Investigación

 

Explicit classical solutions and comments on Higher-Derivative Klein-Gordon equation in (1+1)-D

 

A. Cherman ª, L.G. Ferreira Filho^b, L.L. Santos Guedes^c and J.A. Helayël-Neto^d

 

ª Fundacão Planetário da Cidade do Rio de Janeiro, Rua Vice-Governador Rubens Berardo, 100, 22451-070, Rio de Janeiro, RJ, Brasil, and Centro Brasileiro de Pesquisas Físicas - CBPF, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brasil, e-mail: alexandre.cherman@planetario.rio.rj.gov.br

^b FAT— UERJ/Resende, Estrada Resende-Riachuelo s/n, 27523-000, Resende, RJ, Brasil, e-mail: gonzaga@fat.uerj.br

^c Fundacão Planetario da Cidade do Rio de Janeiro, e-mail: leandro.guedes@planetario.rio.rj.gov.br

^d Centro Brasileiro de Pesquisas Físicas - CBPF, e-mail: helayel@cbpf.br

 

Recibido el 30 de marzo de 2012;
Aceptado el 6 de junio de 2012

 

Abstract

We present a simple and general method to solve higher-power D'Alembert equation in (1+1) dimensions for a set of completely general initial conditions. Explicit solutions are written down for the cases of []² and []³ and the singularity structure is manifest through the derivative terms of some of the initial-condition functions. The explicit solutions found out may be useful if one wishes to device external sources which may suppress the non-physical modes introduced by the higher derivatives.

Keywords: Higher-derivative theories; 2D theories; ghosts.

 

PACS: 03.50.Kk; 03.65.Pm; 03.65.Fd

 

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