Related papers: Generalized Potential and Mathematical Principles …
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…
We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace and positive definite in a complementary subspace. The…
In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of…
In the last 175 years, the physical understanding of nature has seen a revolutionary change. Until about 1850, Newton's theory and the mechanical world view derived from it provided the dominant view of the physical world, later…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the…
Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
Generalized Noether's theory is a useful method for researching the modified gravity theories about the conserved quantities and symmetries. A generally Gauss-Bonnet gravity $f(R,\mathcal{G})$ theory was proposed as an alternative gravity…
General relativity and quantum mechanism are two separate rules of modern physics explaining how nature works. Both theories are accurate, but the direct connection between two theories was not yet clarified. Recently, researchers blur the…
One hundred years ago this year attempts began to generalise general relativity with the ambition of incorporating electromagnetism alongside gravitation in a unified field theory. These developments led to gauge theories and models with…
Compositional Generalization (CG) embodies the ability to comprehend novel combinations of familiar concepts, representing a significant cognitive leap in human intellectual advancement. Despite its critical importance, the deep neural…
In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…
Generalized power asymptotic expansions of solutions to differential equations that depend on parameters are investigated. The changing nature of these expansions as the parameters of the model cross critical values is discussed. An…
Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…
The GENERIC theory provides a framework for the description of non-equilibrium phenomena in isolated systems beyond local thermal equilibrium and beyond linear non-equilibrium (i.e., linear relations between thermodynamic forces and…
This paper describes perturbative framework, on the basis of the closed-time-path formalism, in terms of quasiparticle picture for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary…
Generalized symmetries (also known as categorical symmetries) is a newly developing technique for studying quantum field theories. It has given us new insights into the structure of QFT and many new powerful tools that can be applied to the…
We focus on the general theory to the Cauchy problem for one dimensional nonlinear wave equations with small initial data. In the general theory, we aim to obtain the lower bound estimate of the lifespan of classical solution. In this…