Oliveira, Maria JoãoMendes, Rui Vilela2015-09-222020-12-312015Oliveira, Maria João; Mendes, Rui Vilela - Fractional boson gas and fractional poisson measure in infinite dimensions. In "From particle systems to partial differential equations II" [Em linha]. Editado por Patrícia Gonçalves e Ana Jacinta Soares. [S.l.] : Springer. ISBN 978-3-319-16637-7. p. 293-312978-3-319-16636-0 (Print)978-3-319-16637-7 (Online)http://hdl.handle.net/10400.2/4475As a consequence of Haag’s theorem, to obtain a non-trivial theory, one either works with a non-Fock representation or with a Fock representation in a finite volume. Calculations in the Fock representation taking the N,V→ ∞limit with the ratio N/V=ρ fixed, show the equivalence of the free Boson gas and the infinite-dimensional Poisson measure. The N/V limit provides a way to deal with non-trivial infinite systems using the Fock representation. However, by the very nature of the fixed ρ density limit, it is unable to deal with systems with density fluctuations, a shortcoming that is solved by the use of reducible functionals. A particularly interesting reducible functional is the one associated to the infinite-dimensional fractional Poisson measure which we recall in this work.engBoson gasesFractional poisson measurebook part10.1007/978-3-319-16637-7_11