Expansion In Coupling Constant Research Articles

Entanglement Entropy and Quantum Phase Transition in the O(N) \u03c3-model

We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the σ-model in 3+1 dimensions which is O(N) symmetric as the mass squared parameter μ2 is positive, and undergoes spontaneous symmetry breaking while μ2 becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point μ2 = 0, and decreases while μ2 is tuned away from 0 into either phase.

Production of monopoles: A theoretical attempt

The production of a monopole–antimonopole pair through electromagnetic interaction is considered. The particular process considered involves the annihilation of a pair of leptons into photons and the subsequent formation of the MA pair. The actual calculation involves some approximations but no expansion in coupling constant.

Anomalies in the entanglement properties of the square-lattice Heisenberg model

We compute the bipartite entanglement properties of the spin-half square-lattice Heisenberg model by a variety of numerical techniques that include valence bond quantum Monte Carlo (QMC), stochastic series expansion QMC, high temperature series expansions and zero temperature coupling constant expansions around the Ising limit. We find that the area law is always satisfied, but in addition to the entanglement entropy per unit boundary length, there are other terms that depend logarithmically on the subregion size, arising from broken symmetry in the bulk and from the existence of corners at the boundary. We find that the numerical results are anomalous in several ways. First, the bulk term arising from broken symmetry deviates from an exact calculation that can be done for a mean-field Neel state. Second, the corner logs do not agree with the known results for non-interacting Boson modes. And, third, even the finite temperature mutual information shows an anomalous behavior as T goes to zero, suggesting that T->0 and L->infinity limits do not commute. These calculations show that entanglement entropy demonstrates a very rich behavior in d>1, which deserves further attention.

The Condition for Existence of Complex Modes in Trapped Bose–Einstein Condensate with a Highly Quantized Vortex

We consider a trapped Bose–Einstein condensate with a highly quantized vortex. Pu et al. found numerically the parameter region in which complex eigenvalues arise. Recently, the splitting of a highly quantized vortex into two singly quantized vortices is observed in the experiment. We derive analytically the condition for the existence of complex eigenvalues by using the small coupling constant expansion and the two-mode approximation. We check that our results agree with those by Pu et al.

Transport theory for a scalar quark & gluon model

A model for scalar quarks and gluons that successfully gives rise to a ln s behavior in high-energy qq scattering and which contains a non-trivial three-gluon vertex is used to study collision theory with the following aspects: i) A three-body interaction simulating QCD is present and ii) particle production and annihilation occur naturally. In this paper, the collision term in the model is examined in detail in the quasiparticle approximation. The construction of cross-sections in which self-energy terms are ordered according to a coupling constant expansion is undertaken. It is shown explicitly which terms of second order are required to obtain the scattering amplitudes that are two body in nature. Additional ordering in the number of colors shows that quark loop diagrams are suppressed and gluon production or scattering processes dominate. It is also shown that a consistent calculation of the scattering graphs at the two-loop level also simultaneously yields terms that renormalize one-loop level graphs. This can then be extended to arbitrary m↦n processes. We examine the constraint equation briefly, discussing the appearance of a width. The issue of pinch singularities is also addressed, and examples of the elimination of such singularities in equilibrium are given explicitly.

Non-commutative Gross-Neveu model at large N

The non-commutative O(N) Gross-Neveu model is solved in the large N limit in two and three space-time dimensions. The commutative version of the two dimensional model is a renormalizable quantum field theory, both in a coupling constant expansion and an expansion in 1/N. The non-commutative version has a renormalizable coupling constant expansion where ultraviolet divergences can be removed by adjusting counterterms to each order. On the other hand, in a previous work, we showed that the non-commutative theory is not renormalizable in the large N expansion. This is argued to be due to a combined effect of asymptotic freedom and the ultraviolet/infrared mixing that occurs in a non-commutative field theory. In the present paper we will elaborate on this result and extend it to study the large N limit of the three dimensional Gross-Neveu model. We shall see that the large N limit of the three dimensional theory is also trivial when the ultraviolet cutoff is removed.

Resumming Long-Distance Contributions to the QCD Pressure.

The strict coupling constant expansion for the free energy of hot QCD plasma shows bad convergence at all reasonable temperatures, and does not agree well with its 4D lattice determination. This has recently led to various refined resummations, whereby the agreement with the lattice result should improve, at the cost of a loss of a formal agreement with the coupling constant expansion and particularly with its large infrared sensitive "long-distance" contributions. We show here how to resum the dominant long-distance effects by using a 3D effective field theory, and determine their magnitude by simple lattice Monte Carlo simulations.

Comment on “Coupling constant and quark-loop expansion for corrections to the valence approximation”

Lee and Weingarten have recently criticized our calculation of quarkonium and glueball scalars as being "incomplete" and "incorrect". Here we explain the relation of our calculations to full QCD.

Coupling constant and quark-loop expansion for corrections to the valence approximation

For full QCD vacuum expectation values we construct an expansion in quark loop count and in powers of a coupling constant. The leading term in this expansion is the valence (quenched) approximation vacuum expectation value. Higher terms give corrections to the valence approximation. A test of the expansion is presented for moderately heavy quarks on a small lattice. We consider briefly an application of the expansion to quarkonium-glueball mixing.

Improved error estimate for the valence approximation

We construct a systematic mean-field-improved coupling constant and quark loop expansion for corrections to the valence (quenched) approximation to vacuum expectation values in the lattice formulation of QCD. Terms in the expansion are evaluated by a combination of weak coupling perturbation theory and a Monte Carlo algorithm.

Quantum phase space from string solitons

In this paper we view the sigma-model couplings of appropriate vertex operators describing the interaction of string matter with a certain type of string solitons (0-branes) as the quantum phase space of a point particle. The sigma-model is slightly non critical, and therefore one should dress it with a Liouville mode. Quantization is achieved by summing over world-sheet genera (in the pinched approximation). To leading order in the coupling constant expansion, the quantization reproduces the usual quantum mechanical commutator. We attempt to go beyond leading order and we reproduce the generalized string uncertainty principle.

Hybrid schemes combining the Hartree–Fock method and density-functional theory: Underlying formalism and properties of correlation functionals

Hybrid schemes that combine elements of the Hartree–Fock and the Kohn–Sham procedures are shown here to have a rigorous formal basis within exact density-functional theory. Properties of the exact correlation energy and its functional derivative, corresponding to each hybrid scheme, are introduced and the correlation energy is expressed by a coupling constant integral. The coupling constant expansions of hybrid correlation energies are considered.

Large-order behavior of nondecoupling effects in the standard model and triviality.

We compute some nondecoupling effects in the standard model, such as the $\ensuremath{\rho}$ parameter, to all orders in the coupling constant expansion. We analyze their large order behavior and explicitly show how they are related to the nonperturbative cutoff dependence of these nondecoupling effects due to the triviality of the theory.

Electron mass anomalous dimension at O(1/N2tf) in quantum electrodynamics

The critical exponent corresponding to the renormalization of the composite operator ψψ is computed in quantum electrodynamics at O(1/N2ƒ) in arbitrary dimensions and covariant gauge at the non-trivial zero of the electron mass which is a the large Nƒ expansion and the exponent corresponding to the anomalous dimensions of the electron mass which is a gauge independent object is deduced. Expanding in powers of ϵ=2−d2 we check it is consistent with the known three loop perturbative structure and determine the subsequent coefficients in the coupling constant expansion to all orders in MS.

Stationary solutions of stochastic parabolic and hyperbolic sine-Gordon equations

The authors consider the damped sine-Gordon equation perturbed by (thermal) space-time noise in the form it arises in the theory of the Josephson junction and charge density waves. They announce a rigorous proof that the coupling constant expansion of the solution of the initial value problem converges for small coupling. Taking the limit of the initial time t0 to - infinity they obtain a stationary solution. It is shown that the stationary solution is localized both in time and space even if the solution at finite time is not.

Canonical formalism for path-dependent Lagrangians. Coupling constant expansions

A canonical formalism obtained for path-dependent Lagrangians is applied to Fokker-type Lagrangians. The results are specialized for coupling constant expansions and later on are applied to relativistic systems of particles interacting through symmetric scalar and vector mesodynamics and electrodynamics.

QSGCD: Quantum supergravichromodynamics

We extend the methods of ’t Hooft for the planar model of QCD to their natural supersymmetric generalizations for a pure SUSY Yang-Mills theory with gauge group ℐ. We find, to leading order in the infrared and coupling constant expansions in the respective Dyson-Schwinger and Bethe-Salpeter equations, a massless SUSY multiplet of spins (2,3/2). Following Weinberg, Grisaru and Pendleton, and Kugo and Uehara, we identify this multiplet with the graviton and the gravitino in the spirit of the Sudarshan-Flatoet al. interpretation of the Weinberg-Witten theorem. We propose, therefore, that quantum gravity is really the low-energy remnant of a more fundamental theory: a SUSY Yang-Mills theory with scale parameterΛQSGCD∼MP, whereMP is the Planck mass. The true unification of gravity with the strong, weak and electromagnetic interactions occurs at a scaleMSSU⋍1·1021 GeV in anE8 example, whereE8 is the gauge group of the world. Possible connections with the superstring theories of Green and Schwarz and of Grosset al. are discussed.

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.

Why the conventional theory of dynamical friction in plasmas gives logarithmically divergent results

Abstract The second coefficient of the coupling constant expansion of the average velocity of a test electron moving in a compensated one-component plasma (OCP) is calculated by integrating over initial configurations. It is assumed that correlations are absent at time t =0. The result is convergent and in agreement with the small coupling limit of the frictional force derived earlier. It is further shown that if the three additional assumptions of the conventional theory are made before integration, the logarithmic divergence reappears in the results.

On the phenomenon of dynamical friction for particles interacting by the inverse square law

The dynamics of the homogeneous positive background of a one-component plasma (OCP) is taken into account — compensated system — in order to modify the first coefficient of the coupling constant expansion of the average velocity of a test electron derived in a previous letter for an uncompensated OCP.