Related papers: An Informal Summary of a New Formalism for Classif…
We study toroidal orbifold models with topologically invariant terms in the path integral formalism and give physical interpretations of the terms from an operator formalism point of view. We briefly discuss a possibility of a new class of…
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual…
In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the…
In the comparison of nonholonomic mechanics and constrained variational mechanics, invariant affine subbundles arise in the determination of the initial conditions where the two methods yield the same trajectories. Motivated by this,…
We present a formulation for the construction of first order equations which describe particles with spin, in the context of a manifestly covariant relativistic theory governed by an invariant evolution parameter; one obtains a consistent…
We define the secondary invariants L^2- eta and -rho forms for families of generalized Dirac operators on normal coverings of fibre bundles. On the covering family we assume transversally smooth spectral projections, and Novikov--Shubin…
Classical knot theory deals with {\em diagrams} and {\em invariants}. By means of horizontal {\em trisecants}, we construct a new theory of classical braids with invariants valued in {\em pictures}. These pictures are closely related to…
Massive spin 1/2 particles require 2-spinors for rotations, 4-spinors for rotations and boosts with parity. Including translations requires 8-spinors. Adapting 4-spinor field theory to 8-spinor fields with translation symmetry is discussed…
In this paper, we study the family index of a family of spin manifolds. In particular, we discuss to which extend the real index (of the Dirac operator of the real spinor bundle if the fiber dimension is divisible by 8) which can be defined…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
In various situations in Floer theory, one extracts homological invariants from "Morse-Bott" data in which the "critical set" is a union of manifolds, and the moduli spaces of "flow lines" have evaluation maps taking values in the critical…
The preceding paper constructed tangle machines as diagrammatic models, and illustrated their utility with a number of examples. The information content of a tangle machine is contained in characteristic quantities associated to equivalence…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…
For a space with involutive action, there is a variant of K-theory. Motivated by T-duality in type II orbifold string theory, we establish that a twisted version of the variant enjoys a topological T-duality for Real circle bundles, i.e.…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…
In this paper, we use skein-theoretic techniques to classify all virtual knot polynomials and trivalent graph invariants with certain smallness conditions. The first half of the paper classifies all virtual knot polynomials giving…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual…
We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of…