2019/11/04 by K. Pedro, Pedro, Leonardo
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1911.01213
openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum Yang-Mills theory, Classical Statistical Field Theory (for\nHamiltonians which are non-polynomial in the fields, e.g. General relativistic\nstatistical mechanics) and Quantum Gravity all suffer from severe mathematical\ninconsistencies and produce unreliable predictions at best.\n We define with mathematical rigor, a class of statistical field theories in\nMinkowski space-time where the (classical) canonical coordinates when modified\nby a non-deterministic time evolution, verify the canonical commutation\nrelations. We then extend these statistical field theories to include\nnon-trivial gauge symmetries and show that these theories have all the features\nof a Quantum Yang-Mills theory in four-dimensional space-time. We generalize\nthe Gaussian measure to allow for the definition of Hamiltonians which are\nnon-polynomial in the fields, such as in Classical Statistical Field Theory and\nQuantum Gravity.\n Finally, we test the consistency of our formalism with the quantization of\nthe free Electromagnetic field.\n