http://cds.cern.ch/record/413720/files/CM-P00060268.pdf

A planar diagram theory for strong interactions

This paper presents the results of a functional-integral approach to the dynamics of a two-state system coupled to a dissipative environment. It is primarily an extended account of results obtained over the last four years by the authors; while they try to provide some background for orientation, it is emphatically not intended as a comprehensive review of the literature on the subject. Its contents include (1) an exact and general prescription for the reduction, under appropriate circumstances, of the problem of a system tunneling between two wells in the presence of a dissipative environment to the "spin-boson" problem; (2) the derivation of an exact formula for the dynamics of the latter problem; (3) the demonstration that there exists a simple approximation to this exact formula which is controlled, in the sense that we can put explicit bounds on the errors incurred in it, and that for almost all regions of the parameter space these errors are either very small in the limit of interest to us (the "slow-tunneling" limit) or can themselves be evaluated with satisfactory accuracy; (4) use of these results to obtain quantitative expressions for the dynamics of the system as a function of the spectral density $J(\ensuremath{\omega})$ of its coupling to the environment. If $J(\ensuremath{\omega})$ behaves as ${\ensuremath{\omega}}^{s}$ for frequencies of the order of the tunneling frequency or smaller, the authors find for the "unbiased" case the following results: For $sl1$ the system is localized at zero temperature, and at finite $T$ relaxes incoherently at a rate proportional to $\mathrm{exp}\ensuremath{-}{(\frac{{T}_{0}}{T})}^{1\ensuremath{-}s}$. For $sg2$ it undergoes underdamped coherent oscillations for all relevant temperatures, while for $1lsl2$ there is a crossover from coherent oscillation to overdamped relaxation as $T$ increases. Exact expressions for the oscillation and/or relaxation rates are presented in all these cases. For the "ohmic" case, $s=1$, the qualitative nature of the behavior depends critically on the dimensionless coupling strength $\ensuremath{\alpha}$ as well as the temperature $T$: over most of the ($\ensuremath{\alpha}$,$T$) plane (including the whole region $\ensuremath{\alpha}g1$) the behavior is an incoherent relaxation at a rate proportional to ${T}^{2\ensuremath{\alpha}\ensuremath{-}1}$, but for low $T$ and $0l\ensuremath{\alpha}l\frac{1}{2}$ the authors predict a combination of damped coherent oscillation and incoherent background which appears to disagree with the results of all previous approximations. The case of finite bias is also discussed.

/pdf/dynamics-of-the-dissipative-two-state-system-4kzh83zg4g.pdf

Dynamics of the dissipative two-state system

https://cds.cern.ch/record/416338/files/CM-P00060463.pdf

Magnetic monopoles in unified gauge theories

https://www.physics.rutgers.edu/~friedan/papers/Nucl_Phys_B271_93_1986.pdf

Conformal invariance, supersymmetry and string theory

Gravitation, Gauge Theories and Differential Geometry

The Quantum Collective Field Method and Its Application to the Planar Limit

Field theory interpretation of supergauges in dual models

Quantum Theory of Many Variable Systems and Fields

The method of collective coordinates developed in the study of strong-coupling theory is used for the quantization of the kink solution of a two-dimensional nonlinear field theory. The position of the kink is treated as a collective coordinate, which represents the position of a particle. It is separated from the rest of the coordinates, which represent the internal degrees of freedom of an extended particle. Two similar but different methods are presented; the one is nonrelativistic and suited for the weak-coupling limit, while the other is relativistic.

Extended Particles in Quantum Field Theories

The quantum mechanics of solitary-wave classical solutions of nonlinear wave equations is discussed in detail for the kink solution of two-dimensional φ4 field theory. The formalism provides a natural interpretation of an extended particle, the soliton, for the classical kink. The perturbation theory around the extended particle is developed and used to calculate the radiative corrections for the mass of soliton up to one loop. The mass renormalization is discussed in detail to show that the mass counterterm to the nonsoliton sector also does the job for the present case, i.e. one-soliton sector. Although our formalism is not manifestly Lorentz-covariant, the Lorentz covariance is shown explicitly by calculating the soliton energy for a fixed momentum. Finally, the paper also contains the perturbation calculation of matrix element of φ fields between one-soliton states.

Bunji Sakita

Papers

The Quantum Collective Field Method and Its Application to the Planar Limit

Field theory interpretation of supergauges in dual models

Quantum Theory of Many Variable Systems and Fields

Extended Particles in Quantum Field Theories

Perturbation expansion around extended-particle states in quantum field theory