A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Ricci flow emerges from renormalizing nonlinear Sigma models.
Functional integrals explain quantum mechanics and field theory.
Global EQG sums boundary states over manifold diffeomorphism classes.
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…
Constructs maps from field theories to complexified K-theory and elliptic cohomology.
We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermion…
Quantum field theory uses Lorentzian bordisms to describe time evolution.
Finiteness predicts dualities in quantum gravity.
Abstract: Topological quantum field theory connects graph evaluations to polynomial identities.
Cone structures in quantum field theory linked to information geometry.
Paper compares algebraic quantum field theories and factorization algebras on Lorentzian manifolds.
We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a co…
Introduces noncommutative geometry for modeling quantum spacetime.
Quantum field theory connects Riemannian geometry to quantum fluctuations.
We provide a differential cocycle model for elliptic cohomology with complex coefficients and use analytic methods to construct a cocycle representative for the Witten class in this language. Our motivation stems from the conjectural connection between 2-dimensional field theories and elliptic cohomology originally due…
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…
The paper explores mapping class groups and their quantum field theory representations.
In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, firstly when volatility is taken to be a function of the forward rates…
Renormalization in neural networks linked to quantum field theory.
We prove the linear stability of Schwarzschild-Tangherlini spacetimes and their Anti-de Sitter counterparts under Ricci flow for a special class of perturbations. This is useful in the choice of suitable initial conditions in numerical Ricci-flow-based algorithms for obtaining new solutions to the Einstein equation whe…
We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
Derives localization formulas in Batalin-Vilkovisky formalism.
Introduces geometric quantization and Witten's quantum invariants.
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory, which allows us to prove that these models satisfy the principle of general local co…
We explore homotopies in quantum field theory formalism.
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories for stable equivalence classes.
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a f…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics.…
Finite presentations for skein algebras linked to gauge field theory.
We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a nonco…
Quantum invariants from are q-holonomic.
Link homology theories connect to 4-manifold invariants and TQFTs.
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection "Mathematical Foundations of Quantum Field Theory and Perturbative String Theory".
Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories.
We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's co…
We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of vi…
Tropical geometry aids in computing topological quantum field theories.
Analyzes the concept of fields in classical and quantum physics.
New framework for quantum invariants of 3-manifolds using homology.
Summarizes quantum field theories with discrete symmetry, classifying representations and anomalies.
Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane space K(G,1).
Model financial time series using φ^4 quantum field theory.
Quantum theory improves counting overlapping clusters.
We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Foc…
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field Theories in the Noncommutative geometry / topology realm.