Gauge-invariant Mass Terms and Wave Functions

We outline a method of relating the quantum effective action and the ground state wave function of a field theory. This method, along with a gauge-invariant mass term and the previously obtained vacuum wave function, is used to arrive at the leading terms of the 3d-covariant quantum effective action for the Yang-Mills theory in three (or 2+1) dimensions. Some features of this effective action are also discussed.Comment: 10 pages, Invited talk at the International Workshop on QCD Green's functions, Confinement and Phenomenology, QCD-TNT II, September 201

Polarization-selective branching of stop gaps in three-dimensional photonic crystals

We study the direction- and wavelength-dependent polarization anisotropy in light scattering at the air-photonic crystal interface as a function of angle of incidence for TE and TM polarized light. This is done using optical reflectivity measurements at high-symmetry points in the Brillouin zone of a three-dimensional photonic crystal with fcc symmetry. Polarized reflectivity measurements indicate the presence of stop gap branching for TE polarization, which is absent for TM polarization till the Brewster angle at K point. In contrast, stop gap branching is present for both TE and TM polarizations at W point due to the intricate mixing of crystal planes. This characteristic behavior signifies the inevitable role of energy exchange in the stop gap branching. The measured polarization anisotropy shows a prominent shift in the Brewster angle for on-resonance wavelength as compared to the off-resonance along both K and W points, and that, in accordance with theory. Our results have implications in polarization-induced light scattering in sub-wavelength photonic structures like plasmonic crystals, and meta-materials.Comment: 15 pages, 7 figure

Gauge invariance and mass gap in (2+1)-dimensional Yang-Mills theory

In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.Comment: 10 pages, Plain TeX, talk presented at the Workshop on Low Dimensional Field Theories, Telluride, August 199

A Note on MHV Amplitudes for Gravitons

We show how the maximally helicity violating (MHV) scattering amplitudes for gravitons can be related to current correlators and vertex operators in twistor space. This is similar to what happens in Yang-Mills theory and raises the possibility of a direct twistor-string-like construction for ${\cal N}=8$ supergravity.Comment: 14 pages, LaTe