Eur. Phys. J. C (2012) 72: 2150
https://doi.org/10.1140/epjc/s10052-012-2150-7

Regular Article - Theoretical Physics

Microcausality and quantization of the fermionic Myers–Pospelov model

¹ Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago, Chile
² Departamento de Ciencias Básicas, Universidad del Bío-Bío, Casilla 447, Chillán, Chile

^* e-mail: creyes@ubiobio.cl

Received: 17 July 2012
Revised: 24 August 2012
Published online: 12 September 2012

Abstract

We study the fermionic sector of the Myers and Pospelov theory with a general background n. The spacelike case without temporal component is well defined and no new ingredients came about, apart from the explicit Lorentz invariance violation. The lightlike case is ill defined and physically discarded. However, the other case where a nonvanishing temporal component of the background is present, the theory is physically consistent. We show that new modes appear as a consequence of higher time derivatives. We quantize the timelike theory and calculate the microcausality violation which turns out to occur near the light cone.