Related papers: Electromagnetic Lagrangian on a causal set that re…
The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation…
We introduce new pseudo-metrics on spaces of Lagrangian submanifolds of a symplectic manifold $(M,\omega)$ by considering areas associated to projecting Lagrangian cobordisms in $\mathbb{C} \times M$ to the "time-energy plane" $\mathbb{C}$.…
Temporal networks model a variety of important phenomena involving timed interactions between entities. Existing methods for machine learning on temporal networks generally exhibit at least one of two limitations. First, time is assumed to…
It is well-known that classical linear elasticity equations are not form-invariant under local transformations. This is intrinsically related to the inhomogeneity of elastic media. However, the reported new linear elasticity equations for…
We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by…
We extend the classical edge-triangle Exponential Random Graph Model (ERGM) to an inhomogeneous setting in which vertices carry types determined by an underlying partition. This leads to a block-structured ERGM where interaction parameters…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
Neural ODEs are a widely used, powerful machine learning technique in particular for physics. However, not every solution is physical in that it is an Euler-Lagrange equation. We present Helmholtz metrics to quantify this resemblance for a…
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material…
An effective-mass theory with a deformation-induced (an axial) gauge field is proposed as a theoretical framework to study graphene edge. Though the gauge field is singular at edge, it can represent the boundary condition and this framework…
We describe a new method to parameterise dark energy theories including massive gravity, elastic dark energy and tensor-metric theories. We first examine a framework to describe any second order Lagrangian which depends on the variation of…
Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the…
It is well known that a theory of the (i) Lorentz invariant and (ii) locally interacting (iii) two degrees of freedom of a massless spin 1 particle, the photon, leads uniquely to electromagnetism at large distances. In this work, we remove…
Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the Heisenberg-Euler Lagrangian in traditional quantum…
There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying…
In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical…
We consider entanglement entropy between regions of space in lattice gauge theory. The Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge transformations. By decomposing the edge…
The change of the electromagnetic field in a particular place due to the event of a change in the motion of a charged particle can occur only after the light signal from the event can reach this place. Naive calculations of the…
Granger causality has been employed to investigate causality relations between components of stationary multiple time series. We generalize this concept by developing statistical inference for local Granger causality for multivariate…
Community detection in networks refers to the process of seeking strongly internally connected groups of nodes which are weakly externally connected. In this work, we introduce and study a community definition based on internal edge…