## Fachbereich Physik

- 2D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy (1995)
- The ADM and Bondi mass for the RST model have been first discussed from Hawking and Horowitz's argument. Since there is a nonlocal term in the RST model, the RST lagrangian has to be localized so that Hawking and Horowitz's proposal can be carried out. Expressing the localized RST action in terms of the ADM formulation, the RST Hamiltonian can be derived, meanwhile keeping track of all boundary terms. Then the total boundary terms can be taken as the total energy for the RST model. Our result shows that the previous expression for the ADM and Bondi mass actually needs to be modified at quantum level, but at classical level, our mass formula can be reduced to that given by Bilal and Kogan [5] and de Alwis [6]. It has been found that there is a new contribution to the ADM and Bondi mass from the RST boundary due to the existence of the hidden dynamical field. The ADM and Bondi mass with and without the RST boundary for the static and dynamical solutions have been discussed respectively in detail, and some new properties have been found. The thunderpop of the RST model has also been encountered in our new Bondi mass formula.

- A new look at the RST model (1996)
- The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analysed completely. It is shown that from the view point of local field theories, there exists a hidden dynamical field 1 in the RST model. Thanks to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors TSigma Sigma are recovered to be true tensor quantities. Especially, the part of the stress tensors for the hidden dynamical field 1 gives the precise expression for tSigma . At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical field 1, the fact that the semi-classical static soluti on of the RST model has two independent parameters (P,M), whereas for the classical CGHS model there is only one, can be explained.

- A note on the analyticity of AdS scalar exchange graphs in the crossed channel (2000)
- We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.

- Absorption Cross Section of Scalar Field in Supergravity Background (2000)
- Abstract: It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions of these in terms of products of Bessel functions are used. Leading order terms, including the interesting logarithmic contributions, can be obtained analytically.

- AdS Box Graphs, Unitarity and Operator Product Expansions (2000)
- Abstract: We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis.

- An exactly solvable model of the Calogero type for the icosahedral group (1998)
- We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.

- Application of Instatons: Quenching Of Macroscopic Quantum Coherence And Macroscopic Fermi-Particle Configurations (1996)
- Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels E = ffl0 Gamma 24ffl cos(s + ,)ss of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of cos(s + ,)ss in disagreement with the suppression of tunneling (i.e. 4ffl = 0) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunne- ling rate ( 24fflss ) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.

- Aspects of the conformal operator product expansion in AdS/CFT correspondence (2000)
- We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

- Batalin-Vilkovisky field-antifield quantisation of fluctuations around classical field configurations (1996)
- The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collec- tive coordinate method to soliton quantisation. In field theories with soliton solutions, the Gaussian fluctuation operator has zero modes due to the breakdown of global symmetries of the Lagrangian in the soliton solutions. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to these zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center- of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) oe-model.^L