A version draft on: Estado del Arte sobre Física Simbólica y Diagramas Tensoriales de Penrose

Abstract

The development of Penrose tensor diagrams has transformed the representation of mathematical structures in contemporary physics, providing a graphical language that unites algebraic abstraction with geometric intuition. Over the past decades, these diagrams have become essential tools in quantum physics, field theory, and spacetime geometry, allowing compact descriptions of tensor contractions and correlations. Authors such as Biamonte, Bergholm, Kissinger, and Coecke have extended this formalism to computational and categorical contexts, establishing a framework of graphical calculus that facilitates the visualization and manipulation of complex physical systems.

Within this context, Martín Pomares Calero introduces the concept of Symbolic Physics, an epistemological and ontological approach that interprets Penrose diagrams as symbolic structures of the universe. From this perspective, the symbol is not a mere representational sign but an active component of physical and cognitive processes, capable of encoding the fundamental laws of reality. This approach proposes a synthesis between tensor calculus, scientific semiotics, and visual cognition, oriented toward a physics of meaning.

This paper examines the main research lines connecting tensorial thought and symbolic interpretation, emphasizing how the integration between mathematical and symbolic frameworks opens new paths for the theoretical understanding of the universe.