Study higher order fermionic and bosonic operators on cylinders and Hopf manifolds.
problem Understanding higher order higher spin operators on specific manifolds.
method Analysis of higher order operators on cylinders and Hopf manifolds.
result Construction of kernels for these operators on the studied manifolds.
The paper classifies higher order fermionic and bosonic operators in spin spaces.
problem Understanding higher order conformally invariant differential operators.
method Using higher spin theory in Clifford analysis, constructing operators as generalizations of the Euclidean Dirac operator.
result These operators act on functions in homogeneous harmonic or monogenic polynomial spaces, and are classified as fermionic or bosonic based on spin.
The paper extends higher-order operators in higher spin spaces.
problem Generalizing higher-order operators in higher spin spaces.
method Constructing 3rd order fermionic and 4th order bosonic operators in higher spin spaces.
result Fundamental solutions and intertwining operators of 3rd order fermionic and 4th order bosonic operators are presented.
Defines coherent manifolds and their quantum applications.
problem Understanding quantum spaces and coherent states.
method Generalizes quantum field theory and Schrödinger equation solutions.
result Solves Schrödinger equation on coherent manifolds.
New complex structures on jet spaces help explain Fock space dynamics.
problem Understanding dynamics of Fock spaces from variational principles.
method Endowing jet spaces with almost-complex structures, integrating to canonical complex structures, and analyzing Fock spaces.
result Holomorphic approximation explains dynamics of Fock spaces from variational principles.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
Study the full bosonic string action in Minkowski space to Riemannian manifolds.
problem Modeling the full bosonic string action across different target manifolds.
method Investigate the action for Minkowski space as the domain and Riemannian manifolds as targets, coupling wave map equation to potentials.
result Establish existence results for the scalar and two-form potentials.
Quantum Proof-of-Work uses boson sampling to secure blockchain consensus.
problem Ensuring secure and efficient blockchain consensus.
method Proposes using quantum boson sampling as a Proof-of-Work scheme for blockchain.
result Demonstrates a robust and energy-efficient PoW scheme.
Researchers create initial data for multiple collapsing boson stars.
problem Forming multiple trapped surfaces in spacetime.
method Constructed Cauchy initial data for EMKG system.
result Multiple trapped surfaces form in finite time.
This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here {models a two traders system with information exchange with the help of four fundamental operators: cash and share operators; a portfol…
Global solution found for string heat flow on surfaces.
problem Existence of global weak solutions for bosonic string heat flow.
method Proved existence with smallness conditions on form and potential.
result Global weak solution found, smooth with finitely many singular points.
Defines Killing spinors and bosonic backgrounds in 5D supergravity.
problem Characterizing backgrounds in 5D supergravity.
method Calculates Spencer cohomology, defines Killing spinors, and imposes constraints on spinor connection curvature.
result Recover field equations of 5D supergravity and find new field equations for sp(1)-valued one-form. We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary satisfying local elliptic boundary conditions. The conditions are defined using the additional structure of a framing, …
Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposa…
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are t…
We use standard perturbation techniques originally formulated in quantum (statistical) mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators. In particular we discuss the probability of transition from a given value of the {\em portfolio} of a certain trader to a differ…
We reveal connections between RBMs and Bosons, explaining symmetry breaking in their energy landscapes.
problem Understanding the relationships among different deep generative models and their learning mechanisms.
method Introducing a reciprocal space formulation to RBMs, revealing connections to diffusion processes and Bosons.
result Symmetry breaking in RBM energy landscapes is characterized by singular values and weight matrix eigenvectors.
This paper mainly aims to establish the well-posedness on time interval [0,ε−21T] of the classical initial problem for the bosonic membrane in the light cone gauge. Here ε is the small parameter measures the nonlinear effects. In geometric, the bosonic membrane are timelike submanifo…
The model integrates Standard Model bosons into a higher-dimensional spacetime.
problem Integrating Standard Model bosons into a higher-dimensional spacetime.
method Considered a spacetime of the form P=M4imesK with K=SU(3), integrating the Einstein-Hilbert Lagrangian density over K. result Encodes not only Yang-Mills terms but also a kinetic term for the Higgs field and potential for gauge bosons.
The paper is devoted to the study of BRST charge in perturbed two dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via th…
The paper constructs new supergravity backgrounds using specific geometric constraints.
problem Finding new supergravity backgrounds in eleven-dimensional space.
method Using twisted products of six-dimensional and five-dimensional manifolds, and analyzing the bosonic supergravity equations.
result New supergravity backgrounds appear for special cases of the adapted flux 4-form.
We show that generalised geometry gives a unified description of bosonic eleven-dimensional supergravity restricted to a d-dimensional manifold for all d≤7. The theory is based on an extended tangent space which admits a natural Ed(d)×R+ action. The bosonic degrees of freedom are unified as…
Heat flow method proves existence of harmonic maps.
problem Analyzing harmonic maps from surfaces coupled to potentials.
method Heat flow method
result Existence of critical points in string theory.
New decomposable solutions found in 11D supergravity.
problem Finding new solutions in 11D supergravity.
method Solving bosonic supergravity equations for various flux forms.
result Infinitely many non-symmetric decomposable (5,6)-supergravity backgrounds.
The aim of this paper is to present a short introduction to supergeometry on pure odd supermanifolds. (Pseudo)differential forms, Cartan calculus (DeRham differential, Lie derivative, "inner" product), metric, inner product, Killing's vector fields, Hodge star operator, integral forms, co-differential and connection on…
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal or "thick" morphisms. They are formal canonical relations of a special form, constructed with the help of formal power expansions in cotangent directions. The result is a formal category so that its composition l…
Mathematical proof of string theory convergence on surfaces.
problem Convergence of Polyakov's partition function in higher genus.
method Probabilistic and non-perturbative analysis of Liouville quantum field theory.
result Convergence of Polyakov's partition function over moduli space in genus g≥2.
The study analyzes social and economic systems using bosonic and fermionic statistics.
problem Analyzing hierarchical social and economic systems.
method Intermediate Gentile statistics and derivation of thermodynamic laws.
result Introduces concepts like temperature and pressure for economic systems.
Deep learning improves jet tagging for W boson detection.
problem Improving detection of highly boosted W bosons.
method Developed deep learning algorithms to identify W bosons in jet images.
result Deep learning algorithms outperform traditional feature-driven approaches.
The paper constructs arbitrary order conformally invariant operators in higher spin spaces.
problem Classifying and constructing conformally invariant differential operators in higher spin spaces.
method Explicit expressions and convolution type operators, intertwining operators, and representation theory.
result Explicit expressions and properties of conformally invariant differential operators in higher spin spaces.
A parameter-free statistical model is used to study multiplicity signatures for coherent production of charged-pairs of parabosons of order p=2 in comparison with those arising in the case of ordinary bosons, p=1. Two non-negative real parameters arise because "ab" and "ba" are fundamentally distinct pair operators of …
New method solves differential equations on manifolds, with applications in physics.
problem Solving differential equations on Riemannian manifolds.
method Developed linear homotopy theory for codifferential operator, leading to a direct sum decomposition of differential forms.
result Shows a new way to solve exterior differential systems, applicable to fundamental physics equations.
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Discovering topological quantum field theories in 2+1 and 3+1 dimensions.
problem Exploring topological orders in condensed matter lattice models.
method Calculating braiding statistics and link invariants of anyon excitations.
result Identifying new spin topological quantum field theories with specific knot/link invariants.
We calculate the free energy of Coulomb gas systems on Riemann surfaces.
problem Analyzing the free energy of Coulomb gas systems on Riemann surfaces.
method Using bosonization formula and analytic torsion, we derive the asymptotic expansion of the partition function.
result We prove the geometric version of the Zabrodin-Wiegmann conjecture in the determinantal case.
Positive curvature manifolds from smaller ones using division algebras and geodesic flow.
problem Understanding positive curvature manifolds and their properties.
method Using Conner-Kobayashi reductions and division algebras to build up positive curvature manifolds.
result Existence of two linearly independent harmonic k-forms on positive curvature manifolds.
Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.
problem Integrating quantum flag manifold σ-models with fermions.
method Gauging bosonic Thirring/Gross-Neveu-type systems, adding fermions to cancel anomalies, and checking Ricci flow equations.
result Trigonometrically deformed geometries of flag manifold σ-models satisfy generalized Ricci flow equations.
We classify higher-SPTs and their anomalies via cobordism theory.
problem Understanding higher symmetries and anomalies in quantum field theories.
method Developed a generalized cobordism theory using advanced mathematical tools.
result Classified higher-SPTs and their boundary anomalies.
In this paper we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs potential. Such a vacuum s…
Study on spontaneous symmetry breaking in financial markets using quantum mechanics.
problem Analyzing spontaneous symmetry breaking in financial markets.
method Using Hamiltonian form of Black-Scholes and Merton-Garman equations, analyzing symmetry breaking and interpreting Nambu-Goldstone bosons.
result Interpretation of Nambu-Goldstone bosons in financial markets.
Quantum GBS boosts asset clustering for robust statistical arbitrage portfolios.
problem Identifying co-moving assets from correlation matrices for statistical arbitrage.
method Mapping S&P 500 correlation data to GBS-compatible adjacency matrices, benchmarking classical and quantum clustering algorithms.
result Quantum GBS generates superior alpha during high volatility periods, persisting under low-loss conditions.
Spin geometry reviewed with applications in physics.
problem None explicitly stated, but related to spin geometry and its applications.
method Definitions of spin geometry, Clifford algebras, and spinors; discussion of differential operators, twistor and Killing spinors; holonomy classification; construction of symmetry operators and extended superalgebras.
result Construction of extended superalgebras and methods to find solutions of Seiberg-Witten equations.
This paper tackles class imbalance in high energy physics experiments.
problem Extracting a signal from a large background in high energy physics experiments.
method Overview of class imbalance techniques and case studies.
result Demonstrates the effectiveness of class imbalance techniques in high energy physics experiments.
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.
Iterative subtraction method outperforms other feature ranking techniques in high-energy physics.
problem Determining the most important features for classification in high-energy physics experiments.
method Comparison of feature ranking methods including Iterative Addition, Iterative Removal, and BDT Selection Frequency.
result Iterative Removal method is the most efficient for feature ranking in classification tasks.
The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.
Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically rigorous BRST quantization of the constrained system whose cohomology at ghost numbe…
Differential forms and symmetric tensors show contrasting singular behaviors in a specific geometric setting.
problem Exploring differential forms and symmetric tensors on a specific geometric setting.
method Analyzing differential forms and symmetric tensors on the quadrant C2 with subset diffeology. result Symmetric tensors exhibit singularities that accumulate, while differential forms are smooth.