Q-PLANE WAVE SOLUTIONS OF Q-MAXWELL EQUATIONS

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

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On Plane Wave Solutions in Lorentz-Violating Extensions of Gravity

Galaxies ◽

10.3390/galaxies9020032 ◽

2021 ◽

Vol 9 (2) ◽

pp. 32

Author(s):

J. R. Nascimento ◽

A. Yu. Petrov ◽

A. R. Vieira

Keyword(s):

Plane Wave ◽

Dispersion Relations ◽

Wave Solutions ◽

Higher Derivatives ◽

Additive Term

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.

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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

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