2017/12/04 by Satyajit Guin, Guin, Satyajit
Mathematics · Physics and Astronomy · #58B34 #81T75 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1712.00986
openalex publication_date 2017/12/04 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28
We formulate notions of subadditivity and additivity of the Yang-Mills action functional in noncommutative geometry. We identify a suitable hypothesis on spectral triples which proves that the Yang-Mills functional is always subadditive, as per expectation. The additivity property is much stronger in the sense that it implies the subadditivity property. Under this hypothesis we obtain a necessary and sufficient condition for the additivity of the Yang-Mills functional. An instance of additivity is shown for the case of noncommutative n-tori. We also investigate the behaviour of critical points of the Yang-Mills functional under additivity. At the end we discuss few examples involving compact spin manifolds, matrix algebras, noncommutative n-torus and the quantum Heisenberg manifolds which validate our hypothesis.