Can the principles of quantum mechanics be applied to classical fields? This research delves into the deformation quantization of scalar and Abelian gauge classical free fields, exploring a fascinating intersection between classical and quantum physics. The study obtains Stratonovich–Weyl quantizers, star products, and Wigner functionals using both field and oscillator variables, providing a comprehensive mathematical framework for understanding the quantum behavior of these fields. Particularly intriguing is the analysis of Abelian gauge theory, which reveals that the Wigner functional can be factorized into a physical part and another containing only constraints. This decomposition offers insights into the underlying structure of the theory and its topological properties. The research further considers the effects of nontrivial topology within the deformation quantization formalism, expanding the understanding of these complex systems. By bridging the gap between classical and quantum descriptions, this work has significant implications for theoretical physics, offering new perspectives on field quantization and gauge theory.
This article, appearing in the International Journal of Modern Physics A, is relevant to the journal's coverage of modern physics topics, particularly in the areas of nuclear and particle physics, atomic physics, and the constitution and properties of matter. The paper's theoretical investigation contributes to the understanding of quantum field theory and its mathematical foundations.