### Trace anomaly as a result of the thermodynamic inconsistency in a model of a free neutral scalar field on the lattice and in the continuum

(0 votes over all institutions)

The thermodynamic properties of the free neutral scalar field given in the framework of the method of the path integral quantization both on the lattice and in the continuum limit were investigated. It was revealed that the trace anomaly for the free neutral scalar field at low temperature and finite volume is a consequence of the thermodynamic inconsistency of the model both on the lattice and in the continuum limit. It was also found that the prescription for the free massless neutral scalar field adopted in [J.Engels et al., Nucl. Phys. B 205, 239 (1982)], i.e., the suppression of the $\vec{k}=0,k_{\beta}=0$ term in the summation for the energy density, leads to the inequivalence of the path integral quantization method with the canonical quantization method for such a field.