Space-times produced by a time-dependent scalar field

Models of Lorentz/diffeomorphism violation frequently make use of a time-dependent scalar field. We investigate space-times produced by such a field.Comment: Presented at PASCOS Meeting 200

Size of dot product sets determined by pairs of subsets of vector spaces over finite fields

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space F_q^d over a finite field F_q with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and |E||F|\geq C q^d for some large C>1, then |\Pi(E,F)|\geq c q for some 0<c<1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.Comment: 11 page

Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics

Extending previous work on 2 -- and 3 -- point functions, we study the 4 -- point function and its conformal block structure in conformal quantum mechanics CFT$_1$, which realizes the SO(2,1) symmetry group. Conformal covariance is preserved even though the operators with which we work need not be primary and the states are not conformally invariant. We find that only one conformal block contributes to the four-point function. We describe some further properties of the states that we use and we construct dynamical evolution generated by the compact generator of SO(2.1).Comment: Formula for 4-point function is corrected and generalize

Persistence of zero modes in a gauged Dirac model for bilayer graphene

A recently constructed model for low lying excitations in bilayer graphene exhibits mid-gap, zero energy modes in its Dirac-like spectrum, when a scalar order parameter takes a vortex profile. We show that these modes persist when the dynamics is extended by a gauge field interaction, which also renders finite the vortex energy. The effect of the gauge field on the zero energy wave function is to shift the phase of the (damped) oscillatory component of the wave function in the absence of the gauge field.Comment: 7 pages, no figure