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[...]... bodies and material systems are built from these massive and spinless points, and taking into account the constraints and interactions among the different parts of the system, we are able to derive the dynamics of the essential and independent degrees of freedom of any compound system of spinless particles Now, let us assume that we have a time-machine and we jump back to Newton’s times, we meet him and. .. is our main motivation for the classical analysis of spinning particles: to finally obtain a thorough quantum scheme 1.1 KINEMATICS AND DYNAMICS When facing the project of getting a classical description of matter we have the recent history of Physics on our back And, although we have a huge classical luggage, a glance at the successful way quantum 4 KINEMATICAL THEORY OF SPINNING PARTICLES mechanics... zitterbewegung and the associated intrinsic dipole structure of elementary particles The relationship between the classical and the quantum mechanical description of spin will show how both formalisms are able to complement each other, thus producing, for instance, a kinematical explanation of the gyromagnetic ratio of leptons and charged W ± bosons xix xx KINEMATICAL THEORY OF SPINNING PARTICLES But at the same... come from, elementary objects of nature have spin, in addition to mass m, as a separate intrinsic property What can we do to describe matter?’ Probably he will add some extra degrees GENERAL FORMALISM 3 of freedom to the massive point particle and some plausible dynamical equation for the spin evolution in terms of external torques The compound systems of spinning particles will become more complex mainly... terms of the independent degrees of freedom, but also as a function of the end point variables of the corresponding action integral We shall call these variables the kinematical variables of the system The formalism in terms of kinematical variables proves to be the natural link between classical and quantum mechanics when considered under Feynman’s quantization method It is in terms of the kinematical. .. definition of a classical elementary particle will be stated 1 INTRODUCTION Historically quantum mechanics has been derived from classical mechanics either as a wave mechanics or by means of a canonical commutation relation formalism or using the recipes of the so-called ‘correspondence principle’ Today we know that none of these formalisms are necessary to quantize a system 1 2 KINEMATICAL THEORY OF SPINNING. .. classical equivalent to the free asymptotic states of the scattering theory, 8 KINEMATICAL THEORY OF SPINNING PARTICLES will be defined by pure kinematical arguments and they will be related to what are called homogeneous spaces of the kinematical group In this way, they are intimately related to the kinematical group of symmetries, and by assuming as a basic statement a special relativity principle,... Nature, at the scale of elementary interactions, behaves according to the laws of quantum mechanics The finer the classical analysis of basic objects of matter, the richer will be their quantum mechanical description The quantum mechanical picture when expressed in terms of invariance principles will show the relationship between the classical variables and symmetry group parameters of the manifolds involved... called the kinematical group of space-time transformations and to the so-called internal symmetries group It is usually called to work ‘à la Wigner’ 1 Intrinsic attributes are then interpreted in terms of the group invariants We shall also try to derive the basic kinematical ingredients of the classical formalism by group theoretical methods Quantum dynamics, in the form of either S-matrix theory, scattering... PARTICLES But at the same time, this book also presents a new formalism, based upon group theory, to describe elementary particles from a classical and quantum point of view In this way the structure of an elementary particle is basically related to the kinematical group of space-time transformations that implements the Special Relativity Principle It is within the kinematical group where we have to . Germany Volume 116 Kinematical Theory of Spinning Particles Classical and Quantum Mechanical Formalism of Elementary Particles by Martin Rivas The University of. charged particles with parallel ( a ) and an- tiparallel ( b ), spin and magnetic moment. Representation in the C .M. frame of the motion of the center of mass