2018/06/30 by Daniel N. Blaschke, Francois Gieres, François Gieres +5
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Charge (physics) #Charge conservation #Classical field theory #Classical mechanics #Conservation law #Cosmology and Gravitation Theories #Exact solutions in general relativity #Field (mathematics) #Gravitational field #Harmonic oscillator #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Physics #Quantum field theory #Quantum mechanics #Space (punctuation) #Stress–energy tensor #Theoretical physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.3842/sigma.2018.133
published as SIGMA 14 (2018), 133, 35 pages · Dedicated to the memory of Manfred Schweda who initiated this work, V2: References added. V3: Comments on the symmetries underlying the conservation laws added, V4: Published version
openalex publication_date 2018/12/23 · arxiv created 2018/12/27 · arxiv updated 2018/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss the formulation of classical field theoretical models on n-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field theories in noncommutative space-time to obtain local conservation laws (for the electric charge and for the energy-momentum tensor of free fields) and more generally an energy-momentum balance equation for interacting fields. For free field models an analogy with the damped harmonic oscillator in classical mechanics is pointed out, which allows us to get a physical understanding for the obtained conservation laws. To conclude, the formulation of field theories on curved noncommutative space is addressed.