Mathematical Physics
Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
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The modified Mathieu and doubly confluent Heun equations emerge from Painlevé III3 and III1, yielding the dual gauge period.
· “From Painlev\'e equations to {cal N}=2 susy gauge theories: prolegomena”
For 2d CFT degenerate operators, forbidden singularities dissolve and minimal models emerge from resummation.
· “On the 1/c expansion in 2d CFTs with degenerate operators”
A new L4 Strichartz estimate lowers the needed spatial regularity by a quarter derivative in every dimension d≥2.
· “Local well-posedness for the periodic Boltzmann equation with constant collision kernel”
Beyond a Thouless time, kicked many-body spectra reproduce COE, CUE, and CSE form factors to second order.
The planar calculus once limited to bipartite knots extends to all knots through one universal algebraic formula.
A complete geometric solution for the square root of the threetangle covers the whole Bloch sphere.
· “The exact convex roof for GHZ-W mixtures for three qubits and beyond”
Inverse neural-net analysis exposes a temporary interaction; refitting the equation restores its conservation law.
They solve the recursion and yield the coefficient of every Virasoro monomial.
Method-of-brackets evaluations extend Gradshteyn-Ryzhik entries from integer to real exponents.
· “Quadratic and quartic integrals using the method of brackets”
For cyclic circuits, one observable splits the reachable algebra into K copies for log K extra qubits.
Consistency, asymptotic normality, and exponential error bounds — and it feeds optimal voting weights.
· “Reconstruction of the Probability Measure and the Coupling Parameters in a Curie-Weiss Model”
Pairwise-distance conjugation turns multiple SLE null vector equations into the Calogero-Moser Hamiltonian.
· “Multiple chordal SLE(kappa) and quantum Calogero-Moser system”
First published values in 6−ε dimensions, extending known five-loop results.
Exact full counting statistics interpolate from single-file Mainardi-Wright at pure reflection to Gaussian at pure transmission.
Global solutions and an invariant measure make the non-commutative quantum field theory rigorous for all couplings.
· “Stochastic quantization of λ φ₂⁴- theory in 2-d Moyal space”
Same backpropagation trick that works for depolarizing noise now covers realistic amplitude damping.
Four solar-system tests force the new terms between 10^-9 and 10^-4.
· “Black hole with global monopole charge in self-interacting Kalb-Ramond field”
A rational conformal map fixed by one quartic root gives the equilibrium measure and leading energy in the pre-critical phase.
· “Properties of the one-component Coulomb gas on a sphere with two macroscopic external charges”
A matrix-cocycle calculation gives the exact heating phase boundary and Lyapunov exponent for driven critical systems.
· “Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results”
A circle-based model of blackbody radiation predicts dimmer, narrower, redshifted spectra as curvature grows.
Above band width $N^{1/2+\varepsilon}$, bulk eigenvectors spread out and the local eigenvalue statistics are GUE.
A reduction chain from 3×3 Lax matrices recovers the Adler-Yamilov map and new integrable birational YB maps.
· “Reductions and degenerate limits of Yang-Baxter maps with 3times 3 Lax matrices”
A spherical-harmonic split turns 3D Dirac stability checks into one-dimensional radial problems.
· “On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D”
Idempotents, spinor bases, matrix reps, and norms for every real and complex algebra, extending a 1998 computation.
· “Clifford geometric algebra: Real and complex spinor data tables”
If right, the AB effect follows from topology of the punctured plane, not a coil outside the electron's reach.
An explicit analytic series for the charged scalar correlator, with QNM dispersions and superconducting Tc.
· “Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun”
For intermediate Robin conditions the xi-term is positive; only Dirichlet and Neumann keep it zero.
This theorem gives a mechanical origin for random-Hurst and random-coefficient anomalous diffusion.
At t=q^{-m}, one explicit power series ties Macdonald polynomials and Baker-Akhiezer functions into one triad.
At field strength δ^{15/8}, the interface becomes massive SLE3 with an explicit density; weaker fields keep SLE3, stronger fields flatten…
· “Interface scaling limit for the critical planar Ising model perturbed by a magnetic field”
Starting from SU(2) connections, a Chern-Simons twist turns the square of a Dirac operator into coupled bosonic and fermionic Hamiltonians.
· “A Yang-Mills-Dirac Quantum Field Theory Emerging From a Dirac Operator on a Configuration Space”
The unique entropy-maximizing limit controls all but exponentially few graphs, so the blocks are genuine phases.
For every window, the Bopp transform keeps the eigenvalues and trace of the quantum state on the wavepacket subspace.
New proof transfers rigidity from a rational extension, settling a long-standing logarithmic CFT conjecture.
· “Ribbon categories of weight modules for affine mathfrak{sl}₂ at admissible levels”
Known minimal models emerge from the recipe, plus three new Haagerup-symmetric CFT candidates.
The bound unlocks maximal regularity and a path to global well-posedness for half-space liquid-crystal flows.
· “The mathcal{R}-boundedness of solution operators for the Q-tensor model of nematic liquid crystals”
It also gives the number of master integrals at each singularity, straight from the hypersurface geometry.
A code is decodable for a noise space exactly when that space carries a special inner product; explicit error bases follow.
· “Quantum error-correcting codes via inner products and error bases”
If right, the full higher-category toolkit applies to QFT symmetries, with gauging duality inside the theory.
New transport framework yields explicit convergence bounds for non-symmetric channels and recovers geometric distances.
· “Transportation cost and contraction coefficient for channels on von Neumann algebras”
A rigorous upper bound now includes the logarithmic third-order term predicted in 1959; only the lower bound is missing.
· “Third Order Upper Bound for the Ground State Energy of the Dilute Bose Gas”
A 2x1 tensor RG map plus interval arithmetic turns renormalization into a rigorous phase proof.
Below that threshold a linear-time strategy almost surely wins; above it, every algorithm almost surely loses.
Gauging OSp(6,2|4) yields the complete geometry and the unique Bach tensor for conformal supergravity.
Any anomaly builds an extension whose linear functors are exactly the anomalous representations.
· “Projective and anomalous representations of categories and their linearizations”
A parameter-free, reversible rule on ordered facets sends single particles along geodesics; many interact only when sharing a facet.
It works for any countable list of diffusivities, with exponential growth rate at least 1/4.
In one dimension, all thermodynamic constraints are solved; stresses, heat fluxes and entropy extra-fluxes come out explicitly.
A single photon's OAM and polarization fill the Z2×Z2 sectors, enabling deterministic universal SU(4) gates without nonlinear optics.
A single scalar equation replaces an overdetermined system, making density fields and phase boundaries computable.
· “Two-dimensional equilibrium configurations in Korteweg fluids”
Bending makes overlapping scales slide faster, so trapped fluid dissipates energy nonlinearly with curvature and rate.
· “Viscoelasticity of biomimetic scale beams from trapped complex fluids”
Upper moments and down-Fisher measures extend classical inequalities beyond the stretched-Gaussian setting.
For su3, multiplicative relations among planarized link symbols give classical trefoil A-polynomials, with su2 checks supporting the method.
· “On geometric bases for A-polynomials II: mathfrak{su}₃ and Kuberberg bracket”
A Fock-space duality transfers finite-dimensional gl_d results to infinite-dimensional unitarizable superalgebra modules.
· “Bethe algebras for unitarizable modules over classical Lie (super)algebras and a duality”
New two-microlocal measures reveal the hidden noncompact mass and the quartic-oscillator dynamics behind it.
A two-step model claims to encode partial coherence at the surface, avoiding costly ensemble averaging.
· “Surface-Encoded Partial Coherence Transformation: Modeling Source Coherence Effects in Wave Optics”
Uniform bound on single-site variance: Var(φ0) ≥ c log N for every boundary datum and fiber shift.
· “Quantitative delocalization for solid-on-solid models at high temperature and arbitrary tilt”
For random block arrays the eigenvalue count becomes a fixed continuous curve, computable in linear time via meta-atoms.
· “Universal estimates for the density of states for aperiodic block subwavelength resonator systems”
Refined q,t hyperpolynomials of the Hopf link and torus links T[2,2n] now have a single universal expression.
· “Macdonald deformation of Vogel's universality and link hyperpolynomials”
One-instanton corrections match independent topological recursion; two-instanton terms are new predictions.
· “Non-perturbative effects in JT gravity from KdV equations”
A 16-region case split with monotonicity bounds leaves only the regular pentagon.
· “Uniqueness of star central configurations in the 5-body problem”
A Feynman-Kac pre-factor Lyapunov construction controls overheating and freezing, yielding polynomial convergence.
· “Non-equilibrium steady state for a three-mode energy cascade model”
Rigorous bounds fix the second-order energy density using only three scattering lengths.
Random pipe dreams and bubble-sort operations both converge to computable permutons with a known fluctuation law.
Exact results: the only nonchaotic collapse is unstable, so the approach to the singularity is chaotic.
· “Some exact results on the Belinski-Khalatnikov-Lifshitz scenario”
A Fock-space construction turns LLM autoregressive generation into sequential quantum measurements.
· “Physical models realizing the transformer architecture of large language models”
Ties the flow's Besov regularity to the dimension of its dissipation set, forcing intermittency for all p>3.
One complex equation generates unmodulated oscillons; a two-Q-ball bound state explains their amplitude modulations.
For p,q≥0, moments stay finite below p=min(2/γ²+q/2, 4/γ²), the input needed for the bulk tail profile.
· “Tail Profile of Bulk Gaussian Multiplicative Chaos Measures I: Bulk/Boundary Quotients”
A short proof shows every quantum coordinate is a line, half-line, interval, or lattice—and when momentum needs a larger space.
· “All Hilbert spaces are the same: consequences for generalized coordinates and momenta”
New estimates show high-velocity moments appear at the same rate as in pure energy-exchanging collisions.
· “Moment estimates for polyatomic Boltzmann equation with frozen collisions”
Generalizes the affine Toda spectrum: masses become pairings of an eigenvector with root orbits.
A two-replica ansatz solves the NESS, and a resonance yields robust spin-helix states.
· “Exact NESS of XXZ circuits boundary driven with arbitrary resets or fields”
An exact survival rate shows resetting beats plain drift once the starting distance exceeds a q-dependent threshold.
· “Survival probabilities in biased random walks: To restart or not to restart? that is the question”
Its residues match the perturbative series and the Stokes jumps of resurgence theory.
Multivariate Krawtchouk, Meixner, and Rahman polynomials diagonalize free-fermion Hamiltonians exactly.
A simple variational argument gives the enhancement without imaginary-time path integrals, matching earlier quantum results.
· “Dirac's variational approach to semiclassical Kramers problem in Smoluchowski limit”
Exact metric with black string, string cloud, and quintessence yields a Heun wave solution with a dark phase.
Odd and even qubit counts become polynomial-time, so tomography and entanglement checks scale past a thousand sites.
A new theorem embeds any reversible mass-action system in a closed, thermodynamically consistent network.
· “The detailed balance property and chemical systems out of equilibrium”
