Please use this identifier to cite or link to this item: http://hdl.handle.net/2381/32387
Title: Quantization and quantum-like phenomena:a number amplitude approach
Authors: Robinson, T. R.
Haven, Emmanuel
First Published: 8-Jul-2015
Publisher: Springer Verlag (Germany)
Citation: International Journal of Theoretical Physics 2015
Abstract: Historically, quantization has meant turning the dynamical variables of classical mechanics that are represented by numbers into their corresponding operators. Thus the relationships between classical variables determine the relationships between the corresponding quantum mechanical operators. Here, we take a radically different approach to this conventional quantization procedure. Our approach does not rely on any relations based on classical Hamiltonian or Lagrangian mechanics nor on any canonical quantization relations, nor even on any preconceptions of particle trajectories in space and time. Instead we examine the symmetry properties of certain Hermitian operators with respect to phase changes. This introduces harmonic operators that can be identified with a variety of cyclic systems, from clocks to quantum fields. These operators are shown to have the characteristics of creation and annihilation operators that constitute the primitive fields of quantum field theory. Such an approach not only allows us to recover the Hamiltonian equations of classical mechanics and the Schrodinger wave equation from the fundamental quantization relations, but also, by freeing the quantum formalism from any physical connotation, makes it more directly applicable to non-physical, so-called quantum-like systems. Over the past decade or so, there has been a rapid growth of interest in such applications. These include, the use of the Schrodinger equation in finance, second quantization and the number operator in social interactions, population dynamics and financial trading, and quantum probability models in cognitive processes and decision-making. In this paper we try to look beyond physical analogies to provide a foundational underpinning of such applications.
DOI Link: 10.1007/s10773-015-2726-8
ISSN: 0020-7748
eISSN: 1572-9575
Links: http://link.springer.com/article/10.1007/s10773-015-2726-8
http://hdl.handle.net/2381/32387
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Archived with reference to SHERPA/RoMEO and publisher website. The final publication is available at Springer via http://dx.doi.org/10.1007/s10773-015-2726-8
Appears in Collections:Published Articles, Dept. of Physics and Astronomy

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