Exact plane‐wave solutions of the coupled Maxwell–Klein–Gordon equations

In this paper, we obtain dispersion relations corresponding to plane wave solutions in Lorentz-breaking extensions of gravity with dimension 3, 4, 5 and 6 operators. We demonstrate that these dispersion relations display a usual Lorentz-invariant mode when the corresponding additive term involves higher derivatives.

Download Full-text

THE TACHYON FIELD BELOW THE MASS BARRIER

International Journal of Modern Physics A ◽

10.1142/s0217751x94001382 ◽

1994 ◽

Vol 09 (20) ◽

pp. 3497-3502 ◽

Cited By ~ 3

Author(s):

D.G. BARCI ◽

C.G. BOLLINI ◽

M.C. ROCCA

Keyword(s):

Green Function ◽

Eigenvalue Problem ◽

Plane Wave ◽

Time Evolution ◽

Mass Parameter ◽

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Tachyon Field ◽

Expectation Value ◽

Wave Solutions

We consider a tachyon field whose Fourier components correspond to spatial momenta with modulus smaller than the mass parameter. The plane wave solutions have then a time evolution which is a real exponential. The field is quantized and the solution of the eigenvalue problem for the Hamiltonian leads to the evaluation of the vacuum expectation value of products of field operators. The propagator turns out to be half-advanced and half-retarded. This completes the proof4 that the total propagator is the Wheeler Green function.4,7

Download Full-text

A method for constructing solutions of homogeneous partial differential equations: localized waves

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1992.0086 ◽

1992 ◽

Vol 437 (1901) ◽

pp. 673-692 ◽

Cited By ~ 54

Keyword(s):

Wave Equation ◽

Partial Differential Equations ◽

Differential Equations ◽

Gordon Equation ◽

Partial Differential ◽

Wave Solutions ◽

Propagation Axis ◽

Potential Applications ◽

Klein Gordon ◽

Localized Waves

We introduce a method for constructing solutions of homogeneous partial differential equations. This method can be used to construct the usual, well-known, separable solutions of the wave equation, but it also easily gives the non-separable localized wave solutions. These solutions exhibit a degree of focusing about the propagation axis that is dependent on a free parameter, and have many important potential applications. The method is based on constructing the space-time Fourier transform of a function so that it satisfies the transformed partial differential equation. We also apply the method to construct localized wave solutions of the wave equation in a lossy infinite medium, and of the Klein-Gordon equation. The localized wave solutions of these three equations differ somewhat, and we discuss these differences. A discussion of the properties of the localized waves, and of experiments to launch them, is included in the Appendix.

Download Full-text