We propose a new quantum approach for describing a system of
n interacting particles with variable mass connected by an unknown field with variable form (
n-VMVF systems). Instead of assuming any particular nature for variation of the masses and field, we propose to find them from the laws that rule the dynamic of the systems. In this context, we consider masses and field are functions depending only on the particle positions and velocities, excluding the presence of hidden variables. The quantum approach follows the modern method for constructing the quantum theory where quantum states are defined over a Hilbert space, and the operators are obtained from the canonical transformations of the corresponding classical theory. The classical theory results on two sets of second-order Hamilton constrained equations, while the Hilbert space is defined over the extension of the complex number, which is done from an unsolvable equation on the complex domain. This new approach does not contradict the existing theoretical theories in Particle Physics.
The purpose of this paper is to present an overview of recent work on pilot-wave approaches to quantum field theory. In such approaches, systems are not only described by their wave function, as in standard quantum theory, but also by some additional variables. In the non-relativistic pilot-wave theory of deBroglie and Bohm those variables are particle positions. In the context of quantum field theory, there are two natural choices, namely particle positions and fields. The incorporation of those variables makes it possible to provide an objective description of nature in which rather ambiguous notions such as 'measurement' and 'observer' play no fundamental role. As such, the theory is free of the conceptual difficulties, such as the measurement problem, that plague standard quantum theory.
This paper investigates the potential of quantum computation to revolutionize numerical simulation of quantum systems. Traditional numerical methods often struggle to accurately capture the complexities of quantum phenomena, necessitating the development of novel approaches. We propose a new dynamic variable field theory, leveraging quantum computation's inherent parallelism and superposition properties to provide a fundamentally different approach to simulating quantum behavior. This theory offers the promise of enhanced accuracy, speed, and the ability to predict quantum system evolution, potentially surpassing the limitations of existing numerical methods. The core of our work centers around a quantum-enhanced dynamic variable field formulation, emphasizing the interplay between quantum states and system evolution. The theoretical foundations and initial implementation demonstrate a robust framework for simulating fundamental quantum systems, offering a significant step towards practical quantum simulation.