We derive the $\mathcal{P}(\Phi)_2$ measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding to the $\Phi^{2p}_2$ measure is formulated in the grand-canonical ensemble with a general symmetric $p$-body interaction potential which is not required to have a factorized form. Unlike in the $\Phi^4_2$ case investigated by Fr\"ohlich--Knowles--Schlein--Sohinger in \cite{FKSS25}, in the treatment of higher-order interactions, Wick renormalization generates a full hierarchy of lower-order interactions which we organize systematically using a graphical formalism. One key ingredient of our analysis is a logarithmic stability estimate for both the nonlocal Hartree functional and the many-body Hamiltonian that is uniform in the interaction range, allowing us to use the positivity of the leading $p$-body interaction to control all lower-order terms generated by the Wick counterterms.
We piece together textbook material to re-derive the parameter $\beta$ entering reduced density operators from quantum statistical mechanics. By re-deriving $\beta$, we show that the content of $\beta$ depends on the particular application of statistical mechanics. We focus on two different applications, namely, electr...
Ellen T. Ekstrøm, Jacob Pedersen, Ida-Marie Høyvik· 0 citations
We define a relative $\mathbb{Z}_2$-index $\mathcal{N}(\omega_1,\omega_2)$ for locally-comparable, parity-invariant pure states on a unital $C^*$-algebra. We prove that the index is well-defined, multiplicative, invariant under parity-preserving automorphisms, and locally constant in the norm topology. For the one-dime...
We construct the electric and magnetic Carroll limits of the $\mathcal{O}(F^2)$-truncated $\text{D}_p$-brane via the Polyakov--KK route, which combines a single-mode Kaluza--Klein-like reduction at fixed light-cone momentum with a Dirac classification that keeps the auxiliary worldvolume frame. Unlike the $U(1)$-free I...
We present part one of an SU(3)-flavour-symmetric lattice QCD calculation of the amplitude for a $D$-meson decaying to a $K\pi$ final state in the 27-dimensional irreducible representation of the flavour symmetry group, denoted $(K\pi)_{\mathbf{27}}$. The Wilson--clover gauge ensembles used in this work, generated by t...
Matthew Black, F. Erben, Maxwell T. Hansen et al.· 0 citations
We calculate the three-loop $\mathcal{O}(\alpha\alpha_s^2)$ mixed QCD-EW corrections to the top quark mass and obtain the relationships between the pole ($M_t$) and $\overline{\rm{MS}}$ ($m_t(\mu)$) masses at this order. In performing our calculation, we express the three-loop self-energies as a function of three-loop...
We study the high-temperature derivation of $\Phi^4_d$ measures from grand-canonical Bose gases on two- and three-dimensional tori. Building on the upper-symbol variational approach of the author's earlier work, we use relative entropy to give a simple, unified proof of relative free-energy convergence and Hilbert--Sch...
Hao-Cheng Liang· 0 citations
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