative corrections to fermion bilinears that are used in numerical simulations when extracting weak matrix elements using staggered fermions. This extends previous calculations of Golterman and Smit, and Daniel and…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…