1695 papers
Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.
On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.
This paper demonstrates that the canonical entanglement entropy of the vacuum state is finite for a broad class of conformal nets and establishes that mutual information remains finite in any local quantum field theory satisfying a modular -nuclearity condition for .
This paper introduces -solution spaces for the generalized Vekua equation in higher dimensions and establishes a Hodge decomposition for solutions that yields a factorization of Schrödinger operators, an explicit projection formula, and the existence of reproductive Vekua kernels.
This paper proposes a framework for modeling non-equilibrium and self-organizing systems using generative models and the variational free energy principle, which offers a tractable, parsimonious explanation of system dynamics as a form of variational inference without requiring the system to literally perform inference.
This paper introduces a unified framework utilizing holomorphic functional calculus on a specific ellipse to expand the adjacency matrix of regular graphs in terms of non-backtracking matrices, thereby deriving discrete trace formulas that connect spectral theory with graph combinatorics and offering new proofs for problems such as walk counting, the Ihara-Bass formula, and graph-based heat and Schrödinger equations.
This paper establishes a nonlinear -gluing theorem for vacuum gravitational fields with a cosmological constant near Birmingham-Kottler backgrounds in dimensions, extending previous results to arbitrary finite differentiability.
This paper demonstrates that quantum computers can achieve a super-polynomial sampling advantage over classical computers for Gibbs states of constant-temperature, O(1)-local Hamiltonians (specifically 5-local on a 3D lattice), even in the presence of imperfect measurements.
This paper provides a rigorous mathematical justification for the energy-independent relaxation time approximation in hard interactions, proposes a method to restore collision invariance, and elucidates how interaction types (hard versus soft) and physical parameters determine the non-analytical structures, such as hydrodynamic poles or gapless branch-cuts, in retarded correlators.
This paper characterizes the quality of quantum channel discrimination under limited memory by formulating the problem as constrained separability, enabling the derivation of bounds that reveal when classical or quantum memory is essential and clarify the hierarchical relationships within adaptive discrimination protocols.
This paper determines the center of the universal affine vertex superalgebra at the critical level by proving it is isomorphic to the large level limit of a parafermion vertex algebra, thereby confirming a conjecture by Molev and Ragoucy and proposing a generalization for .
This paper demonstrates that truncating infinite-dimensional quantum Hamiltonians to finite dimensions often leads to numerical simulations converging to the dynamics of an unintended Hamiltonian (specifically, the Friedrichs extension of the basis-restricted operator) rather than the true system, a failure that is generally undetectable without an analytical solution.