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.
Quantum field theory uses Lorentzian bordisms to describe time evolution.
Enhances quantum sensing by eliminating multiple oscillations in field amplitude estimation.
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.
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics and quantum field theory from a functional integral point of view, where the mai…
Quantum field theory connects Riemannian geometry to quantum fluctuations.
Cone structures in quantum field theory linked to information geometry.
Introduces noncommutative geometry for modeling quantum spacetime.
Analyzes the concept of fields in classical and quantum physics.
The paper explores mapping class groups and their quantum field theory representations.
We explore homotopies in quantum field theory formalism.
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.
Superconducting circuit technologies have recently achieved quantum protocols involving closed feedback loops. Quantum artificial intelligence and quantum machine learning are emerging fields inside quantum technologies which may enable quantum devices to acquire information from the outer world and improve themselves …
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
Quantum invariants from are q-holonomic.
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…
Derives localization formulas in Batalin-Vilkovisky formalism.
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where quantum computer may offer significant speedup. Several quantum algorithms for discr…
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.…
New framework for quantum invariants of 3-manifolds using homology.
Quantum machine learning faces challenges similar to variational quantum algorithms in training.
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…
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 paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses, including suitable variants o…
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 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…
Defines coherent manifolds and their quantum applications.
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of optio…
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…
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
This work explores explainability in quantum machine learning.
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…
Meta-learning algorithms prepare quantum Gibbs states efficiently for NISQ devices.
Program connects quantum computing and topological field theories.
Finite presentations for skein algebras linked to gauge field theory.
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.
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
Photonic quantum reinforcement learning for control problems.
Quantum dilogarithms help define invariants of 3-manifolds.
Link homology theories connect to 4-manifold invariants and TQFTs.
Study topological quantum mechanics on orbifolds with geometric interpretation.
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).
Defines a map connecting 3d-index and skein module.
We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.
Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.
Deep quantum neural networks applied to finance for efficient risk management.
A new test of a wide class of interest rate models is proposed and applied to a recently developed quantum field theoretic model and the industry standard Heath-Jarrow-Morton model. This test is independent of the volatility function unlike other tests previously proposed in the literature. It is found that the HJM mod…
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.