相关论文: Beyond Fab Four

In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for a flat metric tensor and constant scalar…

The gravitational Lagrangian based on special relativity and the assumption of a fourth rank tensor interaction, derived by Kennedy (1972), is used to check Mach's principle in a homogeneous isotropic expanding universe. The Lagrangian is…

We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In…

Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can possibly exist, unless it yields contradiction" (Possibility…

Several proposals to deal with the dynamics of general relativity involve gauge fixings or the introduction matter fields in terms of which the theory is deparameterized. The resulting theories have true Hamiltonians for their evolution…

In the extended Lagrange formalism of classical point dynamics, the system's dynamics is parametrized along a system evolution parameter $s$, and the physical time $t$ is treated as a \emph{dependent} variable $t(s)$ on equal footing with…

We observe that in many F-theory models, tuning a specific gauge group $G$ and matter content $M$ under certain circumstances leads to an automatic enhancement to a larger gauge group $G' \supset G$ and matter content $M' \supset M$. We…

Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…

We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the…

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…

The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…

We develop the concept and the calculus of anti-self dual (ASD) Lagrangians which seems inherent to many questions in mathematical physics, geometry, and differential equations. They are natural extensions of gradients of convex functions…

This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many…

A comparative analysis of two different versions of the Legendre transformation is presented. We provide an almost complete although somewhat superficial review of the geometric background for analytical mechanics. Complete coordinate…

The current paper introduces classical, relativistic Lagrangians for point-particle analogs to the field theory description of the Standard-Model Extension (SME) for Lorentz violation. Lagrangians of a form alternative to those derived and…

We prove an extension of Yuan's Lemma to more than two matrices, as long as the set of matrices has rank at most 2. This is used to generalize the main result of [A. Baccari and A. Trad. On the classical necessary second-order optimality…

Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic…

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore…

We consider gauge theories defined in higher dimensions where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a…

The goal of this article is to study necessary and sufficient conditions for the exactness of penalty functions and the existence of global saddle points of augmented Lagrangians for well-posed (in a suitable sense) constrained optimization…