Related papers: A Lagrangian for the quantionic field equation

We give here a field-theoretical derivation of the Hamiltonian of the non-relativistic quantum electrodynamics in the Coulomb gauge using the Lagrange formalism. It leads to the same result as the usual derivation, where one just replaces…

We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…

In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation.…

It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so…

We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar…

Using well known Lagrangean techniques for uncovering the gauge symmetries of a Lagrangean, we derive the transformation laws for the phase space variables corresponding to local symmetries of the Hamilton equations of motion. These…

After a very brief review of the formalism of lattice gauge theories we show how one can calculate the parameters of the continuum chiral Lagrangians proceeding through the derivation of an effective lattice chiral Lagrangian as an…

We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…

We point out that in a recent paper by Chaichian et al. (Phys. Rev.Lett71(1993)3405) Dirac quantization procedure is not properly followed as a result of which the resulting quantum theory is different from what one will get by a…

We construct a general stratified scalar theory of gravitation from a field equation that accounts for the self-interaction of the field and a particle Lagrangian, and calculate its post-Newtonian parameters. Using this general framework,…

The classical Lagrange formalism is generalized to the case of arbitrary stationary (but not necessarily conservative) dynamical systems. It is shown that the equations of motion for such systems can be derived in the standard ways from the…

As is well known, Einstein was dissatisfied with the foundation of quantum theory and sought to find a basis for it that would have satisfied his need for a causal explanation. In this paper this abandoned idea is investigated. It is found…

Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac…

In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…

We present the general formulation of non-covariant Lagrangian of self-dual gauge theory. After specifying the parameters therein the previous Lagrangian in the decomposition of spacetime into $6=D_1+D_2$ and $6=D_1+D_2+D_3$ can be…

Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…

Gauge fields associated to the Dirac matrix algebra used with the standard quadratic gauge field Lagrangian lead to an extended gravitational Lagrangian which includes the Einstein-Hilbert one, plus quadratic, cosmological constant and…

Using the recently developed groupoidal description of Schwinger's picture of Quantum Mechanics, a new approach to Dirac's fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function…

After summarizing basic concepts for the exterior algebra we firstly discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple…