Causal fermion systems explore geometric space-time structures.
problem Understanding geometric structures in space-time.
method Causal fermion systems approach.
result Exploration of geometric space-time structures.
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48 results for “fermionic systems”
Proves a positive mass theorem for static causal fermion systems.
problem Defining mass for complex spacetimes without regularity assumptions.
method Surface layer integrals comparing asymptotically flat and vacuum spacetimes.
result Proves a positive mass theorem for static causal fermion systems.
Develops a mathematical framework for causal fermion systems in infinite dimensions.
problem Analysis of causal fermion systems in infinite-dimensional settings.
method Introduces Banach manifold structure and expedient differential calculus.
result Establishes Hölder continuity of causal Lagrangian and integrated causal Lagrangian.
Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analyzed. The connection to the spin condition in differential…
We define an index of the fermionic signature operator on even-dimensional globally hyperbolic spin manifolds of finite lifetime. The invariance of the index under homotopies is studied. The definition is generalized to causal fermion systems with a chiral grading. We give examples of space-times and Dirac operators th…
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.
Study baryogenesis in conformally flat spacetimes using causal fermion systems.
problem Understanding baryogenesis in specific spacetimes.
method Analysis of baryogenesis mechanism in conformally flat spacetimes with explicit formula derivation.
result Explicit formula for baryogenesis rate in these spacetimes.
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
Geometric derivation of Einstein equations from causal fermion systems.
problem Deriving Einstein's equations from a new theoretical framework.
method Analysis of causal fermion systems and causal action principle.
result Einstein equations derived from causal action principle.
Geometrically describes parity anomaly in fermionic systems.
problem Parity anomaly in fermionic systems coupled to background fields.
method Functorial quantum field theory, geometric cobordism bicategory, symmetric monoidal bicategories, Atiyah-Patodi-Singer index theorem.
result Explicit computation of 2-cocycle of projective representation.
Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordismshep-th
The paper generalizes TQFTs to fermionic systems and classifies SPTs and SETs.
problem Classifying fermionic SPTs and SETs with finite group symmetries.
method Formulating fermionic TQFTs, gauging SPTs, using bordism groups, and constructing anomalous boundary states.
result Explicit classification of fermionic SPTs and SETs, including new anomalous boundary states.
Massive fermions help understand index theorems without chiral symmetry.
problem Understanding index theorems in massive fermion systems.
method Reformulate chiral anomaly and index theorems with massive Dirac operators.
result Nontrivial mathematical relations between massless and massive fermions.
Derives a formula for fermion dimensions in spherically symmetric monopole backgrounds.
problem Calculating the dimension of the plane-wave normalizable kernel for massless fermions in spherically symmetric monopole backgrounds.
method Derives a formula for the dimension of the plane-wave normalizable kernel of the Dirac operator for fermions of any representation of SU(N) in the presence of any spherically symmetric monopole background.
result Derives a formula for the dimension of the plane-wave normalizable kernel of the Dirac operator.
Unveils fermions' geometric nature in the Standard Model as noncommutative forms.
problem Understanding the geometric structure of fermions in the Standard Model.
method Uses noncommutative geometry to represent fermion multiplet as de Rham forms.
result Fermions in the Standard Model are represented as noncommutative de Rham forms.
We introduce the deformed fermionic numbers, corresponding to the skein relations, the main characteristics of knots and links. These fermionic numbers allow one to restore the skein relations. For the Alexander (Jones) skein relation we introduce corresponding Alexander (Jones) fermionic q-numbers, and for the HOMFLY …
Two Pin groups fit fermions in gravity.
problem Matching fermion behavior with gravity.
method Examined eight Pin groups; identified two compatible with gravity.
result Only two Pin groups fit fermions in gravity.
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.
The paper studies Majorana Fermions and their braid group representations.
problem Understanding the braid group representations associated with Majorana Fermions.
method Recalling and proving a general result about braid group representations associated with Clifford algebras, and comparing it with Ivanov braiding.
result Certain strings of Majorana operators give rise to extraspecial 2-groups and braiding representations of the Ivanov type.
New mass inequalities and proofs for causal variational principles.
problem Proving new mass inequalities for causal variational principles.
method Proved a new inequality for minimizers of causal variational principles and applied it to prove the positive mass theorem.
result Introduced a positive quasilocal mass and proved new mass inequalities.
Anomalies in (2+1)D fermionic topological phases and (3+1)D path integral state sums for fermionic SPTscond-mat.str-el
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
problem Anomalies in (2+1)D fermionic topological phases and their computation.
method Combining (2+1)D fermionic topological order with symmetry fractionalization data to construct a (3+1)D path integral.
result Reproduces the anomaly indicator for time-reversal symmetric topological superconductors.
Reformulates mod-two APS index using domain-wall fermion.
problem Non-local APS boundary condition and global anomalies.
method Physicist-friendly reformulation of APS index using domain-wall fermion.
result Equivalence between two formulations of APS index.
No time-periodic Majorana fermions found in Kerr-Newman spacetimes with nontrivial charge.
problem Existence of Majorana fermions in Kerr-Newman spacetimes with nontrivial charge.
method Analysis of Dirac equation in Kerr-Newman spacetimes, leading to algebraic identities.
result No differentiable time-periodic Majorana fermions in Kerr-Newman spacetimes with nontrivial charge.
We show how Ramond free neutral Fermi fields lead to a -function theory of BKP type which describes iso-orthogonal deformations of systems of ortogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.
Paper studies non-associativity in quantum systems with magnetic fields.
problem Non-associativity of magnetic translations in quantum systems.
method Quantum field theory approach with -component fermions.
result Non-associativity described by a 3-cocycle of with values in .
Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of s…
FFT-Accelerated Auxiliary Variable MCMC for Fermionic Lattice Models: A Determinant-Free Approach with Complexitycond-mat.str-el
New MCMC method speeds up quantum physics simulations by a factor of 100.
problem Simulating quantum many-body systems with high computational complexity.
method FFT-accelerated MCMC with coupled particle and auxiliary variables.
result Achieves scaling, significantly faster than traditional methods.
Braiding Majorana Fermionscond-mat.str-el
In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion rules for a Majorana fermion. Majorana fermions can be seen not only in the structu…
Quantization of fermions yields determinant line bundle.
problem Quantizing fermions to derive mathematical structures.
method Batalin-Vilkovisky quantization of massless free fermions.
result Determinant line bundle derived from fermion quantization.
A new, simplified form of 10D supergravity action is derived up to all fermion orders.
problem Deriving a simplified form of 10D supergravity action up to all fermion orders.
method Generalised geometry and second-order formalism to upgrade calculations to all orders in fermions.
result A strikingly simple form of the action and supersymmetry transformations are obtained.
Mathematician-friendly formulation of Atiyah-Patodi-Singer index.
problem Boundary conditions and edge modes in domain-wall fermions.
method Mathematician-friendly derivation of Atiyah-Patodi-Singer index.
result New insights into the interplay of boundary conditions, domain-wall fermions, and edge modes.
Abstract operator calculus solves fermionic quantum harmonic oscillator problems.
problem Eigenvalue problems of fermionic quantum harmonic oscillators.
method Abstract operator calculus using homotopy operator.
result Formulated eigenvalue problem resembling fermionic quantum harmonic oscillator.
Anomaly in free fermion theory revealed in functorial field theory.
problem Chiral anomaly in the free fermion theory.
method Detailed construction of anomaly theory as a functor.
result The anomaly theory assigns elements of complex line to manifolds.
Study perturbs Dirac operators in any dimension, focusing on Majorana fermions.
problem Understanding perturbations of Dirac operators in various dimensions.
method Analyzes canonical perturbations of Dirac operators on Hermitian Clifford modules.
result Characterizes the low-energy spectrum of these operators on complete surfaces.
Method to find critical points in vector bundles with fermionic coupling.
problem Finding solutions to energy functionals coupled with fermionic operators.
method Study of critical points of strongly indefinite functionals on vector bundles.
result Existence and multiplicity of solutions for specific equations.
We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…
Study fermionic theories, their anomalies, and modular transformations.
problem Understanding fermionic theories and their anomalies.
method Use spin-cobordisms, surgeries, and invertible topological quantum field theories.
result Explicit combinatorial expressions for spin-bordism invariants.
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for…
The fermionic signature operator is analyzed on globally hyperbolic Lorentzian surfaces. The connection between the spectrum of the fermionic signature operator and geometric properties of the surface is studied. The findings are illustrated by simple examples and counterexamples.
A 12D spinor encodes fermions in a 4D Kaluza-Klein model.
problem Encoding fermions in a 4D spacetime from a higher-dimensional perspective.
method Using a spacetime with , encoding fermions in 64 spinor components.
result The 64 spinor components couple to Standard Model gauge fields in chiral representations.
Physicists explain a mathematical theorem about topological insulators.
problem Mathematical formulation of APS index theorem not directly related to physical fermion system.
method Reformulated APS index theorem using η invariant of domain-wall Dirac operator.
result Equivalence between APS index and η invariant is generally true.
Geometric interpretations and localisation theory for Kane-Mele invariant.
problem Understanding the Kane-Mele invariant in three-dimensional fermionic systems.
method Homotopy theory, geometric interpretations, Mayer-Vietoris Theorem, bundle gerbes.
result Unified cohomological explanation for equivalence between discrete Pfaffian and local geometric computations.
Using a supergeometric interpretation of field functionals developed in previous papers, we show that for quite a large class of systems of nonlinear field equations with anticommuting fields, infinite-dimensional supermanifolds (smf) of classical solutions can be constructed. Such systems arise in classical field mode…
The paper defines a fermionic part for a path integral on loop spaces.
problem Defining a fermionic part in a supersymmetric path integral on loop spaces.
method Generalizing a formula from finite dimensions to infinite-dimensional loop spaces, using the exponential of the canonical 2-form and transgression of the spin lifting gerbe.
result A section of the Pfaffian line bundle on the loop space is identified with a section of the line bundle obtained by transgression of the spin lifting gerbe.
Derives hyperbolic laws of cosines and sines with fermionic corrections.
problem Deriving hyperbolic laws of cosines and sines with new mathematical corrections.
method Using Minkowski supergeometry, the laws of cosines and sines are derived in the super hyperbolic plane.
result Identical formulae to classical cases with fermionic corrections for cosines and sines.
Holomorphic residue formula for complex supermanifolds.
problem Residue localization on complex supermanifolds.
method Holomorphic residue localization formula for odd vector fields.
result Explicit local residue formula under isolated non-degeneracy hypotheses.
The paper explores how non-Killing fields on internal spaces can produce massive gauge fields with chiral interactions.
problem Traditional Kaluza-Klein models limit gauge fields to Killing vector fields, ignoring chiral interactions.
method Investigates properties of 4D gauge fields linked to non-Killing fields on internal spaces using spin geometry and Riemannian submersions.
result Massive gauge fields linked to non-Killing fields can mix fermions with different masses and have asymmetric couplings to left- and right-handed fermions.
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin group. The differential operators can be seen as a generalization to higher spin …