Next Article in Journal
Global Asymptotic Stability and Nonlinear Analysis of the Model of the Square Immunopixels Array Based on Delay Lattice Differential Equations
Next Article in Special Issue
Forms of the Symmetry Energy Relevant to Neutron Stars
Previous Article in Journal
Efficient C2 Continuous Surface Creation Technique Based on Ordinary Differential Equation
Previous Article in Special Issue
Local External/Internal Symmetry of Smooth Manifolds and Lack of Tovariance in Physics
Open AccessArticle

Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem

by 1,2 and 3,*
1
ICRANet, P.le della Repubblica 10, 65100 Pescara, Italy
2
Department of Physics and ICRA, University of Rome “Sapienza”, P.le A. Moro 5, 00185 Rome, Italy
3
Department of Physics and Center for High Energy and High Field Physics, National Central University, Chung-Li 32054, Taiwan
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 39; https://doi.org/10.3390/sym12010039
Received: 5 November 2019 / Revised: 4 December 2019 / Accepted: 17 December 2019 / Published: 23 December 2019
(This article belongs to the Special Issue Symmetry Principles in Quantum Systems)
The earlier treatments of the Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We present here a full solution avoiding those problems. The complete set of Fock states is obtained, together with the corresponding explicit wavefunctions and their inner product integrals free from any divergence problem and with Lorentz symmetry fully maintained without additional constraints imposed. By a simple choice of the pseudo-unitary representation of the underlying symmetry group, motivated from the perspective of the Minkowski spacetime as a representation for the Lorentz group, we obtain the natural non-unitary Fock space picture commonly considered, although not formulated and presented in the careful details given here. From a direct derivation of the appropriate basis state wavefunctions of the finite-dimensional irreducible representations of the Lorentz symmetry, the relation between the latter and the Fock state wavefunctions is also explicitly shown. Moreover, the full picture, including the states with a non-positive norm, may give a consistent physics picture as a version of Lorentz covariant quantum mechanics. The probability interpretation for the usual von Neumann measurements is not a problem, as all wavefunctions restricted to a definite value for the `time’ variable are just like those of the usual time independent quantum mechanics. A further understanding from a perspective of the dynamics from the symplectic geometry of the phase space is shortly discussed. View Full-Text
Keywords: Covariant Harmonic Oscillator; Pseudo-unitary Representation; Lorentz Symmetry Covariant Harmonic Oscillator; Pseudo-unitary Representation; Lorentz Symmetry
MDPI and ACS Style

Bedić, S.; Kong, O. Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem. Symmetry 2020, 12, 39. https://doi.org/10.3390/sym12010039

AMA Style

Bedić S, Kong O. Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem. Symmetry. 2020; 12(1):39. https://doi.org/10.3390/sym12010039

Chicago/Turabian Style

Bedić, Suzana; Kong, Otto. 2020. "Analysis on Complete Set of Fock States with Explicit Wavefunctions for the Covariant Harmonic Oscillator Problem" Symmetry 12, no. 1: 39. https://doi.org/10.3390/sym12010039

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop