Quantum Master Equation for QED in Exact Renormalization Group

Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the abelian nature of the gauge symmetry is lost, breaking the nilpotency of the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action.Comment: 15 pages, no figur

Realization of symmetry in the ERG approach to quantum field theory

We review the use of the exact renormalization group for realization of symmetry in renormalizable field theories. The review consists of three parts. In part I (sects. 2,3,4), we start with the perturbative construction of a renormalizable field theory as a solution of the exact renormalization group (ERG) differential equation. We show how to characterize renormalizability by an appropriate asymptotic behavior of the solution for a large momentum cutoff. Renormalized parameters are introduced to control the asymptotic behavior. In part II (sects. 5--9), we introduce two formalisms to incorporate symmetry: one by imposing the Ward-Takahashi identity, and another by imposing the generalized Ward-Takahashi identity via sources that generate symmetry transformations. We apply the two formalisms to concrete models such as QED, YM theories, and the Wess-Zumino model in four dimensions, and the O(N) non-linear sigma model in two dimensions. We end this part with calculations of the abelian axial and chiral anomalies. In part III (sects. 10,11), we overview the Batalin-Vilkovisky formalism adapted to the Wilson action of a bare theory with a UV cutoff. We provide a few appendices to give details and extensions that can be omitted for the understanding of the main text. The last appendix is a quick summary for the reader's convenience.Comment: 166 pages, 27 figure

Anomalies in the ERG Approach

The antifield formalism adapted in the exact renormalization group is found to be useful for describing a system with some symmetry, especially the gauge symmetry. In the formalism, the vanishing of the quantum master operator implies the presence of a symmetry. The QM operator satisfies a simple algebraic relation that will be shown to be related to the Wess-Zumino condition for anomalies. We also explain how an anomaly contributes to the QM operator.Comment: 13 page

Ward-Takahashi identity for Yang-Mills theory in the Exact Renormalization Group

We give a functional derivation of the Ward-Takahashi identity for Yang-Mills theory in the framework of the exact renormalization group. The identity realizes non-abelian gauge symmetry nontrivially despite the presence of a momentum cutoff. The cutoff deforms the gauge transformation by introducing composite operators. In our functional method, which is an extension of the method used in our previous work on QED, these composite operators are expressed in terms of the Wilson action that depends on both a UV cutoff and an IR cutoff.Comment: 12 page

Hydrogen generation from greenhouse gas by discharge plasma

CH4 is decomposed by a low-pressure DC glow discharge, and partial pressures of H2 and other byproducts are measured by the mass spectrometry. The decomposition rate of CH4 and H2 conversion rate are calculated from the partial pressure, and the effects of mixed gases with CH4 on the decomposition characteristics of CH4 and H2 conversion rate are investigated. It is found that CH4 is completely decomposed in the DC glow discharge, and that 80%, 75% and 70% of hydrogen atoms contained in CH4 are converted into H2 in CH4-Ar mixture, pure CH4 and CH4-CO2 mixture, respectively. It is also found that CO, which can be used as fuel, is produced in the DC glow discharge by the decomposition of CO2 in CH4-CO2 mixture.特集 : 「資源、新エネルギー、環境、防災研究国際セミナー

Decomposition Characteristics of Benzene, Toluene and Xylene in an Atmospheric Pressure DC Corona Discharge II. Characteristics of Deposited By-products and Decomposition Process

Gaseous by-products and deposited material obtained from the decomposition of benzene, toluene and xylene in an atmospheric pressure DC corona discharge were minutely investigated by gas chromatograph mass spectrometry and infrared absorption spectroscopy, and the decomposition processes of benzene, toluene and xylene were estimated. It was found that carbon dioxide (CO2), carbon monoxide (CO), formic acid (HCOOH) and formic anhydride ((CHO)2) were the major gaseous by-products from benzene, toluene and xylene, while acetic formic anhydride (CH3COOCHO) and acetic acid (CH3COOH) were the major by-products from toluene and xylene. Benzaldehyde (C6H5CHO) and methyl benzaldehyde (CH3CH4CHO) were produced from toluene and xylene, respectively. It was hypothesized that the decomposition of benzene, toluene, and xylene was initiated by the production of phenyl radicals, phenyl and benzyl radicals, and methyl benzyl and methyl phenyl radicals, respectively. These radicals are deposited on electrodes, wall, etc., resulting in the polymerization of aromatic rings and the substitution of function groups. Also, those radicals are decomposed and converted into by-products described above. In addition, it is probably that benzyl and methyl benzyl radicals are precursors of C6H5CHO and CH3C6H4CHO, respectively, and that C6H5CHO and CH3C6H4CHO are decomposed, contributing to by-product production and deposition. Furthermore, some intermediate by-products, produced by the cleavage of the aromatic ring in benzene, toluene and xylene decomposition and containing O=C-O, C=O, O-H, and C-H groups, may be deposit on the electrodes