From first principles, I present a concrete realization of Carlip's idea on the black hole entropy from the conformal field theory on the horizon in any dimension. New formulation is free of inconsistencies encountered in Carlip's. By considering a correct gravity action, whose variational principle is well defined at the horizon, I derive a correct classical Virasoro generator for the surface deformations at the horizon through the canonical method. The existence of the classical Virasoro algebra is crucial in obtaining an operator Virasoro algebra, through canonical quantization, which produce the right central charge and conformal weight ∼ A + /hG for the semiclassical black hole entropy. The coefficient of proportionality depends on the choice of ground state, which has to be put in by hand to obtain the correct numerical factor 1/4 of the Bekenstein-Hawking (BH) entropy. The appropriate ground state is different for the rotating and the non-rotating black holes but otherwise it has a universality for a wide variety of black holes. As a byproduct of my results, I am led to conjecture that non-commutativity of taking the limit to go to the horizon and computing variation is proportional to the Hamiltonian and momentum constraints. It is shown that almost all the known uncharged black hole solutions satisfy the conditions for the universal entropy formula.

Recently, the BTZ black hole in the presence of the gravitational Chern-Simons term has been studied and it is found that the usual thermodynamic quantities, like as the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like as the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner-horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such as the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative term of gravitational Chern-Simons. This provides a non-trivial check of the AdS/CFT-correspondence, in the presence of higher-derivative terms in the gravity action.

I consider the classical Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary within the Dirac's canonical method and Noether procedure. It is shown that the usual (bulk) Gauss law constraint becomes a second-class constraint because of the boundary effect. From this fact, the Dirac bracket can be constructed explicitly without introducing additional gauge conditions and the classical Kac-Moody and Virasoro algebras are obtained within the usual Dirac method. The equivalence to the symplectic reduction method is presented and the connection to the Bañados's work is clarified. It is also considered the generalization to the Yang-Mills-Chern-Simons theory where the diffeomorphism symmetry is broken by the (three-dimensional) Yang-Mills term. In this case, the same Kac-Moody algebras are obtained although the two theories are sharply different in the canonical structures. The both models realize the holography principle explicitly and the pure CS theory reveals the correspondence of the Chern-Simons theory with boundary/conformal field theory, which is more fundamental and generalizes the conjectured anti-de Sitter/conformal field theory correspondence.Recently, there has been vast interest on the role of the space boundary in diverse areas of physics [1 -3]. Though the complete understanding of the boundary physics has not been attained yet, this boundary theory opened new rich areas both in physics and mathematics. One of the interesting areas is what comes from the existence of the central terms in the Kac-Moody algebra and Virasoro algebra even at "classical" level. These unusual classical algebras were found first in the asymptotic isometry group SO(2, 2) of the three-dimensional anti-de Sitter space (AdS 2+1 ) more than 10 years ago [4]. It is only in recent times that this algebra was applied to a practical physical problem of the statistical entropy calculation for BT Z black hole [5] by Strominger, which might provide important clues for understanding the mystery of black holes [6].On the other hand, recently there was also an interesting report on the similar "classical" central terms in the Kac-Moody and Virasoro algebras in the Chern-Simons (CS) theory [7] with boundary [1,8] using the Regge-Teitelboim's canonical method [4,9] by Bañados [10]. However, in this work he considered several hypothetical procedures which make it difficult to understand the work by the usual and familiar field theory methods. Motivated by this problem, the well-known symplectic reduction method [11] was considered more recently [12] and the Bañados's Kac-Moody and Virasoro algebras were rigorously derived with the help of the Noether procedure for constructing the conserved charges [13]. Then, following the equivalence of the CS theory to the (2+1)-dimensional gravity theory with a cosmological constant [14,15], it was straightforward to apply the Bañados's algebras to the BTZ black hole (negative cosmological constant) entropy [16] and Kerr-de Sitter space (positive cosmological constant) entropy [17] a...

The BRST quantization of the Abelian Proca model is performed using the BatalinFradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is more simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev-Jackiw formalisms.Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the Stückelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.