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A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.
Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…
We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when…
We extend the gauge invariant variational approach of Phys. Rev. D52 (1995) 3719, hep-th/9408081, to theories with fermions. As the simplest example we consider the massless Schwinger model in 1+1 dimensions. We show that in this solvable…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
We show that a high frequency standing wave in SU(2) gauge theory is unstable against decay into long wavelength modes. This provides a non-perturbative mechanism for energy transfer from initial high momentum modes to final states with low…
In this work, we consider the problem of bounding the values of a covariance function corresponding to a continuous-time stationary stochastic process or signal. Specifically, for two signals whose covariance functions agree on a finite…
This is a short review of present and future limits on new neutral gauge bosons, in particular on hadrophilic or leptophobic $Z'$s recently proposed to interpret the observed fluctuations of $\Gamma _{c,b}$ at LEP. Light gauge bosons…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] and [P. Grohs and M. Rathmair. Stable Gabor phase retrieval for multivariate functions.…
We develop a stable and efficient numerical scheme for modeling the optical field evolution in a nonlinear dispersive cavity with counter propagating waves and complex, semiconductor physics gain dynamics that are expensive to evaluate. Our…
The aims of this letter are two. First, to show the angular gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after resuming for completeness results on the Transverse-Traceless (TT) gauge,…
Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature,…
We calculate the quantum corrections to the gauge-invariant gravitational potentials of spinning particles in flat space, induced by loops of both massive and massless matter fields of various types. While the corrections to the Newtonian…
In this paper, we propose a gauge-invariant way to define and calculate the effective mass for quasiparticles in systems with gauge interactions, and apply it to a model closely related to the half-filled Landau level problem. Our model is…
We reexamine the invariance of two-photon transition matrix elements and corresponding two-photon Rabi frequencies under the "gauge" transformation from the length to the velocity gauge. It is shown that gauge invariance, in the most…
The RI/MOM non-perturbative renormalization scheme is studied on the lattice in SU(3) quenched QCD with Wilson fermions. The gauge dependence of some fermion bilinear renormalization constants is discussed by comparing data which have been…
The problem of defining a gauge invariant effective potential with a strict energetic interpretation is examined in the context of spontaneously broken gauge theories. It is shown that such a potential can be defined in terms of a composite…
In the presence of consistent regulators, the standard procedure of BRST gauge fixing (or moving from one gauge to another) can require non-trivial modifications. These modifications occur at the quantum level, and gauges exist which are…
We are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. We establish stability estimates of logarithmic type when the measurements…