Spectral actions for q-particles and their asymptotic (Part II)

Abstract: For spectral actions made of the average number of particles and arising from open systems made of general free $q$-particles (including Bose, Fermi and classical ones corresponding to $q=\pm1$ and $0$, respectively) in thermal equilibrium, we compute the asymptotic expansion with respect to the natural cut-off. We treat both relevant situations relative to massless and massive particles, where the natural cut-off is $1/\beta=k_{\rm B}T$ and $1/\sqrt{\beta}$, respectively. We show that the massless situation enjoys less regularity properties than the massive one. We also consider the passage to the continuum describing infinitely extended open systems in thermal equilibrium. We briefly discuss the appearance of condensation phenomena occurring for Bose-like $q$-particles, for which $q\in(0,1]$, after passing to the continuum. We also compare the arising results for the finite volume situation (discrete spectrum) with the corresponding infinite volume one (continuous spectrum).

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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