Real Gauge Fields Research Articles

Special topic on synthetic gauge field photonics

Gauge fields are a fundamental concept in physics that describes the basic interactions between charged particles. Naturally, all neutral particles are decoupled from real gauge fields. Nevertheless, if we properly design a physical system, we can generate synthetic gauge fields that would govern the effective dynamics of the chargeless particles, such photons. In this way, synthetic gauge fields enable uncharged particles to behave as if affected by external fields. For example, a photon propagating in an elaborately designed photonic lattice will flow in a similar fashion as an electron in a magnetic flux due to the synthetic gauge fields generated by such lattice. Consequently, synthetic gauge fields allow us to endow photonic systems with a wide range of exciting features that are naturally not expected for them.

Octonion Quantum Chromodynamics

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann \lambda matrices of SU(3)symmetry and octonion basis elements. Consequently, the quantum chromo dynamics (QCD) has been reformulated and it is shown that the theory of strong interactions could be explained better in terms of non-associative octonion algebra. Further, the octonion automorphism group SU(3) has been suitably handled with split basis of octonion algebra showing that the SU(3)_{C}gauge theory of colored quarks carries two real gauge fields which are responsible for the existence of two gauge potentials respectively associated with electric charge and magnetic monopole and supports well the idea that the colored quarks are dyons.

Nonlinear self-duality in even dimensions

We show that the Born–Infeld theory with n complex abelian gauge fields written in an auxiliary field formulation has a U(n,n) duality group. We conjecture the form of the Lagrangian obtained by eliminating the auxiliary fields and then introduce a new reality structure leading to a Born–Infeld theory with n real gauge fields and an Sp(2n,R) duality symmetry. The real and complex constructions are extended to arbitrary even dimensions. The maximal noncompact duality group is U(n,n) for complex fields. For real fields the duality group is Sp(2n,R) if half of the dimension of space-time is even and O(n,n) if it is odd. We also discuss duality under the maximal compact subgroup, which is the self-duality group of the theory obtained by fixing the expectation value of a scalar field. Supersymmetric versions of self-dual theories in four dimensions are also discussed.

Coherent State Transforms for Spaces of Connections

The Segal–Bargmann transform plays an important role in quantum theories of linear fields. Recently, Hall obtained a non-linear analog of this transform for quantum mechanics on Lie groups. Given a compact, connected Lie groupGwith its normalized Haar measureμH, the Hall transform is an isometric isomorphism fromL2(G, μH) toH(GC)∩L2(GC, ν), whereGCthe complexification ofG,H(GC) the space of holomorphic functions onGC, andνan appropriate heat-kernel measure onGC. We extend the Hall transform to the infinite dimensional context of non-Abelian gauge theories by replacing the Lie groupGby (a certain extension of ) the spaceA/Gof connections modulo gauge transformations. The resulting “coherent state transform” provides a holomorphic representation of the holonomyC* algebra of real gauge fields. This representation is expected to play a key role in a non-perturbative, canonical approach to quantum gravity in 4 dimensions.

Meissner effect in scalar QED with magnetic moment interactions.

We examine a model which describes the interactions of charged magnetic scalar particles with real gauge fields in 2+1 dimensions. At zero temperature and finite density, in the nonrelativistic mean field limit, the scalar fields have fractional statistics, and the theory contains the Meissner effect. In this limit, our model is effectively a reparametrization of the model that contains a Chern-Simons term for a statistical gauge field and couples the scalar field to the statistical gauge field and a real, dynamical gauge field. At high temperature, our model has a phase transition to the state where magnetic fields penetrate the system.

METRIC FROM NONMETRIC ACTION OF GRAVITY

The action of general relativity proposed by Capovilla, Jacobson and Dell is written in terms of SO(3) gauge fields and gives Ashtekar's constraints for Einstein gravity. However, it does not depend on the spacetime metric nor its signature explicitly. We discuss how the spacetime metric is introduced from algebraic relations of the constraints and the form of the Hamiltonian by focusing our attention on the signature factor. The system describes both Euclidean and Lorentzian metrics depending on reality assignments of the gauge connections. That is, Euclidean metrics arise from the real gauge fields. On the other hand, self-duality of the gauge fields, which is well known in the Ashtekar formalism, is derived in this theory from the consistency condition of the Lorentzian metric. We also show that the metric so determined is equivalent to that given by Urbantke, which is usually accepted as a definition of the metric for this system.

Non-self-dual static gauge fields

We exhibit exact non-self-dual static solutions to the SU(2) Yang-Mills field equations by solving the equation ${\ensuremath{\nabla}}^{2}V+\ensuremath{\lambda}{V}^{3}=0$ using cylindrical and spherical coordinates. The resulting gauge fields are complex and have singularities. For the cylindrically symmetric solution, we convert it into a real gauge field coupled to the Higgs field in the limit in which the self-interaction potential of the Higgs field vanishes.