Abstract
Quantum chromodynamics (QCD) is the fundamental quantum field theory of quarks and gluons. To discuss it in a mathematically well-defined way, the theory has to be regularized by replacing space-time with a Euclidean lattice. This regularized theory, called lattice QCD (LQCD), has proven to be an efficient approach which allows for both theoretical understanding and computational analysis. LQCD has become a standard tool in elementary particle physics, which can be solved by the hybrid Monte Carlo method. The calculation of force is most difficult part in the hybrid Monte Carlo method. This lecture gives the details of the force calculation in one-loop Symanzik improved action, Wilson fermion with clover term, asqtad fermion, HISQ fermion, rooted staggered fermion, smeared fermion, staggered Wilson fermion, overlap fermion and domain wall fermion. The even-odd precondition are also considered in these calculations.
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