相关论文: Difficulties with the Klein-Gordon Equation

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…

The present paper develops a variational theory of discrete fields defined on abstract cellular complexes. The discrete formulation is derived solely from a variational principle associated to a discrete Lagrangian density on a discrete…

3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum…

A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically…

We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current satisfies on the classical level a relation that is…

We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…

We investigate the asymptotic behavior of the solutions to the Klein-Gordon and Dirac equations using the local spatial averaging approach to Bohr's correspondence principle in the large principal quantum number regime. The procedure is…

An equation, we call Dirac gamma-equation, is introduced with the help of the mathematical tools connected with the Clifford algebra. This equation can be considered as a generalization of the Dirac equation for the electron. Some features…

We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some…

An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to…

The semi-classical quantisation of the two lowest energy static solutions of boundary sine-Gordon model is considered. A relation between the Lagrangian and bootstrap parameters is established by comparing their quantum corrected energy…

We obtain Bargmann-Michel-Telegdi equations of motion of classical spinning particle using Lagrangian variational principle with Grassmann variables.

We suppose that our Universe is closed manifold in real embedding higher dimensional space. This model well describes expanding character of Universe where each point becomes more far from any other point with time. We have derived…

We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…

We consider the massive Klein-Gordon field on the half line with and without a Robin boundary potential.The field is coupled at the boundary to a harmonic oscillator.We solve the system classically and observe the existence of classical…

A first- and second-order relation between cosmic density and peculiar-velocity fields is presented. The calculation is purely Lagrangian and it is derived using the second-order solutions of the Lagrange-Newton system obtained by Buchert &…

The interaction between singular and regular fields is considered for Lorentz-invariant scalar and vector wave equations. The singular field is generated by a Dirac source term. Its dynamics are deduced from the total field Lagrangian. At…

The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…

We show that the correctly evaluated effective Lagrangian should include short-distance interaction terms which have been avoided under the protection of usual regularization and must be properly identified and reinstated if regularization…

We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…