WZW action in odd dimensional gauge theories

It is shown that Wess-Zumino-Witten (WZW) type actions can be constructed in odd dimensional space-times using Wilson line or Wilson loop. WZW action constructed using Wilson line gives anomalous gauge variations and the WZW action constructed using Wilson loop gives anomalous chiral transformation. We show that pure gauge theory including Yang-Mills action, Chern-Simons action and the WZW action can be defined in odd dimensional space-times with even dimensional boundaries. Examples in 3D and 5D are given. We emphasize that this offers a way to generalize gauge theory in odd dimensions. The WZW action constructed using Wilson line can not be considered as action localized on boundary space-times since it can give anomalous gauge transformations on separated boundaries. We try to show that such WZW action can be obtained in the effective theory when making localized chiral fermions decouple.Comment: 19 pages, text shortened, reference added. Version to appear in PR

On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations

Operator cutoff regularization based on the original Schwinger's proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual momentum cutoff prescription yet preserves gauge symmetry even in the presence of the cutoff scales. Similarity between the operator cutoff regularization and the method of higher (covariant) derivatives is also observed. The invariant nature of the operator cutoff regularization makes it a promising tool for exploring the renormalization group flow of gauge theories in the spirit of Wilson-Kadanoff blocking transformation.Comment: 28 pages in plain TeX, no figures. revised and expande

Coarse-Graining and Renormalization Group in the Einstein Universe

The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes is constructed in a nonflat background and explicitly computed within the loop-expansion approximation for an Einstein universe. The curvature turns out to be dominant in setting the crossover scale from a double-peak and a symmetric distribution of the block variables. The evolution of all the coupling constants generated by the blocking procedure is examined: the renormalized trajectories agree with the standard perturbative results for the relevant vertices near the ultraviolet fixed point, but new effective interactions between gravity and matter are present. The flow of the conformal coupling constant is therefore analyzed in the improved scheme and the infrared fixed point is reached for arbitrary values of the renormalized parameters.Comment: 18 pages, REVTex, two uuencoded figures. (to appear in Phys. Rev. D15, July) Transmission errors have been correcte

Hole burning in a nanomechanical resonator coupled to a Cooper pair box

We propose a scheme to create holes in the statistical distribution of excitations of a nanomechanical resonator. It employs a controllable coupling between this system and a Cooper pair box. The success probability and the fidelity are calculated and compared with those obtained in the atom-field system via distinct schemes. As an application we show how to use the hole-burning scheme to prepare (low excited) Fock states.Comment: 7 pages, 10 figure

Flow Equations for U_k and Z_k

By considering the gradient expansion for the wilsonian effective action S_k of a single component scalar field theory truncated to the first two terms, the potential U_k and the kinetic term Z_k, I show that the recent claim that different expansion of the fluctuation determinant give rise to different renormalization group equations for Z_k is incorrect. The correct procedure to derive this equation is presented and the set of coupled differential equations for U_k and Z_k is definitely established.Comment: 5 page

Decomposition of stochastic flows with automorphism of subbundles component

We show that given a $G$-structure $P$ on a differentiable manifold $M$, if the group $G(M)$ of automorphisms of $P$ is big enough, then there exists the quotient of an stochastic flows $phi_t$ by $G(M)$, in the sense that $\phi_t = \xi_t \circ \rho_t$ where $\xi_t \in G(M)$, the remainder $\rho_t$ has derivative which is vertical but transversal to the fibre of $P$. This geometrical context generalizes previous results where $M$ is a Riemannian manifold and $\phi_t$ is decomposed with an isometric component, see Liao \cite{Liao1} and Ruffino \cite{Ruffino}, which in our context corresponds to the particular case of an SO(n)-structure on $M$.Comment: To appear in Stochastics and Dynamics, 201

On the Convergence of the Expansion of Renormalization Group Flow Equation

We compare and discuss the dependence of a polynomial truncation of the effective potential used to solve exact renormalization group flow equation for a model with fermionic interaction (linear sigma model) with a grid solution. The sensitivity of the results on the underlying cutoff function is discussed. We explore the validity of the expansion method for second and first-order phase transitions.Comment: 12 pages with 10 EPS figures included; revised versio

Renormalization Group Approach to Field Theory at Finite Temperature

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda phi^4 theory are performed in d=4 Euclidean space for both low and high temperature limits. We generate a set of coupled equations for the mass parameter and the coupling constant from the renormalization group flow equation. Dimensional reduction and symmetry restoration are also explored with our improved approach.Comment: 29 pages, can include figures in the body of the text using epsf.st