Path integral of oscillating free particle from nonlocal-in-time kinetic energy approach

Path integral of oscillating free particle from nonlocal-in-time kinetic energy approach 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Studies: Mathematics and Foundations Springer Journals

Path integral of oscillating free particle from nonlocal-in-time kinetic energy approach

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Chapman University
Subject
Mathematics; Mathematical Physics; Theoretical, Mathematical and Computational Physics; Quantum Physics; History and Philosophical Foundations of Physics
ISSN
2196-5609
eISSN
2196-5617
D.O.I.
10.1007/s40509-018-0166-x
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Quantum Studies: Mathematics and FoundationsSpringer Journals

Published: May 30, 2018

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