Strongly-coupled Quantum Research Articles

BLACK HOLE THERMODYNAMICS FROM CALCULATIONS IN STRONGLY COUPLED GAUGE THEORY

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in the 't Hooft large-N limit. The entropy of the quantum mechanics calculated using this approximation agrees well with the Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. Our approximation scheme provides a model for the density matrix which describes a black hole in the strongly-coupled quantum mechanics.

Critical exponents from seven-loop strong-couplingφ4theory in three dimensions

Using strong-coupling quantum field theory we calculate highly accurate critical exponents nu, eta from new seven-loop expansions in three dimensions. Our theoretical value for the critical exponent alpha of the specific heat near the lambda-point of superfluid helium is alpha =-0.01294+-0.00060, in excellent agreement with the space shuttle experimental value alpha =-0.01285+-0.00038.

Towards a strong coupling Liouville gravity

The possibility of strong coupling quantum Liouville garvity is investigated via infinite dimensional representations of U q s l(2, C) with q at a root of unity. It is explicitly shown that the vertex operator in this model can be written by a tensor product of a vertex operator of the classical Liouville theory and that of weak coupling quantum Liouville theory. Some discussions about the strong coupling Liouville gravity within this formulation are given.

Dyson-Schwinger equations and their application to hadronic physics

We review the current status of nonperturbative studies of gauge field theory using the Dyson-Schwinger equation formalism and its application to hadronic physics. We begin with an introduction to the formalism and a discussion of renormalisation in this approach. We then review the current status of studies of Abelian gauge theories [e.g., strong coupling quantum electrodynamics] before turning our attention to the non-Abelian gauge theory of the strong interaction, quantum chromodynamics. We discuss confinement, dynamical chiral symmetry breaking and the application and contribution of these techniques to our understanding of the strong interactions.

CRITICAL LINE AND BETHE-SALPETER EQUATION IN STRONG-COUPLING QED WITH FOUR-FERMION INTERACTIONS

On the basis of Bethe-Salpeter equations for electron-positron bound states in strong-coupling quantum electrodynamics with additional four-fermion interactions, the formula for the critical line dividing the chiral-symmetry-breaking phase from the symmetric phase is derived. The beta functions near the critical line are calculated explicitly and the phase structure is discussed based on these beta functions.

Strong-coupling quantum gravity. III. Quasiclassical approximation.

The ultralocal representation of gravity is used to obtain a quasiclassical approximation for the evolution of wave functionals towards the initial singularity. The whole dynamical content of this process is encoded in the successive asymptotic scatterings of Kasner wave functions by the gravitational potential term V = gR. It is indicated how this can be used to prepare the state (density operator) of the gravitational field in the immediate neighborhood of the singularity.

Strong-coupling quantum gravity. II. Solution without gauge fixing

The quantization of a strong-coupling limit of general relativity begun in a previous paper is continued. The theory is quantized without fixing a gauge since in this form the problem of properly taking into account the gauge degrees of freedom can be directly attacked in the perturbation theory. The formalism of the scattering theory on R\ifmmode\times\else\texttimes\fi{}SL(3,R)/SO(3) is developed with strong use made of analysis on that space.

Strong-coupling quantum gravity. I. Solution in a particular gauge

The strong-coupling limit of general relativity is quantized in a fixed gauge. An exact solution to the quantum field theory is given (it does not require any artifice such as a lattice), and the dynamical properties of the theory are discussed. The configuration space is closely related to the symmetric space SL(3,R)/SO(3), and this connection is exploited.

Variational Approach to Strong-Coupling Quantum Chromodynamics

We consider a superposition of string configurations as a meson trial wave function in quantum chromodynamics and regard its amplitude as a variational parameter. By minimizing the meson energy we obtain a Schr\"odinger equation and an effective Hamiltonian for the amplitude.

A classical statistical theory for chemical reactions

A trajectory approach is used to derive cross section expressions for the reactive and dissociative products of an A + BC collision in the statistical approximation. The formalism is sufficiently general to accommodate any definition of the strong coupling region. The theory is shown to satisfy time reversal symmetry. The role of canonical variables in statistical theories and the nature of the statistical approximation on a trajectory level are clarified. Problems of implementation are discussed for a variety of strong coupling regions and quantum statistical theories are reviewed in relation to the present classical formalism.

Strong-coupling field theories. II. Fermions and gauge fields on a lattice

This paper (the second in a series) reports our recent progress in the study of strong-coupling quantum field theories on a lattice. In particular we study theories involving fermions and gauge fields and pay special attention to the peculiar problems encountered when one formulates theories of fermions on a lattice. It is unique to our approach that we preserve local chiral symmetry and at the same time correctly count the number of fermionic states. We demonstrate how our formalism works with the lattice Thirring and Schwinger models, whose continuum limits are solvable in one space and one time dimension. We show in the strong-coupling limit that these theories are equivalent to a Heisenberg antiferromagnetic chain. We also discuss briefly some general features of non-Abelian gauge theory of quarks and gluons in three space and one time dimension. The most interesting results we have to report at this stage are as follows: (i) The only ''gauge-invariant states'' which remain at low mass in the limit of very strong gauge coupling have the quantum number of physical hadrons. (ii) The resulting ''effective strong-coupling'' theory preserves the full chiral symmetry of the exact theory (SU(3) x SU(3) if we introduce three flavors ofmore » quarks each with three colors) and describes a theory of ''massless bare hadrons'' interacting with one another through a quark interchange mechanism of finite strength. (AIP)« less