2548 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 establishes the existence of smooth solutions to the symmetric maximal surface equation under degenerate boundary conditions and proves that these solutions maximize the associated area functionals, serving as a Lorentzian analogue to minimal graphs in hyperbolic spaces.
This paper investigates the algebraic and differential structure of the Riemann tensor in higher-dimensional Kerr-NUT-(A)dS spaces to pursue an IDEAL characterization of these metrics, proving a no-go theorem that no non-trivial 2-form can be covariantly constructed from the undifferentiated Riemann tensor alone while successfully characterizing the family of valid curvature tensors through specific algebraic and differential conditions derived from the principal tensor's integrability and the Bianchi identity.
This paper establishes the complete mapping properties of two-dimensional Schrödinger wave operators at the critical endpoints and , revealing that unlike in higher dimensions, an s-wave resonance at zero energy unexpectedly improves endpoint boundedness while other spectral configurations impose specific Calderón–Zygmund type estimates or require precise moment cancellations for boundedness.
This paper establishes that a massive Dirac operator in the plane with an attractive Lorentz-scalar -shell interaction supported on a smooth, unbounded curve that locally deforms a broken line possesses a finite number of discrete eigenvalues within its spectral gap, provided the curve bounds a convex domain and the interaction strength is sufficiently extreme, thereby demonstrating that the discrete spectrum is induced by the geometric deformation of the support.
This paper reformulates the statistical mechanics relaxation problem by identifying local time statistics of signals as the operational objects of relaxation, demonstrating that global irreversible prediction relaxation is possible for finite bounded systems, and interpreting entropy as mutual information between an observer and the system's unknown past.
This paper establishes that complete ALF Ricci-flat 4-manifolds with bounded Killing vector fields are linearly stable if and only if they are locally hyperkähler, a result that confirms the instability of recently discovered metrics by Li-Sun and extends to show that stability in higher-dimensional generalizations forces the universal cover to split a line.
This paper establishes the equivalence between the Polchinski flow and Connes-Kreimer approaches to perturbative renormalisation by demonstrating that a combinatorial procedure based on decorated graphs solves the Polchinski equation, thereby deriving a highly general form of the renormalised potential for Euclidean quantum field theories.
This paper extends a generalized Bethe ansatz framework to open boundary conditions with time-dependent bulk and boundary couplings, demonstrating that integrability leads to boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations whose solutions yield exact wavefunctions and reveal that the dynamical invariants of the time-dependent model correspond to the renormalization group invariants of the associated static system.
This paper establishes the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces by constructing code words as automorphic forms, while proving a fundamental no-go theorem that non-amenable stabilizer groups on higher-genus surfaces preclude the existence of normalizable exact code states, thereby distinguishing them from standard GKP codes.
This paper demonstrates that while finding local energy minima in quantum systems is computationally hard for classical computers, it can be efficiently solved by quantum computers using a thermal gradient descent algorithm, thereby establishing a scenario where quantum computation outperforms classical computation even for tasks simpler than finding ground states.