Collapse of Self-Interacting Scalar Field in Anti-de Sitter Space

The gravitational collapse of a massless scalar field with a self-interaction term λφ~4 in anti-de Sitter space is investigated.We numerically investigate the effect of the self-interaction term on the critical amplitudes,forming time of apparent horizon,stable island,and energy transformation.The results show that a positiveλsuppresses the formation of black hole,while a negativeλenhances the process.We define two susceptibilities to characterize the effect of the self-interaction on the black hole formation,and find that near the critical amplitude,there exists a universal scaling relation with the critical exponentα≈0.74 for the time of black hole formation.     

Crossing of specific heat curves in some correlated fermion systems

Specific heat versus temperature curves for various pressures, or magnetic fields (or some other external control parameter) have been seen to cross at a point or in a very small range of temperatures in many correlated fermion systems. We show that this behavior is related to the possibility of existence of a quantum critical point. Vicinity to a quantum critical point in these systems leads to a crossover from quantum to classical fluctuation regime at some temperature . The temperature at which the curves cross turns out to be near this crossover temperature. We have discussed the case of the normal phase of liquid Helium three and the heavy fermion systems CeAl₃ and UBe₁₃ in detail within the spin fluctuation theory, a theory which inherently contains a low energy scale which can be identified with . When the crossover scale is a homogeneous function of these control parameters there is always crossing at a point. We also mention other theories exhibiting a low energy scale near a quantum critical point and discuss this phenomenon in those theories. Received 25 June 1999     

Interacting Singletons

There is a chance that singleton fields, that in the context of strings and membranes have been regarded as topological gauge fields that can interact only at the boundary of anti-De Sitter space, at spatial infinity, may have a more physical manifestation as constituents of massless fields in spacetime. The composite character of massless fields is expressed by field-current identities that relate ordinary massless field operators to singleton currents and stress-energy tensors. Naive versions of such identities do not make sense, but when the singletons are described in terms of dipole structures, then such constructions are at least formally possible. The new proposal includes and generalizes an early composite version of QED, and includes quantum gravity, super gravity and models of QCD. Unitarity of such theories is conjectural.     

Scaling in ordered and critical random boolean networks

Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks lie at or near a critical point in parameter space that divides "ordered" from "chaotic" attractor dynamics. We study the scaling of the average number of dynamically relevant nodes and the median number of distinct attractors in such networks. Our calculations indicate that the correct asymptotic scalings emerge only for very large systems.     

Gaupta-Bleuler triplet for massless spin-3/2 field in de Sitter space

Physicists have been interested in quantization of spinor and vector free fields in 4-dimensional de Sitter space-time,in ambient space notation.The Gupta-Bleuler formalism has been extensively applied to the quantization of gauge invariant theories.The field equation of the massless spin-3/2 fields is gauge invariant in de Sitter space.In this paper,we study the quantization of massless spin-3/2 gauge fields in de Sitter space-time by the Gupta-Bleuler formalism.This triplet carries an indecomposable representation of the de Sitter group.     

Scalar Tachyons in the de Sitter Universe

We provide a construction of a class of local and de Sitter covariant tachyonic quantum fields which exist for discrete negative values of the squared mass parameter and which have no Minkowskian counterpart. These quantum fields satisfy an anomalous non-homogeneous Klein–Gordon equation. The anomaly is a covariant field which can be used to select the physical subspace (of finite co-dimension) where the homogeneous tachyonic field equation holds in the usual form. We show that the model is local and de Sitter invariant on the physical space. Our construction also sheds new light on the massless minimally coupled field, which is a special instance of it.     

The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.     

Geometrical approach to the thermodynamical theory of phase transitions of the second kind

A geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure P and variable temperature T is proposed. Equilibrium states of a system at zero external field and fixed P and T are described by points in three-dimensional space with coordinates η, the order parameter, T, the temperature and /gf, the thermodynamic potential. These points form the so-called zero field curve in the (η, T, /gf) space. Its branch point coincides with the critical point of the system. The small parameter of the theory (the distance from the critical point along the zero-field curve) is shown to be more convenient than the small parameter of the Landau theory. It is emphasized that no explicit functional dependency of /gf on η and T is imposed.

It is shown that using (η, T, /gf) space one cannot overcome well-known difficulties of the Landau theory of phase transitions and describe non-analytical behavior of real systems in the vicinity of the critical point. This becomes possible only if one increases the dimensionality of the space, taking into account the dependency of the thermodynamic potential not only on η and T, but also on near (local) order parameters λ_i. In this case under certain conditions it is possible to describe anomalous increase of the specific heat when the temperature of the system approaches the critical point from above as well as from below the critical temperature T_c.     

Vortex dynamics and the Fulde-Ferrell-Larkin-Ovchinnikov state in a magnetic-field-induced organic superconductor

Under special conditions, a superconducting state where the order parameter oscillates in real space, the so-called FFLO state, is theoretically predicted to exist near the upper critical field, as first proposed by Fulde and Ferrell, and Larkin and Ovchinnikov. We report systematic measurements of the interlayer resistance in high magnetic fields to 45 T in the two-dimensional magnetic-field-induced organic superconductor lambda-(BETS)2FeCl4, where BETS is bis(ethylenedithio)tetraselenafulvalene. The resistance is found to show characteristic dip structures in the superconducting state. The results are consistent with pinning interactions between the vortices penetrating the insulating layers and the order parameter of the FFLO state. This gives strong evidence for an oscillating order parameter in real space.     

Dirac point degenerate with massive bands at a topological quantum critical point

The quasilinear bands in the topologically trivial skutterudite insulator CoSb(3) are studied under adiabatic, symmetry-conserving displacement of the Sb sublattice. In this cubic, time-reversal and inversion symmetric system, a transition from trivial insulator to topological point Fermi surface system occurs through a critical point in which massless (Dirac) bands appear, and moreover are degenerate with massive bands. Spin-orbit coupling, while small due to the type of band character, coupled with tetragonal strain opens the gap required to give the topological insulator. The mineral skutterudite (CoSb(3)) is very near the critical point in its natural state.     

Point charge in a static,spherically symmetric Brans-Dicke field

We determine in closed form the electrostatic potential of a point test charge held at rest in a static, spherically symmetric Brans-Dicke field. This result is a generalization of the previously obtained expression for the potential of a test charge at rest near a Schwarzschild black hole. Moreover, our solution is valid for the coupled gravitational and massless scalar fields.     

Statistical mechanics and stability of random lattice field theory

The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities.     

Conformal symmetry of relativistic and nonrelativistic systems and AdS/CFT correspondence

The nonlinear realization of conformal so(2,d) symmetry for relativistic systems and the dynamical conformal so(2,1) symmetry of nonrelativistic systems are investigated in the context of AdS/CFT correspondence. We show that the massless particle in d-dimensional Minkowski space can be treated as the system confined to the border of the AdS_d+1 of infinite radius, while various nonrelativistic systems may be canonically related to a relativistic (massless, massive, or tachyon) particle on the AdS₂ × S^d−1. The list of nonrelativistic systems “unified” by such a correspondence comprises the conformal mechanics model, the planar charge-vortex and three-dimensional charge-monopole systems, the particle in a planar gravitational field of a point massive source, and the conformal model associated with the charged particle propagating near the horizon of the extreme Reissner-Nordström black hole.     

Compton scattering in the Buchholz–Roberts framework of relativistic QED

We consider a Haag–Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that massive single-particle states are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result, we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis, we use our new technique to further simplify scattering theory of massless bosons in the vacuum sector. A general discussion of the status of the infrared problem in the setting of Buchholz and Roberts is given.     

A classification of massless totally antisymmetric tensor field in arbitrary dimensional space-time

A formulation of the massless fields is given in terms of a system of first-order equations. There are two such systems, and the massless fields are accordingly classified into two families. Successive gauge transformations exist, by which the sequential FP ghosts are induced. The number of physical modes is counted easily by looking at the field strength.     

Lyapunov exponents in unstable systems

We investigate the dynamical behavior of unstable systems in the vicinity of the critical point associated with a liquid-gas phase transition. By considering a mean-field treatment, we first perform a linear analysis and discuss the instability growth times. Then, coming to complete Vlasov simulations, we investigate the role of nonlinear effects and calculate the Lyapunov exponents. As a main result, we find that near the critical point, the Lyapunov exponents exhibit a power-law behavior, with a critical exponent beta=0.5. This suggests that in thermodynamical systems the Lyapunov exponent behaves as an order parameter to signal the transition from the liquid to the gas phase.     

Massless D-Branes on Calabi–Yau Threefolds and Monodromy

We analyze the link between the occurrence of massless B-type D-branes for specific values of moduli and monodromy around such points in the moduli space. This allows us to propose a classification of all massless B-type D-branes at any point in the moduli space of Calabi–Yau’s. This classification then justifies a previous conjecture due to Horja for the general form of monodromy. Our analysis is based on using monodromies around points in moduli space where a single D-brane becomes massless to generate monodromies around points where an infinite number become massless. We discuss the various possibilities within the classification.     

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge

Using Poincaré parametrization of AdS space, we study totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four. CFT adapted gauge invariant formulation for such fields is developed. Gauge symmetries are realized similarly to the ones of Stueckelberg formulation of massive fields. We demonstrate that the curvature and radial coordinate contributions to the gauge transformation and Lagrangian of the AdS fields can be expressed in terms of ladder operators. Realization of the global AdS symmetries in the conformal algebra basis is obtained. Modified de Donder gauge leading to simple gauge fixed Lagrangian is found. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. Interrelations between our approach to the massless AdS fields and the Stueckelberg approach to massive fields in flat space are discussed.