## About this Research Topic

Foundations of Physics, intended as the investigation of the conceptual starting points and mathematical articulations of physical principles, can affect physics as a whole. These principles may be at the basis of quite different areas of physics such as quantum theory or general relativity theory and we are ...

The aim of this research topic is to highlight new approaches, rather than reproducing aspects of already well-known developments such as string theory. We are interested in new understandings of physical laws and the spectrum of physical particles, with a particular emphasis on symmetry, conceptual simplicity, and unification. The emphasis of the collection is to highlight original points of view that shed light on our understanding of the physical world.

This research topic is open to authors addressing the foundations of physics, provided that the focus is on the interplay between physics and mathematics. Current work in topology, algebra, group theory and geometry act back to physics to change partly the basic principles. The contribution should discuss this interplay between mathematics and physics. The following list of topics are examples for this interplay and the basic principles:

• Topology and quantum (field) theory: explorations of the nature of entanglement in quantum computing, in cosmology aka black holes etc, in relations with topology

• Topology and spacetime: foundations of general relativity, loop quantum gravity and spacetime by using knots and links as in Kauffman

• Algebraic foundations of physics: particle models and algebraic structures as in Rowlands and others using E8, octonions or Tits magic square

• Logic and physics: quantum logical foundations as in David Finkelstein or causal set theory as in Rafael Sorkin

• Rebuild physics by category and model theory: categorical or model theoretic foundations as in Abramsky, Coecke or Isham, Doebner

• Fractal structures and spacetime: relations with fractal geometry and differential structure as in Asselmeyer-Maluga

• Geometry and quantum theory: non-commutative geometry as in Connes

• Algebraic structures and quantum field theory: approaches to renormalization via mathematical structures such as Hopf algebras or fractals/scaling.

• Discrete structures and quantum theory: emergent quantum mechanics from cellular automata as in t’Hooft.

• Non-linear differential equations and quantum mechanics: reformulations of quantum mechanics changing the measurement structure as in Bohm.

**Keywords**:
symmetry, conceptual similarity, unification, Dirac equation, quantum relativity, quantum set theory

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.