By Boris V. Alexeev

*Unified Non-Local Relativistic thought of delivery Processes* highlights the main major positive aspects of non-local relativistic concept, that is a powerful software for fixing many actual difficulties in parts the place the classical neighborhood concept runs into problems. The publication offers the basic technological know-how at the back of new non-local physics - generalized for relativistic situations and utilized in various scales - from delivery phenomena in massless actual structures to unified idea of dissipative buildings.

The publication enhances the author’s earlier monograph on *Unified Non-Local idea of delivery Processes* (Elsevier, 2015), that is normally dedicated to non-relativistic non-local physics. however, the idea as dealt with during this new paintings is printed independently so the booklet may be studied by itself.

- Comprehensive number of non-local relativistic idea with examples which may formerly merely be stumbled on scattered within the literature
- Provides purposes in quantum non-local relativistic hydrodynamics, quantum solitons in good topic, and plasmas
- Uses generalized non-local kinetic thought as a powerful device for fixing many actual difficulties past classical physics
- Presents non-local relativistic physics in lots of comparable difficulties of hydrodynamics, gravity, nonlinear optics, time quantization, and utilized mathematics
- Includes concrete mathematical difficulties which are bodily constant and will be solved and studied either analytically and numerically

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**Sample text**

383 Þ 0 0 0 These formulae determine the transformation of velocities. Get now the Lorentz transformation law for an arbitrary direction (relative to the axes of coordinate systems) of the velocity υ of motion of a system relative to system K. To do this, carry out the rotation of e be the system K after the rotation, eхα is the coordinate systems K and К0 . 32), then we have a table that contains directional coordinates in К. 39) i where aji is the directional cosines of the angles relative to the old axes x regarding new axes xej .

The spatial components of the antisymmetric tensor (Aij , i, j ¼ 1,2,3) compose (in relation to purely spatial transformations) three-dimensional antisymmetric tensor, whose components can be expressed through the components of three-dimensional axial vector (for example, Ci). Components A01, A02, A03 comprise, relative to the same spatial transformation, a three-dimensional polar vector, for example Pi. 141) αβ Substituting Eqs. 141) in Eq. 142) 0 As usual, α numbers the lines, α ¼ 0,1,2,3, and the index β enumerates columns β ¼ 0,1, 2,3.

M. Teopeтичecкaя физикa. 2. Teopия пoля. , Haукa, 1988. 512 c]. 33. Cercignani C, Kremer GM. The relativistic Boltzmann equation: theory and applications. Basel: Birkh€auser Verlag; 2002. 384 p. 1. “DERIVATION” OF THE DIRAC EQUATION Let’s look at some principles of quantum mechanics and quantum electrodynamics, based on Dirac’s equation for fermions. In detail, these questions are considered in Refs. 1–4 As is known, for particles with spin, a description of the state with the wave function must determine not only the probability of its different positions in space, but also the probability of the various possible orientations of its spin.