### $\mathcal{P}\mathcal{T}$ symmetry and QCD: finite temperature and density.

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In this paper we extend to arbitrary number fields a construction of Bost-Connes of a ${C}^{*}$-dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.

The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and creation operators obey the quon algebra which interpolates between fermions and bosons. In this paper we generalize these models by introducing a deformation of the quon algebra generated by a collection of operators ${a}_{i,k}$, $(i,k)\in {\mathbb{N}}^{*}\times \left[m\right]$, on an infinite dimensional vector space satisfying the...

In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.

A generalisation of quantum principal bundles in which a quantum structure group is replaced by a coalgebra is proposed.