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A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
The Standard Model cannot explain the dominance of matter over anti-matter in our universe. This imbalance indicates undiscovered physics that violates combined CP symmetry. Many extensions to the Standard Model seek to explain the…
A dynamical Maxwell system is \begin{align*} & e_t={\rm curl\,} h, \quad h_t=-{\rm curl\,} e &&{\rm in}\,\,\Omega \times (0,T) & e|_{t=0}=0,\,\,\,\,h|_{t=0}=0 &&{\rm in}\,\,\Omega & e_\theta =f &&{\rm in}\,\,\, \partial\Omega \times [0,T]…
In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard…
Gill and Zachary's proper-time reformulation of Maxwell's equations introduces a source-dependent speed b = sqrt(c^2 + u^2), distinct from standard electrodynamics. This study applies Lie symmetry analysis to the resulting wave equations,…
Passive resonators-systems that exhibit loss but no gain-are foundational elements across nearly every domain of physics and many types of of systems such as subwavelength particles, dielectric slabs, electric circuits, biological…
We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\mu \nu}$ replaced by a unit-determinant metric $h_{\mu…
Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave…
We consider the evolution of open quantum systems coupled to one or more Gaussian environments. We demonstrate that such systems can be described by a Markovian quantum master equation (MQME) up to a correction that decreases exponentially…
We develop a quasi-normal mode theory (QNMT) to calculate a system's scattering $S$ matrix, simultaneously satisfying both energy conservation and reciprocity even for a small truncated set of resonances. It is a practical reduced-order…
Conformal field theories (CFT) play an important role in quantum field theories as they allow for exact studies that are hard to access without the conformal symmetries in place. A remarkable recent development is the application of…
The curved spacetime Maxwell equations are applied to the anisotropically expanding Kasner metrics. Using the application of vector identities we derive 2$^\textrm{nd}$-order differential wave equations for the electromagnetic field…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
I summarise a method to quantitatively assess the consistency of power-counting proposals in Effective Field Theories which are non-perturbative at leading order. It uses the fact that the Renormalisation Group evolution of an observable…
Detailed study of the energy and momentum carried by the electromagnetic field can be a source of clues to possible new physics underlying the Maxwell Equations. But such study has been impeded by expressions for the parameters of the…
We develop an approach to chiral kinetic theories for electrons close to equilibrium and neutrinos away from equilibrium based on a systematic power counting scheme for different timescales of electromagnetic and weak interactions. Under…
For over 30 years, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the liquid-glass transition. MCT, however, is limited by its ad hoc construction and lacks a mechanism to institute corrections.…
Various models are under consideration with metric type flat FRW whose energy-momentum tensor is described by a perfect fluid whose generic equation state and taking into account the conservation principle, but considering some of the…
Generating probabilistic forecasts of potential outcomes and individual treatment effects (ITE) is essential for risk-aware decision-making in domains such as healthcare, policy, marketing, and finance. We propose two novel methods: the…
A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte-Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space…