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.
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48 results for “boson stars”
We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.
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…
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.
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.
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.
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 -valued one-form.
We prove the existence of a unique global weak solution to the full bosonic string heat flow from closed Riemannian surfaces to an arbitrary target under smallness conditions on the two-form and the scalar potential. The solution is smooth with the exception of finitely many singular points. Finally, we discuss the con…
This paper mainly aims to establish the well-posedness on time interval of the classical initial problem for the bosonic membrane in the light cone gauge. Here 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 with , integrating the Einstein-Hilbert Lagrangian density over .
result Encodes not only Yang-Mills terms but also a kinetic term for the Higgs field and potential for gauge bosons.
We study harmonic maps from surfaces coupled to a scalar and a two-form potential, which arise as critical points of the action of the full bosonic string. We investigate several analytic and geometric properties of these maps and prove an existence result by the heat flow method.
We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely …
We study the action of the full bosonic string for the domain being two-dimensional Minkowski space and the target a Riemannian manifold. Its critical points couple the wave map equation to a scalar and a two-form potential. Besides investigating their basic features we establish existence results for the latter.
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.
Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…
We show that generalised geometry gives a unified description of bosonic eleven-dimensional supergravity restricted to a -dimensional manifold for all . The theory is based on an extended tangent space which admits a natural action. The bosonic degrees of freedom are unified as…
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.
Star-Shaped deviationsq-fin.RM
Introduces Star-Shaped deviation measures for risk analysis.
problem Risk measurement and analysis in finance.
method Characterizes Star-Shaped deviation measures through acceptance sets and convex deviation measures.
result Exposes the relationship between Star-Shaped risk measures and deviation measures.
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.
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization of Thom-Madsen-Tillmann spectra, Adams spectral sequence, and Freed-Hopkins's t…
Algorithm achieves optimal regret for unknown Lipschitz convex losses.
problem Online learning with unknown Lipschitz constant and target vector norm.
method Develops an online learning algorithm without knowledge of or .
result Matches optimal regret bound up to logarithmic factors.
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.
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
Complex Structures on Jet Spaces and Bosonic Fock Space Dynamics for Causal Variational Principlesmath-ph
Based on conservation laws for surface layer integrals for critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under which conditions the almost-complex structure can be integrated to a canonical complex structure. Combined with the sc…
Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.
problem What conditions guarantee global existence of Gage's area-preserving flow for nonconvex initial curves?
method Using Dittberner's singularity analysis theory, constructed a ``flying wing'' curve to show limitations.
result Gage's area-preserving flow does not always preserve star-shapedness of evolving curves.
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.
In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric . It is proved that there exist no Hopf hypersurfaces in , with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on …
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…
Classifies star products on Lie algebroid duals and extends to projectable quantizations.
problem Classifying and extending quantizations on Lie algebroid duals.
method Classification through second Lie algebroid cohomology, extension to projectable quantizations.
result Quantization commutes with reduction in the considered setting.
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.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
Flow turns star-shaped curves into circles.
problem Transforming star-shaped curves into circles.
method Gage's area-preserving flow.
result Curves evolve into circles over time.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Paper disproves symmetry of stars at infinity in a specific graph.
problem Symmetry of stars at infinity in a specific graph.
method Defined incidence geometry of stars at infinity; provided an example.
result Relation of one boundary point being included in a star of another is not symmetric.
Study star products on Poisson manifolds compatible with reduction.
problem Finding star products compatible with coisotropic reduction.
method Compute second constraint Hochschild cohomology of constraint algebra.
result Determine infinitesimal star products on Poisson manifolds.
The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
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.
Deform moment map on symplectic connections using star product algebras.
problem Understanding symplectic connections and their deformations.
method Study vector bundle of Fedosov star product algebras, formal connection, curvature, and star product trace.
result Showed star product trace as a formal symplectic form and moment map.
CasVAE outperforms supervised methods for star-galaxy classification.
problem Challenges in machine learning for astronomy data.
method Cascade Variational Auto-Encoder (CasVAE) for unsupervised star-galaxy classification.
result CasVAE outperforms baseline models in accuracy and stability.
Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.
problem Finding vertex correspondence between two graphs to maximize edge overlap.
method Birkhoff relaxation as a convex relaxation of the quadratic assignment problem (QAP).
result Theoretical guarantees on the performance of Birkhoff relaxation under specific conditions.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
We compare the star surgery operations introduced in [KS] to the generalized rational blow-down. We show that star surgery shares the properties that make rational blow-down useful for constructions of small exotic symplectic 4-manifolds. Then we show that star surgery operations provide a strictly more general class o…
We derive a closed formula for a star-product on complex projective space and on the domain using a completely elementary construction: Starting from the standard star-product of Wick type on and performing a quantum analogue of Marsden-Weinstein reduction, we ca…
We analyze social and economic systems with a hierarchical structure and show that for such systems, it is possible to construct thermostatistics, based on the intermediate Gentile statistics. We show that in social and economic hierarchical systems there are elements that obey the Fermi-Dirac statistics and can be cal…
These notes form part of a lecture course on gauge theory. The material covered is standard in the physics literature, but perhaps less well-known to mathematicians. The purpose of these notes is to make spontaneous symmetry breaking and the Higgs mechanism of mass generation for elementary particles more easily access…
Estimates how many times a star appears due to gravitational lensing.
problem Estimating the number of times an observer sees a star due to gravitational lensing.
method Use affine linking numbers to estimate the number of times an observer sees a star.
result Estimates the number of times an observer sees a star due to gravitational lensing.
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.