On the Thermodynamics of Particles Obeying Monotone Statistics.

The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called , based on a partial order arising from the natural one on the spectrum of a positive Hamiltonian with compact resolvent. The block-monotone scheme is never comparable with the weak monotone one and is reduced to the usual monotone scheme whenever all the eigenvalues of the involved Hamiltonian are non-degenerate.

The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields.

A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making use of Gauss' law, it is shown that the string-localized operators, which necessarily connect the charges, induce outer automorphisms of the algebra of the electromagnetic field. Thus they carry additional degrees of freedom which cannot be created by the field.

On the Thermodynamics of the -Particles.

Since the grand partition function Zq for the so-called -particles (i.e., quons), q∈(-1,1), cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for q=0, and its -deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to q∈[-1,1].