Classical and Quantum Relativistic Mechanics of a Spinning Particle

  • Alexei Deriglazov


Search for the relativistic equations that describe evolution of rotational degrees of freedom and their influence on the trajectory of a spinning body, represents a problem with a long and fascinating history. Closely related problem consists in establishing of classical equations that could mimic quantum mechanics of an elementary particle with spin in a semiclassical approximation. The relationship among classical and quantum descriptions has an important bearing, providing interpretation of results of quantum-field-theory computations in usual terms: particles and their interactions. In this Chapter we develop the Lagrangian and Hamiltonian formulations of a particle with rotational degrees of freedom. Taking a variational problem as the starting point, we avoid the ambiguities and confusion, otherwise arising in the passage from Lagrangian to Hamiltonian description and vice-versa. Besides, it essentially fixes the possible form of interaction with external fields. We show that so called vector model of spin represents a unified conceptual framework, allowing to collect and tie together a lot of remarkable ideas, observations and results accumulated over almost a century of studying this subject. On the classical level, the vector model adequately describes spinning particle in an arbitrary gravitational and electromagnetic fields. Moreover, taking into account the leading relativistic corrections it explains the famous one-half factor in non-relativistic Hamiltonian. Canonical quantization of the model yields one-particle relativistic quantum mechanics with positive-energy states.


Dirac Equation Vector Model Anomalous Magnetic Moment Covariant Formalism Primary Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Alexei Deriglazov
    • 1
    • 2
  1. 1.Universidade Federal de Juiz de Fora Dept. of MathematicsJuiz de ForaBrazil
  2. 2.Laboratory of Mathematical PhysicsTomsk Polytechnic UniversityTomskRussian Federation

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