Physics NotePublished
Higher-Derivative Wave Equations in (1+1)D: Exact Solutions with External Sources
L. G. Ferreira Filho; José Abdalla Helayel Neto; Alexander William Smith
2004
Publication details
- Authors
- L. G. Ferreira Filho; José Abdalla Helayel Neto; Alexander William Smith
- Type
- Physics Note
- Status
- Published
- Publication date
- 2004
- Description
- Two space-time dimensions exhibit the relevant property of Lorentz-invariant left-right-mover factorisation. This special result is crucial for the attainment of exact analytic solutions to higher-derivative wave equations such as $\square ^m\Phi =0$ and $i\gamma ^\mu \partial _\mu \square ^n\Psi =0$, with $m\geq 2$ and $n\geq 1$ and $\Phi $ and $\Psi $ being scalar and fermionic functions, respectively. The exact (classical) field solutions can be worked out for an arbitrary set of initial conditions that specify the funtions and their required time derivatives at t=0. In this work, we take into account external sources and the method previously developped is extended to include the effect of the sources. The whole idea underneath the approach consists in suitably shifting the source contributions to the initial value problem of the corresponding sourceless problem. To ilustrate the general procedure, we present explicit solutions to the equation $\square ^2 \Phi =J(t;x)$ , where the source $J$ is left arbitrary. We discuss the possibility that the external source be so chosen that it suppresses the unphysical modes present in $\Phi$ by virtue of the higher space and time derivatives that control the dynamics.
- Year
- 2004
- Number
- CBPF-NF-010/04
- Linked to a thesis
- No
- Linked to a grant
- No