Dilatation Covariance and Exact Solutions in Local Relativistic Field Theories

25 July 1969

journal article
research article
Published by American Physical Society (APS) in Physical Review B

Vol. 183 (5) , 1186-1188
https://doi.org/10.1103/physrev.183.1186

Abstract

Consideration is given to the invariance of field equations under space-time dilatations with (induced) transformation of constant parameters therein. Analysis of such "dilatation covariance" facilitates the determination of rigorous closed-form singularity-free solutions to essentially nonlinear classical field equations. More over, for essentially nonlinear quantized (boson) field theories, dilatation-covariance considerations facilitate the determination of rigorous closed-form solutions to the Schrödinger stationary-state equation.

Keywords

This publication has 7 references indexed in Scilit:

Relativistic Particle-Antiparticle Stationary States in a Model Quantum Field Theory: Mesons from Quarks
Physical Review B, 1968
Time decay for the nonlinear Klein-Gordon equation
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1968
Nonlinear partial differential equations in quantum field theory
Published by American Mathematical Society (AMS) ,1965
Quantization of nonlinear field theories and scale transformation
Il Nuovo Cimento (1869-1876), 1964
Hydrodynamics
Published by Walter de Gruyter GmbH ,1961
Das Anfangswertproblem in Gro en f r eine Klasse nichtlinearer Wellengleichungen
Mathematische Zeitschrift, 1961
THE REDUCTION BY ONE OF THE NUMBER OF INDEPENDENT VARIABLES IN SOME SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
The Quarterly Journal of Mathematics, 1952