Coherent State Variational Methods for Large N Gauge Theories: Numerical Calculations and Strong Coupling Expansions
Abstract
Coherent state techniques have proved a useful formal tool for obtaining the N = infty limit of a variety of quantum mechanical systems, in part because they allow one to explicitly construct the classical Hamiltonian and classical phase space that define the dynamics of the large N system. This construction is sufficiently concrete that it naturally suggests methods for carrying out practical calculations. We discuss two such methods, one numerical and the other a classical strong coupling expansion, for calculating the mass spectrum of pure U (infty) Hamiltonian lattice gauge theory. Both involve calculating coherent state expectation values of the quantum Hamiltonian to obtain a classical Hamiltonian as a function on the space of coherent states, and solving for the coherent state (the point in classical configuration space) that minimizes this classical Hamiltonian. Finally the frequencies of classical small oscillations about this minimum give the large N limit of the quantum mechanical excitation spectrum.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT.......125B
 Keywords:

 QUANTUM FIELD THEORY;
 Physics: Elementary Particles and High Energy