Related papers: An Informal Summary of a New Formalism for Classif…
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
For several objects of interest in geometric complexity theory, namely for the determinant, the permanent, the product of variables, the power sum, the unit tensor, and the matrix multiplication tensor, we introduce and study a fundamental…
We describe the invariant structure common to abelian fractional quantum Hall systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized…
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 we discus the main structures…
For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
This paper presents a generalisation of Sylvester's law of inertia to real non-degenerate quadratic forms on a fixed real vector bundle over a connected locally connected paracompact Hausdorff space. By interpreting the classical inertia as…
We study the Hamiltonian dynamics and spectral theory of spin-oscillators. Because of their rich structure, spin-oscillators display fairly general properties of integrable systems with two degrees of freedom. Spin-oscillators have…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
We present the applications of variational--wavelet approach to nonlinear (rational) model for spin-orbital motion: orbital dynamics and Thomas-BMT equations for classical spin vector. We represent the solution of this dynamical system in…
A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum…
Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…
The correspondence between BRST and unfolded formulations of field equations on group manifolds and homogeneous spaces is described. The previously introduced nonstandard BRST operator, that underlies Sp(2M) invariant higher-spin field…
In this article, we consider fixed spin-1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give approximate evolutions of coherent states. This uses spins-photon classical Hamiltonian…
A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…
This work has as the main aim to explore the nature of the fermionic fields, through a classification of spinor fields about physical space of interest, such as the bulk and the compactified space $S^7$ from the supergravity theories. This…
We propose an analogue of spin fields for the relativistic RNS-particle in 4 dimensions, in order to describe Ramond-Ramond states as "two-particle" excitations on the world line. On a natural representation space we identify a differential…
The 24 components of the relativistic spin tensor consist of 3+3 basic spin fields and 9+9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one…
Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full…
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…