1668 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 a comprehensive Hamilton–Jacobi theory for non-conservative classical field theories within the -contact framework by introducing evolution -contact -vector fields, developing both -independent and -dependent approaches, and validating the formalism through diverse applications ranging from dissipative wave equations to relativistic thermodynamics.
This paper establishes that hypergeometric functions of nilpotent operators undergo a "functional collapse" into finite polynomials, introducing a "nilpotent depth criterion" that quantifies how the contact order of a function at an exceptional point reduces the Jordan depth of the associated non-Hermitian Hamiltonian.
This review outlines the geometrical structures of pre-symplectic and pre-contact manifolds and develops corresponding constraint algorithms to ensure well-defined Hamiltonian dynamics for both conservative and dissipative singular systems, illustrated through specific examples.
This paper reviews the Batalin–Vilkovisky quantization of -theory on -Minkowski space by comparing standard and braided approaches, demonstrating that while standard quantization produces two inequivalent classes of tree-level diagrams with distinct noncommutative contributions, braided quantization yields a single class of diagrams where noncommutativity manifests only as an overall phase factor dependent on external momenta.
This contribution introduces discrete Bessel and Mathieu functions by applying the discrete dihedral group to the Helmholtz equation in polar and elliptic coordinates, and demonstrates that these functions serve as high-precision approximants of finite sums of their continuous counterparts, while preserving essential relations of special functions.
This paper derives new, simplified period formulae for the planar Euler problem in the quasi-periodic regime using Keplerian limits and complex analysis, thereby proving H. Dullin and R. Montgomery's conjecture that these periods and their ratio (the rotation number) are monotone functions of the non-trivial first integral at any fixed energy level.
This paper provides a comprehensive classification of the edge singularities and interior zeros of the Brown measure for deformed -valued circular elements, establishing that the measure possesses a real-analytic density with specific jump discontinuities at the spectral boundary and demonstrating that all identified singularity types are realizable in the context of large non-Hermitian random matrices.
This paper introduces a novel parallel athermal quasistatic deformation scheme that utilizes a two-level stepping approach to significantly accelerate the computation of molecular system trajectories, achieving speed-ups between 2.02 and 6.33 times while maintaining simulation accuracy.
This paper derives an explicit formula for spherically symmetric solutions to the Klein-Gordon equation in a de Sitter expanding universe and applies these results to analyze the temporal decay of fields generated by a pionic atom.
This contribution presents a theory-independent, geometric analysis of the interior of Schwarzschild black holes, demonstrating that dynamical evolution generically produces new singularities absent in static configurations, thereby imposing stringent constraints on gravitational collapse.