相关论文: Exterior Differential Forms in Field Theory
Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics,…
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas…
The features of vacuum particle creation in an external classical field are studied for simplest external field models in $3 + 1$ dimensional QED. The investigation is based on a kinetic equation that is a nonperturbative consequence of the…
In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the…
In our previous paper [International Journal of Theoretical Physics, 41 (2002), 1165-1190] we have shown, following the tradition of synthetic differential geometry, that div and rot are uniquely determined, so long as we require that the…
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to…
This article examines how the physical presence of field energy and particulate matter could influence the topological properties of space time. The theory is developed in terms of vector and matrix equations of exterior differential forms.…
A formal correspondence is established between the curvature theory of generalized implicit hypersurfaces, electromagnetism as expressed in terms of exterior differential systems, and thermodynamics. Starting with a generalized implicit…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
The analysis of the dynamics of a material point perfectly constrained to a submanifold of the three-dimensional euclidean space and subjected to a locally conservative force's field, namely a force's field corresponding to a closed but not…
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of…
This paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…
We construct a class of interacting $(d-2)$-form theories in $d$ dimensions that are `third way' consistent. This refers to the fact that the interaction terms in the $p$-form field equations of motion neither come from the variation of an…
In the Lagrangian framework for symmetries and conservation laws of field theories, we investigate globality properties of conserved currents associated with non-global Lagrangians admitting global Euler--Lagrange morphisms. Our approach is…
A tight-binding model of electron dynamics in mesoscopic normal rings is studied using boundary conformal field theory. The partition function is calculated in the low energy limit and the persistent current generated as a function of an…
We lay down a set of requirements for a field theory to produce a covariant conservation law out of Noether's second theorem, and show that neither local invariance implies a covariant conservation law, nor the existence of a covariant…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
I present a derivation of form factors in the Algebraic Cluster Model for an arbitrary number of identical clusters. The form factors correspond to representation matrix elements which are derived in closed form for the harmonic oscillator…
We introduce a variational principle for field theories, referred to as the Hamilton-Pontryagin principle, and we show that the resulting field equations are the Euler-Lagrange equations in implicit form. Secondly, we introduce multi-Dirac…