This is the Hamiltonian for an infinite number of uncoupled harmonic oscillators. Thus different modes of the field are independent and satisfy the commutation relations: [ a k λ λ ( t ) , a k ′ λ λ ′ † † ( t ) ] = δ δ k , k ′ 3 δ δ λ λ , λ λ ′ [ a k λ λ ( t ) , a k ′ λ λ ′ ( t ) ] = [ a k λ λ † † ( t ) , a k ′ λ λ ′ † † ( t ) ] = 0