PATH INTEGRAL APPROACH IN QUANTUM-LIKE THEORY. TWO APPLICATIONS: LHC AND HIDIF

A formulation of the Quantum-like theory based on Feynman’s propagator is presented for particle beams. Applications to betatronic oscillations of LHC and HIDIF show encouranging predictions. The so-called Quantum-like approach for beams in particle accelerators (or more generally in beams Physics) may be looked at as a bridge between two basic theories, namely Classical and Quantum Mechanics. Indeed it uses quantum methods and formalism for describing the evolution of charged particle beams which is almost entirely based on classical mechanics and classical electromagnetism. Several arguments in favour of such a methodology are given in detail by other authors 1 in this conference. To be more specic one uses the Schrodinger equation, with an appropriate new denition of the fundamental parameters, for the description of a beam particle that moves under known electromagnetic forces plus others that are perturbative, not predictable in detail, due to various causes such as imperfections of the magnets in the lattice, misalignements, intrabeam scattering, beam-strahlung, wall-particle interaction etc. These eects usually determine non-linear terms and tend to create a sort of stochastic motion that must be compatible with the timereversal invariance (a basic property of the Classical Dynamics). To describe all these features one considers a stochastic process that is Markovian and Brownian and easily gets to a modication of the equation of motion that leads nally to a non-linear or, afterwards, a linear Schrodinger equation related with a fundamental physical parameter that has the dimension of an action. The Quantum-like-theory of beams makes it coincide with the normalized emittance (in quantum mechanics its correspondent parameter is the Planck constant ~) whereas the mass and charge parameters are those of the individual physical particle of the beam. Along these lines we may use the path-integral method, 2 try to calculate the Feynman propagator K( xf; tfj xi; ti) connected with a given potential and introduce one or more parameters for a global phenomenological description of the non-linear eects