# Derivative of a "particle" field

Working with Lagrangian we often encounter derivatives of particles fields, for example let's consider the first term of the LO chiral Lagrangian $$\mathcal{L}_{B\phi}^{LO}=\text{Tr}[\overline{B}(i\gamma^\mu \nabla_{\mu} - M_B)B]$$ where $$B$$ is the baryons matrix, and $$\nabla_\mu = \partial_{\mu}B + [\Gamma_{\mu}, B]$$ is the covariant derivative. Here I do not understand the meaning of $$\partial_\mu B$$. What does it mean (physically and non) to compute the derivative of a matrix whose elements are particles?

• a matrix whose elements are particles Its elements aren’t particles. Its elements are mathematical functions describing particles, and these functions are differentiable. Commented May 2, 2023 at 1:02
• yeah, fields as I said at the beginning, right? Commented May 2, 2023 at 1:04
• Yes, so why are you confused that you can compute the derivative of a field? Commented May 2, 2023 at 3:31
• You're right, perhaps I thought there was something more profound about it. I should have thought more by myself. Commented May 3, 2023 at 18:06