Related papers: Demystifying the Lagrangians of special relativity
The structure of a diffeomorphism invariant Lagrangians for an extended object W embedded in a bulk space M is discussed by following a close analogy with the relativistic particle in electromagnetic field as a system that is…
Different formulations of special relativity are theoretically discussed. First an invariant formulation, i.e., the ''true transformations (TT) relativity,'' is exposed. There a physical quantity is represented by a true tensor which…
This manuscript provides a characterisation of the equivalence class of classical smooth Lagrangian densities that involve terms depending on two distinct points of the underlying Euclidean base space of the theory. Theories of this type…
Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum…
In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact…
According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic. Nonetheless many inconsistencies arise…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial…
In this paper we show how relativistic tensor dynamics and relativistic electrodynamics can be formulated in a biquaternion tensor language. The treatment is restricted to mathematical physics, known facts as the Lorentz Force Law and the…
The development of both special and general relativity is accomplished in a series of 6 papers using a simple approach. The purpose is to explain the how and why of relativity to a broad public, and to be useful for students of physics by…
In this article, the axioms presented in the first one are reformulated according to the special theory of relativity. Using these axioms, quantum mechanic's relativistic equations are obtained in the presence of electromagnetic fields for…
We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify…
A theory of electromagnetism is proposed that is based on the Fermi Lagrangian, which is symmetric under electromagnetic spin rotation. Its features are: - the four-potential is unambiguously determined by the inhomogeneous wave equation…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
This paper presents an approach to the creation of a variant of Extended Special Relativity that takes into consideration the existence of limiting relativistically invariant quantities (Planck parameters). It shows the possibility of…
We present a new Lagrangian formulation of General Relativity with cosmological constant, coupled to Yang-Mills gauge theory. The formulation has a manifest color/kinematics-dual structure, both in the choice of fundamental fields and in…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
The so-called $\Gamma\Gamma$-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General…
This article devoted to relativistic dynamics of a charged massive particle in an electroscalar field. It represents a continuation of paper [1] where the authors constructed a non-relativistic theory which describes transverse…
A new Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time…