Relativistic dynamics, Green function and pseudodifferential operators

DIEGO JULIO CIRILO

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2016

0022-2488

The central role played by pseudodifferential operators in relativistic dynamics isknown very well. In this work, operators like the Schrodinger one (e.g., square root)are treated from the point of view of the non-local pseudodifferential Green functions.Starting from the explicit construction of the Green (semigroup) theoretical kernel, atheorem linking the integrability conditions and their dependence on the spacetimedimensions is given. Relativistic wave equations with arbitrary spin and the causalityproblem are discussed with the algebraic interpretation of the radical operator andtheir relation with coherent and squeezed states. Also we perform by means of puretheoretical procedures (based in physical concepts and symmetry) the relativisticposition operator which satisfies the conditions of integrability: it is a non-local,Lorentz invariant and does not have the same problems as the ?local?position operatorproposed by Newton and Wigner. Physical examples, as zitterbewegung and roguewaves, are presented and deeply analyzed in this theoretical framework.