A Quantum-Theoretical Lagrangian Formalism for Quasi-Linear Field Theories. I : General Theory

概要

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A quantum-theoretical lagrangian formalism for quasi-linear field theories is proposed. Quasi-linear fields are defined by the following conditions: i)The coefficient of the term involving the highest order of derivative of the field in the lagrangian density is not a constant but a regular matrix function of the field. ii)in quantum field theories the divergence of the energy-momentum and the angular-momentum tensor density operators are zero or at most space-derivatives of some operators. The preferred fields in the non-linear realization and pion field interacting with itself through the current-current interaction are typical examples of quasi-linear fields. The present formalism is devised to be able to reproduce all results that have been achieved in the quantum field theory of non-linear realization based on the characteristics of displacement operators in Minkowski space. However, the variation method proposed here has the form which can be applied also to general quasi-linear fields. the points in the present formalism are in the order of operators in the quantum-theoretical 'covariant' derivatives and in throwing away the virtual variation technique which seems not to work in quantum theories of quasi-linear fields.
理論物理学刊行会の論文
1974-11-25