article of mass is given by Let us now denote by the space-time point Then the derivative of this point w.r.t. time is a space-time vector ponents Thus, the energy-momentum of the particle is given by 11 Note that the analytical formulation of this theorem does not require the restriction to rectangular axes. y Π z ∫∫∫ z Π y – yZ zY –()∫∫∫∫= dtdxdydz z Π x ∫∫∫ x Π z – zX xZ –() t dx dy dz d ∫∫∫∫= x Π y ∫∫∫ y Π x – xY yX –() t dx dy dz , d ∫∫∫∫= yd Π z [] zd Π y [] –0 = zd Π x [] xd Π z [] –0 = xd Π y [] yd Π x [] –0, = p zy p yz –0 = p xz p zx –0 = p yx p xy –0. = e 0 e 1 e 2 e 3 ,,, 1000,,, () , 0100 ,,, () , 0010 ,,, () , 0001 ,,, () . [41] m m e 0 xd td----- e 1 yd td----- e 2 zd td ---- - e 3 +++ ????. m txyz,,, () . d m dt ? 1 xd td----- yd td----- zd td ---- - ,,, ????.
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