Nonperturbative weak-coupling analysis of the quantum Liouville field theory

Nonperturbative weak-coupling analysis of the quantum Liouville field theory

ABSTRACTS and Department 02139. of OF PAPERS Physics, TO APPEAR Massachusetts Institute IN FUTURE of Technology, 491 ISSUES Cambridge, Massa...

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ABSTRACTS and Department 02139.

of

OF PAPERS

Physics,

TO APPEAR

Massachusetts

Institute

IN FUTURE of Technology,

491

ISSUES Cambridge,

Massachusetts

Intermediate energy nuclear photoabsorption and Compton scattering within the d-hole approach are studied. The same d-nucleus dynamics used to describe a variety of pion-induced reactions are employed. A dynamical model for the photon-nucleon amplitude is constructed, including both resonantMedium corrections to the full channel and nonresonant backgrounds in addition to d-excitation. amplitude are included for nuclear scattering. A doorway state expansion allows quantitative discussion of the role of various contributions to the d-hole Hamiltonian, thereby clarifying the level of sensitivity to the structure of the d spreading potential. The reactive content of the total cross section is discussed. The results are compared with available photoabsorption data for 4He. 12C, and I60 and present results for the d contribution to the electron scattering transverse response function. for coherent rr” photoproduction, and for nuclear elastic Compton scattering. Photoabsorption strength is spread over a larger energy range by the d dynamics, in agreement with the data, but is centered at too high an energy. The helicity flip Compton cross section is especially sensitive to the d-nucleus interaction, such as the spin-orbit potential strength.

Nonperturbative

Weak-Coupling

CURTRIGHT.

Florida

G. GHANDOUR.

Analysis AND

of the Quantum

C. THORN,

Physics

Liouville

Department,

Field

Theory.

University

E. BRAATEN.

of Florida,

T.

Gainesville.

3261 I.

Two independent weak-coupling expansions are developed for the Liouville quantum field theory on a circle. In the first, the coupling of the non-zero modes is treated as a perturbation on the exact solution to the zero-mode problem (quantum mechanics with an exponential potential). The second approach is a weak-coupling approximation to an explicit operator solution which expresses various Liouville operators as functions of a free massless field using a Backlund transformation. It is shown that the free state space associated with this latter solution must be restricted to the sector which is odd with respect to a type of “parity.” Various matrix elements are computed to order g” using both approaches, yielding identical results.

Evaluation

of Ensemble

VERBAARSCHOT,

Heidelberg,

H.

Federal

Averages A.

for

Simple

WEIDENM~LLER,

Republic

AND

Hamiltonians M.

ZIRNBAUER.

Perturbed

by a GOE

Max-Planck-Institut

Interaction. fiir

J.

Kernphysik.

of Germany.

Using an expansion in powers of N-l, where N is the dimension of the Hamiltonian matrix, ensemble averages of the resolvent, of products involving several resolvents, and of the moments of the Hamiltonian H, + l.V are evaluated. Here, H, is arbitrary but fixed, and V is a GOE ensemble. The nature of the N-’ expansion is also discussed.