Frank Wilczek

Hawking radiation as tunneling

We present a short and direct derivation of Hawking radiation as a tunneling process, based on particles in a dynamical geometry. The imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. Because the derivation respects conservation laws, the exact spectrum is not precisely thermal. We compare and contrast the problem of spontaneous emission of charged particles from a charged conductor.

Geometric Phases in Physics

During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berrys phase’) in addition to the usual dynamical phase derived from Schrodingers equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.

Cosmology of the Invisible Axion

Abstract We identify a new cosmological problem for models which solve the strong CP puzzle with an invisible axion, unrelated to the domain wall problem. Because the axion is very weakly coupled, the energy density stored in the oscillations of the classical axion field does not dissipate rapidly; it exceeds the critical density needed to close the universe unless fa ⩽ 1012GeV, wherefa is the axion decay constant. If this bound is saturated, axions may comprise the dark matter of the universe.

Geometric and renormalized entropy in conformal field theory

Abstract In statistical physics, useful notions of entropy are defined with respect to some coarse-graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However, the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the “information problem” in black hole physics.

QCD at finite baryon density: Nucleon droplets and color superconductivity

Abstract We use a variational procedure to study finite density QCD in an approximation in which the interaction between quarks is modelled by that induced by instantons. We find that uniform states with conventional chiral symmetry breaking have negative pressure with respect to empty space at all but the lowest densities, and are therefore unstable. This is a precisely defined phenomenon which motivates the basic picture of hadrons assumed in the MIT bag model, with nucleons as droplets of chiral symmetry restored phase. At all densities high enough that the chirally symmetric phase fills space, we find that color symmetry is broken by the formation of a 〈 qq 〉 condensate of quark Cooper pairs. A plausible ordering scheme leads to a substantial gap in a Lorentz scalar channel involving quarks of two colors, and a much smaller gap in an axial vector channel involving quarks of the third color.

Color-flavor locking and chiral symmetry breaking in high density QCD

Abstract We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3) color × SU(3) L × SU(3) R symmetries are broken down to the diagonal subgroup SU(3) color+ L + R by the formation of a condensate of quark Cooper pairs. We discuss general properties that follow from this hypothesis, including the existence of gaps for quark and gluon excitations, the existence of Nambu-Goldstone bosons which are excitations of the diquark condensate, and the existence of a modified electromagnetic gauge interaction which is unbroken and which assigns integral charge to the elementary excitations. We present mean-field results for a Hamiltonian in which the interaction between quarks is modeled by that induced by single-gluon exchange. We find gaps of order 10–100 MeV for plausible values of the coupling. We discuss the effects of non-zero temperature, non-zero quark masses and instanton-induced interactions on our results.

Diquarks and exotic spectroscopy

We propose that the recently discovered Theta(+) baryon is a bound state of four quarks and an antiquark, containing two highly correlated ud pairs. If so, the theta(+) has positive parity, and it lies in an near-ideally mixed SU(3)(f) 10;(f) plus sign in circle 8(f). The Roper resonance and the P11(1710) fit naturally into this classification. We predict an isospin 3/2 multiplet of Xis (S=-2) with J(Pi)=1 / 2(+) around 1750 MeV. A search for manifestly exotic Xi(+) and Xi(--) in this mass range could provide a sharp test of our proposal. We predict that charm and bottom analogs of the Theta(+) may be stable against strong decays.

On geometric entropy

Abstract We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy. We describe two methods for calculating this entropy - a straightforward Hamiltonian approach, and a less direct but more powerful Euclidean (heat kernel) method. The entropy diverges in quantum field theory in the absence of an ultraviolet cutoff. Various related finite quantities can be extracted with further work. We briefly discuss the corresponding question in string theory.

Particle–antiparticle annihilation in diffusive motion

We study both numerically and analytically the time development of a system of particles and antiparticles moving diffusively and annihilating irreversibly. The asymptotic behavior is found to depend dramatically on whether the initial fluctuations are localized or entirely random. Physical examples of each kind are identified.

Self-interaction correction to black hole radiance

We consider the modification of the formulas for black hole radiation, due to the self-gravitation of the radiation. This is done by truncating the coupled particle-hole system to a small set of modes, that are plausibly the most significant ones, and quantizing the reduced system. In this way we find that the particles no longer move along geodesics, nor is the action along the rays zero for a massless particle. The radiation is no longer thermal, but is corrected in a definite way that we calculate. Our methods can be extended in a straightforward manner to discuss correlations in the radiation, or between incoming particles and the radiation.