Related papers: An Elementary Characterization of Bargmann Invaria…
Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ with two columns are constructed within a metric-like formulation in a…
Always dealing with an arbitrary field we consider the variety $(k^{n\times n})^{p}$ under the action of $GL_{n}$ by simultaneous similarity. We define discrete and continuous invariants which completely determine the orbits. The discrete…
We define an uncertainty observable, acting on several replicas of a continuous-variable bosonic state, whose trivial uncertainty lower bound induces nontrivial phase-space uncertainty relations for a single copy of the state. By exploiting…
Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties…
We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…
In this work we consider the permutational properties of multipartite entanglement monotones. Based on the fact that genuine multipartite entanglement is a property of the entire multi-qubit system, we argue that ideal definitions for its…
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally…
Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchstaber invariants and classical invariants of simplicial…
We show how to define invariants of graphs related to quantum $\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions.
The Newman-Penrose (NP) formalism is traditionally used to analyze the polarization content of gravitational waves, while the gauge-invariant Bardeen formalism provides a complementary, and often simpler, description based on the…
The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $q=1$ case. These equations, defining the…
We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop…
We prove several trace inequalities that extend the Golden-Thompson and the Araki-Lieb-Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb's triple matrix inequality. As an example application of our four…
Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann…
We show that quark models of current matrix-elements based on the Bakamjian-Thomas construction of relativistic states with a fixed number of particles, plus the additivity assumption, are covariant in the heavy-quark limit and satisfy the…
Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…
Using the Rost invariant for non split simply connected groups, we define a relative degree $3$ cohomological invariant for pairs of orthogonal or unitary involutions having isomorphic Clifford or discriminant algebras. The main purpose of…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
For an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can…
We develop a simple method for constructing polynomial invariants of degree 4 for even-$n$ qubits and give explicit expressions for these polynomial invariants. We demonstrate the invariance of the polynomials under stochastic local…