1605 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 extends Emmy Noether's variational approach to singular extremals in nonlinear elastodynamics, deriving generalized integral relations that transform into inequalities for thermodynamically admissible solutions and revealing that kinetic energy can be entirely eliminated from the expression for dynamically stored elastic energy even in the presence of shocks.
This paper derives new integral relations in nonlinear elasticity that generalize Clapeyron's Theorem by utilizing "partial variational symmetries" within the Calculus of Variations to express stored energy through the combined work of physical and configurational forces.
This paper constructs two explicit unitary intertwiners that map the energy-definite portions of the Hilbert space for 1D generalized Coulomb problems to unitary lowest-weight representations of the universal cover of , thereby providing a quantum symmetry regularization analogous to the classical maps defined by Ma, Meng, and Xiao.
This paper establishes that the Cartan distribution on a finite-order jet bundle constitutes a polarised -contact structure, thereby providing a unified geometric framework that characterizes jet geometry, reconstructs its fundamental components, and enables new reduction methods for partial differential equations.
This paper establishes a unified framework linking macroscopic Geometric Thermodynamics and microscopic Information Geometry by introducing a Kähler metric on thermodynamic manifolds and deriving exact partition functions for Calabi-Vesentini event manifolds, which leads to a generalized Souriau thermodynamics featuring spontaneous symmetry breaking analogous to magnetization and provides exact Gibbs distributions for Cartan Neural Networks.
This paper diagnoses the degeneracy of the centre comonad model for quantum modalities, proving that its reliance on precomposition causes the collapse of linear logic to classical logic by annihilating non-commutative algebras, thereby establishing that non-degenerate quantum modalities must be constructed without precomposition.
This paper critiques existing semi-classical and quantum gravity frameworks to propose a teleparallel approach based on coframe and spin-connection variables, arguing that encoding gravity in torsion offers a geometrically refined foundation for future quantum gravity investigations.
This paper demonstrates that in finite-dimensional Bayesian inverse problems with equality constraints, sampling via penalized residuals in the full parameter-state space yields a posterior distinct from the reduced-space posterior due to a missing Jacobian determinant factor, and it derives specific determinant corrections required to ensure that zero-noise residual limits correctly recover the graph-lifted reduced posterior.
This paper demonstrates that appropriately engineered linear periodic media can suppress wave propagation to create discrete pass bands, thereby enabling classical waves to exhibit quantized energy and frequency spectra analogous to those in quantum mechanics without requiring nonlinear constraints.
This paper proposes and studies all-multiplicity building blocks for tree-level string amplitudes in AdS, deriving monodromy relations for open-string integrals and KLT factorization for closed-string integrals to extend non-commutative AdS uplifts to general -point kinematics.