Relativistic dynamics for spin-zero and spin-half particles |
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Authors: | J Thakur |
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Institution: | (1) Department of Physics, Patna University, 800 005 Patna, India |
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Abstract: | The classical and quantum mechanics of a system of directly interacting relativistic particles is discussed. We first discuss
the spin-zero case, where we basically follow Rohrlich in introducing a set of covariant centre of mass (CM) and relative
variables. The relation of these to the classic formulation of Bakamjian and Thomas is also discussed. We also discuss the
important case of relativistic potentials which may depend on total four-momentum squared. We then consider the quantum mechanical
case of spin-half particles. The negative energy difficulty is solved by introducing a number of first class constraints which
fix the spinor structure of physical solutions and ensure the existence of proper CM and relative variables. We derive the
form of interactions consistent with Lorentz invariance, space inversion, time reversal and charge conjugation and with the
above mentioned first class constraints and find that it is analogous to that for the non-relativistic case. Finally the relationship
of the present work with some previous work is briefly discussed. |
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Keywords: | Direct interactions spin zero spin half covariant centre of mass first class constraints |
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