Nonlocal scalar field in an external potential: WKB approximation

Abstract

We consider a nonlocal theory of a scalar massive field in a flat spacetime background in the presence of an external potential and construct WKB solutions for this theory. We use a model in which the kinetic part of the scalar field action is modified by changing $\square$ to $\square f(\square )$ operator. We discuss conditions when the corresponding form factor $f$ is chosen so that the theory does not contain new unphysical degrees of freedom. We applied the obtained WKB solutions for study energy levels of the field trapped by a one-dimensional potential and the probability of the barrier penetration. This allows us to illustrate how the effects of the nonlocality change the known results obtained for the local field theory.

14 pages 8 figures, a few misprints are correscted

References in corpus (6)

• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Black holes in an ultraviolet complete quantum gravity
• Counting ghosts in the "ghost-free" non-local gravity
• Nonlocal quantum gravity and M-theory
• Nonlocal star as a blackhole mimicker
• Non-singular and ghost-free infinite derivative gravity with torsion