Quantum Noisy Fields, Classical and Quantum Physics and Neural Networks, Heat and Mass Transfer in General Relativity
Inge Svein Helland, Harish Parthasarathy · 2025
Let L ( x,ϕ ( x ) ,∂ ¼ ϕ ( x )) be the Lagrangian density of the field ϕ ( x ). Assume that this Lagrangian is linear-quadratic in ∂ ¼ ϕ as for example in Yang-Mills non-Abelian matter and gauge field theory and also in the general theory of relativity. Thus we can express this Lagrangian as https://www.w3.org/1998/Math/MathML" display="block"> L = a 0 ( x , ϕ ( x ) ) + a 1 μ ( x , ϕ ( x ) ) T ∂ μ ϕ ( x ) + ( 1 / 2 ) ∂ μ ϕ ( x ) T a 2 μ ν ( x , ϕ ( x ) ) ∂ ν ϕ ( x )