Construction of an Identically Nilpotent BRS Charge in the Kato-Ogawa String Theory

In previous work, the conformal-gauge two-dimensional quantum gravity in the BRS formalism has been solved completely in terms of Wightman functions. In the present paper, this result is extended to the closed and open bosonic strings of finite length; the open-string case is nothing but the Kato-Ogawa string theory. The field-equation anomaly found previously, which means a slight violation of a field equation at the level of Wightman functions, remains existent also in the finite-string cases. By using this fact, a BRS charge nilpotent even for $D\not=26$ is explicitly constructed in the framework of the Kato-Ogawa string theory. The FP-ghost vacuum structure of the Kato-Ogawa theory is made more transparent; the appearance of half-integral ghost numbers and the artificial introduction of indefinite metric are avoided.Comment: 23 pages, LaTe

Anomaly Problem in a Simple Model Analogous to the Lightcone-Gauge Two-Dimensional Quantum Gravity

It was found in the two-dimensional quantum gravity both in the de Donder gauge and in the lightcone gauge that one of field equations breaks down at the level of the representation, though the breakdown is very little. It is shown that this anomalous behavior occurs also in a very simple model analogous to the lightcone-gauge two-dimensional quantum gravity. This model, however, can be transformed into a free field theory by a nonsingular transformation. Of course, the latter has no anomaly. The cause of the discrepancy is analyzed.Comment: 16 pages, LaTeX, overcite.st

Proof of the Gauge Independence of the Conformal Anomaly of Bosonic String in the Sense of Kraemmer and Rebhan

Kraemmer and Rebhan claimed the gauge independence of the conformal anomaly of bosonic string for various gauge fixings in the framework of the perturbation theory of two-dimensional quantum gravity. It is pointed out that their proof is wrong. The gauge independence is proved for the gauge-fixings which reduce to the linearized de Donder gauge in the flat limit of the background metric. Similar remarks are made also for the Rebhan-Kraemmer current anomaly.Comment: 14 pages, LaTeX, two stylefiles include

Perturbative or Path-Integral Approach versus Operator-Formalism Approach

In the conformal-gauge two-dimensional quantum gravity, the solution obtained by the perturbative or path-integral approach is compared with the one obtained by the operator-formalism approach. Treatments of the anomaly problem in both approaches are different. This difference is found to be essentially caused by the fact that the perturbative or path-integral approach is based on the T*-product (covariantized T-product), which generally violates field equations. Indeed, this fact induces some extra one-loop Feynman diagrams, which would not exist unless a nonzero contribution arose from a zero field. Some demerits of the path-integral approach are explicitly demonstrated.Comment: 16 pages, PTPTe

Exact Solutions to the Two-dimensional BF and Yang-Mills Theories in the Light-cone Gauge

It is shown that the BRS-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the $\widetilde{B}^2$ term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang-Mills theory is also obtained.Comment: 11 pages, LaTe

D=26 and Exact Solution to the Conformal-Gauge Two-Dimensional Quantum Gravity

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: All n-point Wightman functions are explicitly obtained. The field-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D=26 of the bosonic string, the field-equation anomaly is shown to be absent. However, this result is not equivalent to the statement that the conformal anomaly is proportional to D-26. The existence of the FP-ghost number current anomaly is seen to be an illusion.Comment: 18 pages, LaTe

Sound collection and visualization system enabled participatory and opportunistic sensing approaches

This paper presents a sound collection system to visualize environmental sounds that are collected using a crowd-sourcing approach. An analysis of physical features is generally used to analyze sound properties; however, human beings not only analyze but also emotionally connect to sounds. If we want to visualize the sounds according to the characteristics of the listener, we need to collect not only the raw sound, but also the subjective feelings associated with them. For this purpose, we developed a sound collection system using a crowdsourcing approach to collect physical sounds, their statistics, and subjective evaluations simultaneously. We then conducted a sound collection experiment using the developed system on ten participants.We collected 6,257 samples of equivalent loudness levels and their locations, and 516 samples of sounds and their locations. Subjective evaluations by the participants are also included in the data. Next, we tried to visualize the sound on a map. The loudness levels are visualized as a color map and the sounds are visualized as icons which indicate the sound type. Finally, we conducted a discrimination experiment on the sound to implement a function of automatic conversion from sounds to appropriate icons. The classifier is trained on the basis of the GMM-UBM (Gaussian Mixture Model and Universal Background Model) method. Experimental results show that the F-measure is 0.52 and the AUC is 0.79