Abstract
In this paper we consider the possible modification of the anti Snyder model so that it have the non-zero minimal length, momentum cutoff and the convergent partition function. For the modified anti Snyder model we discuss the representations, eigenstates of position operator, momentum wave function, one dimensional box problem, and harmonic oscillator problem. We extend this model into D-dimensional case so that it also may guarantee the convergent partition function. Using this partition function we discuss the thermodynamics of the free particle system and cosmological constant problem.
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