Lorentz and CPT violations in Finsler spacetime

Standard model with intrinsic Lorentz and CPT violations is proposed in a Finsler geometric framework. We present explicitly Lorentz and CPT--breaking Lagrangians of the matter fields and the gauge fields in locally Minkowski spacetime. The Lorentz invariance violation is found to be originated from the spacetime background deviating from the Minkowski one. Similarly, the CPT violation is determined by the behaviors of the locally Minkowski metric under the parity and time reversal operations. To help understanding phenomenologies, we compare the Finslerian model with the standard--model extension (SME) term by term at a first order approximation.