相关论文: Geometric Nonlinearities in Field Theory, Condense…

The paper discusses the basic paradoxes of thermodynamics and quantum mechanics. The approaches to solution of these paradoxes are suggested. The first one relies on the influence of the external observer (environment), which disrupts the…

Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the…

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental…

We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and…

We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…

We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…

Symmetry invariant local interaction of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.

A shift symmetry is a ubiquitous ingredient in inflationary models, both in effective constructions and in UV-finite embeddings such as string theory. It has also been proposed to play a key role in certain Dark Energy and Dark Matter…

We show the existence of a noncommutative spacetime structure in the context of a complete discussion on the underlying spacetime symmetries for the physical system of a free massless relativistic particle. The above spacetime symmetry…

We review discoveries in the nonlinear dynamics of curved spacetime, largely made possible by numerical solutions of Einstein's equations. We discuss critical phenomena and self-similarity in gravitational collapse, the behavior of…

Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…

We outline a program with the potential to solve both the cosmological constant and quantum gravity problems within a single, comprehensive framework, one that is formulated entirely in four spacetime dimensions. The program is based on an…

We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar…

The noninvertible axial symmetry constructed from the ABJ-anomaly has attracted enormous interest. We discuss the mechanism of "symmetry-from-anomaly" in condensed matter-related models in both 1d and 3d spaces (which correspond to (1+1)d…

The purpose of these lectures is to illustrate how symmetry and pattern recognition play essential roles in the progression from experimental observation to an understanding of nuclear phenomena in terms of interacting neutrons and protons.…

The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…

Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or…

We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…

Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…

The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…