Related papers: Difficulties with the Klein-Gordon Equation
The classical Maxwell-Dirac and Maxwell-Klein-Gordon theories admit solutions of the field equations where the corresponding electric current vanishes in the causal complement of some bounded region of Minkowski space. This poses the…
Variational principles for field theories where variations of fields are restricted along a parametrization are considered. In particular, gauge-natural parametrized variational problems are defined as those in which both the Lagrangian and…
Requiring covariance of Maxwell's equations without {\it a priori} imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules,…
In spite of its problems with interactions, the first-quantized Klein-Gordon equation is a satisfactory theory of free spinless particles. Moreover, the usual theory may be extended to describe Lorentz-violating behavior, of the same types…
This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with the cubic…
The mathematical logic of a true nature of mirror symmetry expresses, in the case of the Dirac Lagrangian, the ideas of the left- and right-handed photons referring to long- and short-lived particles, respectively. Such a difference in…
We analyse the complex-valued Klein-Gordon Equation from an integrability perspective by the implementation of the Lie Theory of Continuous Groups, where this equation is governed by power-law nonlinearity. We write the equations in terms…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
We make a rigorous study of classical field equations on a 2-dimensional signature changing spacetime using the techniques of operator theory. Boundary conditions at the surface of signature change are determined by forming self-adjoint…
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry…
Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely, (i) $\vec{E}=\alpha\beta_0e^{-\alpha x_2}\hat{x}_2$, $\vec{B}=\alpha\beta_1e^{-\alpha…
We couple a nonlinear evolution equation with an associated one and derive the action principle. This allows us to write the Lagrangian density of the system in terms of the original field variables rather than Casimir potentials. We find…
Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein-Gordon equation. This allows us to describe this algebra in…
Building on the Utiyama principle we formulate an approach to Lagrangian field theory in which exterior covariant differentials of vector-valued forms replace partial derivatives, in the sense that they take up the role played by the latter…
A succinct presentation of the algebraic structure of the quantized Klein-Gordon field can be given in terms of a Lorentz invariant inner product. A presentation of a classical Klein-Gordon \emph{random} field at non-zero temperature can be…
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived.…
We consider a modified Klein-Gordon equation that arises at ultra high energies. In a suitable approximation it is shown that for the linear potential which is of interest in quark interactions, their confinement for example,we get…
The mystery that the real scalar Klein-Gordon field has vanishing current densities is resolved. The scalar field is shown to be a complex field due to the condition of possessing a proper non-relativistic limit. Like the Schr\"odinger…
There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies…
We derive a Lagrangian density of Dirac field by employing the local gauge invariance and the Maxwell equation as the fundamental principle. The only assumption made here is that the fermion field should have four components. The present…