Quantum Stud.: Math. Found. CHAPMAN INSTITUTE FOR UNIVERSITY QUANTUM STUDIES https://doi.org/10.1007/s40509-018-0166-x REGULAR PAPER Path integral of oscillating free particle from nonlocal-in-time kinetic energy approach Rami Ahmad El-Nabulsi Received: 28 March 2018 / Accepted: 23 May 2018 © Chapman University 2018 Abstract Higher derivative theories play a fundamental role in quantum ﬁeld theories although they are accom- panied with a number of undesirable properties such as the occurrence of ghosts and instabilities. However, it is believed that higher order derivative theories associated with nonlocality removed merely all problems encountered within them. Recently, a new higher derivative nonlocal theory was introduced by Suykens (Phys Lett A 373:1201– 1211, 2009) based on nonlocal-in-time kinetic energy approach which holds a number of remarkable features at classical and quantum levels. In this letter, we construct the path integral approach for this special class of theory where we discuss in particular the free particle which exhibits for speciﬁc initial conditions in Suykens’ approach a growing outward oscillatory trajectory with constant amplitude. It was observed that a free particle at rest with zero energy and zero momentum is unstable and has an oscillatory decaying energy with a particular wave function. Keywords Nonlocal-in-time kinetic energy · Path
Quantum Studies: Mathematics and Foundations – Springer Journals
Published: May 30, 2018
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