[Paper Review] The substructure of a Quantum Oscillator field

Giovanni Guido|arXiv (Cornell University)|Aug 4, 2012

Cold Atom Physics and Bose-Einstein Condensates3 citations

TL;DR

This paper proposes an elementary oscillator (IQuO) with two-component quantum operators (a, a⁺) composed of 'semi-quanta' (1/2h), introducing a novel substructure for quantum fields. It derives commutation relations for these semi-quanta, constructs scalar fields with and without electric charge, and interprets electric charge and isospin as internal rotations, offering a probabilistic model for quark fractional charges via IQuO substructure.

ABSTRACT

An oscillator (IQuO) more elementary than the quantum one is formulated. This is expressed by quantum operators (a, a+), with two-components and it is composed of sub-oscillators, each with "semi-quanta" (1/2h). The commutation relation of the (a,a+) "semi-quanta" operators is then calculated and the structure by IQuO of the scalar fields is defined with and without electric charge. Processing a coupling mechanism of electrically neutral IQuO that produces a pair (matter-antimatter) with electric charge and not. Through the IQuO-structure it is possible to interpret the electric charge and the isospin (in hadrons) as rotations in an inside space in the particle. Finally, a sub-structure of the quarks is conjectured and one define in probabilistic terms the non-integer value of their electrical charge.

Motivation & Objective

• To propose a more fundamental quantum oscillator (IQuO) than the standard quantum oscillator, based on two-component operators with semi-quanta (1/2h).
• To define the commutation relations for the semi-quanta operators (a, a⁺) within the IQuO framework.
• To construct scalar quantum fields—both charged and neutral—using the IQuO substructure.
• To explain electric charge and isospin in hadrons as rotations in an internal space within the particle.
• To conjecture a substructure for quarks and assign their fractional electric charges probabilistically through the IQuO model.

Proposed method

• Formulate an elementary oscillator (IQuO) with two-component quantum operators (a, a⁺), each associated with a 'semi-quantum' of 1/2h.
• Derive the commutation relations between the semi-quanta operators (a, a⁺) to define their algebraic structure.
• Construct scalar quantum fields by aggregating IQuO components, distinguishing between charged and neutral field configurations.
• Introduce a coupling mechanism between electrically neutral IQuOs that can produce matter-antimatter pairs with or without electric charge.
• Model electric charge and isospin as rotational degrees of freedom in an internal space within the particle's substructure.
• Define the electric charge of quarks in probabilistic terms based on the IQuO substructure and semi-quantum composition.

Experimental results

Research questions

• RQ1 What is the algebraic structure of a quantum oscillator composed of semi-quanta (1/2h), and how do its operators (a, a⁺) commute?
• RQ2 How can scalar quantum fields be constructed from IQuO components, both with and without electric charge?
• RQ3 How can the electric charge and isospin quantum numbers of particles emerge from internal rotational symmetries in the IQuO framework?
• RQ4 What is the substructure of quarks, and how can their fractional electric charges be explained via IQuO-based probabilistic models?
• RQ5 How does a coupling mechanism between neutral IQuOs lead to the production of matter-antimatter pairs with or without electric charge?

Key findings

• The IQuO model introduces a new quantum oscillator structure based on two-component operators (a, a⁺) with semi-quanta of 1/2h, forming a foundational unit below the standard quantum oscillator.
• The commutation relation between the semi-quanta operators (a, a⁺) is derived, establishing the algebraic basis for the IQuO framework.
• Scalar fields are constructed both with and without electric charge using the IQuO substructure, demonstrating field consistency.
• Electric charge and isospin are interpreted as rotational degrees of freedom in an internal space, providing a geometric explanation for these quantum numbers.
• A coupling mechanism between neutral IQuOs is proposed that can generate matter-antimatter pairs with or without electric charge.
• The fractional electric charges of quarks are conjectured to arise probabilistically from the IQuO substructure, offering a novel explanation for their non-integer values.