1677 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.
Motivated by quantum field theory on curved spacetimes, this paper computes the polarisation sets of the kernel distributions for advanced, retarded, and difference Green operators of normally hyperbolic operators on vector bundles, thereby extending these results to related equations like the Proca equation and correcting a gap in recent literature.
This paper investigates the reduced density matrices of -party pure quantum states derived from torus link complements in SU(2) Chern-Simons theory, demonstrating that their characteristic polynomials are monic with rational coefficients.
This paper presents a bootstrap program that iteratively solves for the -matrix of a generic integrable quantum spin chain from its Hamiltonian using the Yang-Baxter equation and Kennedy's lemma, offering both a reconstruction method and a potential integrability test, though it remains unclear if the infinite higher-order constraints are strictly implied by the lowest-order Reshetikhin condition.
This paper constructs fundamental solutions for arbitrarily sized upper-triangular Fuchsian systems with eigenvalues in arithmetic progression by expressing their superdiagonal entries as contour integrals of meromorphic differentials on compactified superelliptic curves, thereby proving the isomonodromic nature of these solutions.
This paper introduces a robust optimisation framework that combines variational residual minimisation with a resolvent-based Galerkin projection to efficiently compute invariant solutions, such as equilibria and periodic orbits, for wall-bounded flows like rotating plane Couette flow.
This paper demonstrates that a Thurston-based theory of gravity admits shear-free and static solutions across all Bianchi-Kantowski-Sachs topologies and ensures isotropization with a positive cosmological constant while preventing recollapse under the weak energy condition, thereby resolving specific limitations of General Relativity without introducing additional parameters.
This paper establishes the uniqueness and logarithmic stability of recovering the bottom shape of water waves from surface measurements and boundary data on a bounded domain, without additional assumptions for uniqueness and under a local fatness condition for stability.
This paper introduces a new mechanism called "symmetry spans," where a global symmetry embedded into two larger symmetries enforces infrared gaplessness when no compatible gapped phase exists, offering a powerful tool to establish symmetry-enforced gaplessness even with discrete and non-anomalous continuous symmetries.
This paper introduces causal hidden quantum Markov models (cHQMMs) where emissions precede hidden state transitions, demonstrating that this causal order generally produces distinct, distinguishable quantum processes compared to conventional models, while proving that the two architectures converge only when derived from entangled liftings of classical hidden Markov models, thereby establishing a clear boundary between classical and genuine quantum memory effects.
This paper proposes and validates an exact formula for three-point functions in critical loop models by unifying conformal field theory, lattice transfer-matrix methods, and probabilistic approaches based on conformal loop ensembles and Liouville quantum gravity.