Energy Momentum Tensor in Conformal Field Theories Near a Boundary

The requirements of conformal invariance for the two point function of the energy momentum tensor in the neighbourhood of a plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary invariant. It is shown that the general solution may contain an arbitrary function of a single conformally invariant variable $v$, except in dimension 2. The functional dependence on $v$ is determined for free scalar and fermion fields in arbitrary dimension $d$ and also to leading order in the \vep expansion about $d=4$ for the non Gaussian fixed point in $\phi^4$ theory. The two point correlation function of the energy momentum tensor and a scalar field is also shown to have a unique expression in terms of $v$ and the overall coefficient is determined by the operator product expansion. The energy momentum tensor on a general curved manifold is further discussed by considering variations of the metric. In the presence of a boundary this procedure naturally defines extra boundary operators. By considering diffeomorphisms these are related to components of the energy momentum tensor on the boundary. The implications of Weyl invariance in this framework are also derived.Comment: 22 pages, TeX with epsf.tex, DAMTP/93-1. (original uuencoded file was corrupted enroute - resubmitted version has uuencoded figures pasted to the ended of the Plain TeX file

Design Considerations for Low Power Internet Protocols

Over the past 10 years, low-power wireless networks have transitioned to supporting IPv6 connectivity through 6LoWPAN, a set of standards which specify how to aggressively compress IPv6 packets over low-power wireless links such as 802.15.4. We find that different low-power IPv6 stacks are unable to communicate using 6LoWPAN, and therefore IP, due to design tradeoffs between code size and energy efficiency. We argue that applying traditional protocol design principles to low-power networks is responsible for these failures, in part because receivers must accommodate a wide range of senders. Based on these findings, we propose three design principles for Internet protocols on low-power networks. These principles are based around the importance of providing flexible tradeoffs between code size and energy efficiency. We apply these principles to 6LoWPAN and show that the resulting design of the protocol provides developers a wide range of tradeoff points while allowing implementations with different choices to seamlessly communicate

Conformal Field Theories Near a Boundary in General Dimensions

The implications of restricted conformal invariance under conformal transformations preserving a plane boundary are discussed for general dimensions $d$. Calculations of the universal function of a conformal invariant $\xi$ which appears in the two point function of scalar operators in conformally invariant theories with a plane boundary are undertaken to first order in the \vep=4-d expansion for the the operator $\phi^2$ in $\phi^4$ theory. The form for the associated functions of $\xi$ for the two point functions for the basic field $\phi^\alpha$ and the auxiliary field $\lambda$ in the the $N\to \infty$ limit of the $O(N)$ non linear sigma model for any $d$ in the range $2<d<4$ are also rederived. These results are obtained by integrating the two point functions over planes parallel to the boundary, defining a restricted two point function which may be obtained more simply. Assuming conformal invariance this transformation can be inverted to recover the full two point function. Consistency of the results is checked by considering the limit $d\to 4$ and also by analysis of the operator product expansions for $\phi^\alpha\phi^\beta$ and $\lambda\lambda$. Using this method the form of the two point function for the energy momentum tensor in the conformal $O(N)$ model with a plane boundary is also found. General results for the sum of the contributions of all derivative operators appearing in the operator product expansion, and also in a corresponding boundary operator expansion, to the two point functions are also derived making essential use of conformal invariance.Comment: Plain TeX file, 52 pages, with 1 postscript figur

Finite VEVs from a Large Distance Vacuum Wave Functional

We show how to compute vacuum expectation values from derivative expansions of the vacuum wave functional. Such expansions appear to be valid only for slowly varying fields, but by exploiting analyticity in a complex scale parameter we can reconstruct the contribution from rapidly varying fields.Comment: 39 pages, 16 figures, LaTeX2e using package graphic

Heat kernel asymptotics: more special case calculations

Special case calculations are presented, which can be used to put restrictions on the general form of heat kernel coefficients for transmittal boundary conditions and for generalized bag boundary conditions.Comment: Invited talk at International Meeting on Quantum Gravity and Spectral Geometry, Naples, Italy, 2-6 July 2001. 9 pages, LaTe

The Schrodinger Wave Functional and Vacuum State in Curved Spacetime II. Boundaries and Foliations

In a recent paper, general solutions for the vacuum wave functionals in the Schrodinger picture were given for a variety of classes of curved spacetimes. Here, we describe a number of simple examples which illustrate how the presence of spacetime boundaries influences the vacuum wave functional and how physical quantities are independent of the choice of spacetime foliation used in the Schrodinger approach despite the foliation dependence of the wave functionals themselves.Comment: 26 pages, 4 figures, LATE