Relativistic Properties of a Lagrangian and a Hamiltonian in Quantum Theories
Eliahu Comay *
Charactell Ltd., P.O.Box 39019, Tel-Aviv, 61390, Israel.
*Author to whom correspondence should be addressed.
Abstract
Relativistic properties of a Dirac Lagrangian density are compared with those of a Dirac Hamiltonian density. Differences stem from the fact that a Lagrangian density is a Lorentz scalar, whereas a Hamiltonian density is a 00-component of a second rank tensor, called the energy-momentum tensor. This distinction affects the form of an interaction term of a Dirac particle. In particular, a tensor interaction term of a Dirac Lagrangian density transforms to a difference between a vector and an axial vector of the corresponding Hamiltonian density. This outcome shows that fundamental principles can prove the V-A attribute of weak interactions. A further analysis supports these results. Inherent problems of the electroweak theory are discussed.
Keywords: Dirac Lagrangian density, Dirac Hamiltonian density, Dirac generalized momentum, weak interactions.