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Page 369
... invariant . Thus ds2 = dx2 + dy2 + dz2 = ds'2 dr2 = dt'2 ( 11.59 ) For Lorentz transformations , on the other hand , the time and space coordinates are interrelated . From ( 11.21 ) it is easy to show that the invariant " length ...
... invariant . Thus ds2 = dx2 + dy2 + dz2 = ds'2 dr2 = dt'2 ( 11.59 ) For Lorentz transformations , on the other hand , the time and space coordinates are interrelated . From ( 11.21 ) it is easy to show that the invariant " length ...
Page 407
... Lorentz invariant , but depends on the path taken . For purposes of calculation , consider a reference frame in which the particle is initially at rest . From definition ( 11.62 ) of proper time it is clear that , if the particle stays ...
... Lorentz invariant , but depends on the path taken . For purposes of calculation , consider a reference frame in which the particle is initially at rest . From definition ( 11.62 ) of proper time it is clear that , if the particle stays ...
Page 632
... Lorentz transformation of coordinates , 376 in transforming delta functions , 79 Kinematics , relativistic , 394 f ... invariant , see Scalar , Relativ- istic invariance Lorentz line shape , 436 , 601 , 604 for cavity , 256 Lorentz ...
... Lorentz transformation of coordinates , 376 in transforming delta functions , 79 Kinematics , relativistic , 394 f ... invariant , see Scalar , Relativ- istic invariance Lorentz line shape , 436 , 601 , 604 for cavity , 256 Lorentz ...
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4-vector Ampère's law angle angular distribution approximation atomic axis boundary conditions calculate Chapter charge density charge q charged particle coefficients collisions component conductor consider coordinates cross section current density cylinder d³x delta function dielectric constant diffraction dimensions dipole direction discussed E₁ electric field electromagnetic fields electron electrostatic energy loss expansion expression factor frequency given Green's function impact parameter incident particle inside integral inversion Laplace's equation linear Lorentz transformation macroscopic magnetic field magnetic induction magnetic moment magnitude Maxwell's equations meson modes molecules momentum motion multipole nonrelativistic normal obtain oscillations P₁ parallel plasma point charge Poisson's equation polarization problem radiation radius region relativistic result scalar scalar potential scattering shown in Fig shows solution spherical surface surface-charge density theorem transverse unit V₁ vanishes vector potential velocity volume wave equation wave number wavelength written zero ΦΩ