# ND-Wavelets Derived from Anti-symmetric Systems of Isolated Particles using the Determinant of Slater

## TL;DR

This paper introduces a novel method for constructing multi-dimensional wavelet systems based on the antisymmetric properties of fermionic particle states, utilizing the determinant of Slater to bridge quantum physics and wavelet theory.

## Contribution

It presents a new approach to generate multi-dimensional wavelets from fermionic antisymmetric systems using the determinant of Slater, linking quantum physics with wavelet analysis.

## Key findings

- New multi-dimensional wavelet systems derived from fermionic states
- Framework for integrating particle physics into wavelet analysis
- Potential for further applications in physics and signal processing

## Abstract

Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states is used to generate new \textit{n}-dimensions wavelets, $n\ge2$, by the determinant of Slater. As pioneering paper in exchanging formalism between particle wave-functions and wavelets, it opens some perspectives for further adaptations derived from the physics of particles in the wavelet analysis scope.