Gauge Invariant Spin Research Articles

Quantum phases of two-dimensional Z2 gauge theory coupled to single-component fermion matter

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $\mathbb{Z}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $\mathbb{Z}_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $\mathbb{Z}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization. The rich phenomenology discussed in this paper can be probed in analog and digital quantum simulators of discrete gauge theories and in Kitaev spin-orbital liquids.

On gauge invariant nucleon spin decomposition

A non-uniqueness problem of gauge invariant separation of quark and gluon contributions to nucleon spin is considered. We show that there is a wide number of gauge invariant spin decompositions, and each of them reduces to the canonical one in a special gauge. A class of physical gauge equivalent nucleon spin decompositions is selected by requirements of consistence with helicity notion described within the E(2) little group representation theory and with the gluon helicity Δg measured in the experiment.

Inner structure of QED and its gauge invariant angular momenta: A new viewpoint to the final resolution of the nucleon spin crisis

We discover an inner structure of QED while the gauge potential is decomposed into two orthogonal components. Based on this, the Lagrangian of the electron-photon system is expanded to a new form and by the general method of field theory, the gauge invariant spin and orbital angular momentum operators of the electron and photon are naturally obtained from Noether's theorem. Our method, which can be generalized to the non-Abelian systems to investigate the inner structure of QCD, provides a new perspective to look on the nucleon spin crisis and opens a window into a strict and systematic resolution of this long-standing problem.

Spin and Orbital Angular Momentum in Gauge Theories: Nucleon Spin Structure and Multipole Radiation Revisited

We address and solve the long-standing gauge-invariance problem of the nucleon spin structure. Explicitly gauge-invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task and opens a more promising avenue towards the understanding of the nucleon spin. Our research also justifies the traditional use of the canonical, gauge-dependent angular momentum operators of photons and electrons in the multipole-radiation analysis and labeling of atomic states and sheds much light on the related energy-momentum problem in gauge theories, especially in connection with the nucleon momentum.

Q̂operator for canonical quantum gravity

We study the properties of $\hat{Q}[\omega]$ operator on the kinematical Hilbert space ${\cal H}$ for canonical quantum gravity. Its complete spectrum with respect to the spin network basis is obtained. It turns out that $\hat{Q}[\omega]$ is diagonalized in this basis, and it is a well defined self-adjoint operator on ${\cal H}$. The same conclusions are also tenable on the SU(2) gauge invariant Hilbert space with the gauge invariant spin network basis.

Phase structure of four-dimensional gonihedric spin system

We perform Monte Carlo simulations of a gauge invariant spin system which describes random surfaces with gonihedric action in four dimensions. The Hamiltonian is a mixture of one-plaquette and additional two- and three-plaquette interaction terms with specially adjusted coupling constants. For the system with the large self-intersection coupling constant $k$ we observe the second-order phase transition at temperature $\beta_{c}\simeq 1.75$. The string tension is generated by quantum fluctuations as it was expected theoretically. This result suggests the existence of a noncritical string in four dimensions. For smaller values of $k$ the system undergoes the first order phase transition and for $k$ close to zero exhibits a smooth crossover.

Gauge invariance versus masslessness in de Sitter spaces

The connection between gauge invariance, masslessness and null cone propagation is a flat space property which does not persist even in constant curvature geometries. In particular, we show that both the gauge invariant spin 3 2 and 2 fields in anti-de Sitter space have support inside the cone, whereas where are conformally invariant, but gauge variant, models which do propagate on the light cone. The Maxwell field in constant curvature spaces of dimension other than four also does not have null cone propagation; again there is a conformally invariant model which does.

Anomalous propagation of gauge fields in conformally flat spaces

Gauge invariant spin 3 2 and 2 fields in (anti-) de Sitter space propagate inside as well as on the null cone. This is also true for antisymmetric tensor gauge fields and ( D ≠ 4) phitins. In each case, there exist gauge variant but Wey invariant models with purely null cone support.