Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus

Abstract

We show that the solitonic contribution of toroidally compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of compactification on a circle, the Hamiltonian is the Laplacian on the 2g-dimensional Jacobian torus associated with the genus g Riemann surface corresponding to the string world sheet. T duality leads to a symmetry of the partition function mixing time and temperature. Such a classical-quantum correspondence and T duality shed some light on the well-known interplay between time and temperature in quantum field theory and classical statistical mechanics.

Abelian gerbes as a gauge theory of quantum mechanics on phase space

“…Related analyses concerning the meaning of quantum vs. classical were carried out in refs. [16,17,18,19,20,21,22,23], albeit under different, apparently unrelated guises.…”

“…Hence the 1-form potential A on the gerbe might be called the quanton, because the gauge property it carries is quantumness as opposed to classicality: the property of being quantum as opposed to classical. Related analyses concerning the meaning of quantum versus classical were carried out in [15][16][17][18][19][20][21][22], albeit under different, apparently unrelated guises.…”

"Thermodynamique cachée des particules" and the quantum potential

“…Eq. ( 4) may be related to t − T duality and non-commutative geometry (see [10] and references therein). In this respect, it is worth recalling de Broglie view [1].…”

“…In [10] it has been considered a string model where time-temperature and classicalquantum dualities, emerge naturally. It turns out that the solitonic sector of compactified strings have a dual description as quantum statistical partition function on higher dimensional spaces, built in terms of the Jacobian torus of the string worldsheet and of the compactified space.…”

“…It turns out that the solitonic sector of compactified strings have a dual description as quantum statistical partition function on higher dimensional spaces, built in terms of the Jacobian torus of the string worldsheet and of the compactified space. More precisely, in [10] it has been shown that in the case of compactification on a circle m,n∈Z g e −βSm,n = tr e −βH , (5) where β = 2R 2 /α ′ , with R the compactification radius, and the Hamiltonian H is ∆ J Ω /2π, with ∆ J Ω the Laplacian on the Jacobian torus J Ω of the worldsheet. Eq.…”