Self-interacting scalar fields with geometrical interpretations

The idea is advanced that particles arise as distortions of a reimannian background and that such distortions represent particular conformally flat solutions of the “cosmological” Einstein equations with extremely large “cosmological” constants. Particle interactions then appear as gravitational in origin. The idea is illustrated with the help of two scalar models. In the first one the “De Sitter” space can be interpreted as a relativistic field whose ground state undergoes a transition from degenerate to nondegenerate for the critical value of some parameter. In the second one a deeper understanding is reached of the role of the “De Sitter” space in confinement problems and of the nature of the ensemble of vacuum states recently introduced in conformally invariant field theories by Fubini.     

Self-interacting scalar field trapped in a DGP brane: The dynamical systems perspective

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a DGP brane. The simplest kinds of self-interaction potentials are investigated: (a) constant potential, and (b) exponential potential. It is shown that the dynamics of DGP models can be very rich and complex. One of the most interesting results of this study shows that dynamical screening of the scalar field self-interaction potential, occurring within the Minkowski cosmological phase of the DGP model and that mimics 4D phantom behaviour, is an attractor solution for a constant self-interaction potential but not for the exponential one. In the latter case gravitational screening is not even a critical point of the corresponding autonomous system of ordinary differential equations.     

Advanced linked cluster expansion scalar fields at finite temperature

Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they result into convergent hopping parameter-like series for free energies, correlation functions and in particular susceptibilities. We consider scalar fields with O(N)-symmetric nearest-neighbour interactions on hypercubic lattices with possibly finite extension in some directions, thus including field theories at finite temperature T. We improve known and develop new techniques and algorithms to increase the order n. The expansions can be computed too in such a way that detailed information on critical behaviour can be extracted from the susceptibility series. This concerns both simple moments as well as higher correlations such as 4- and 6-point functions used to define renormalized coupling constants. Particular emphasis is done on finite-temperature field theory. In order to be able to measure finite-temperature critical behaviour, the order of explicit computation n has to be sufficiently large compared to T⁻¹ in lattice units. 2- and 4-point susceptibility series are computed up to and including the 18th order and beyond.     

Self-interacting one-dimensional oscillators

Energy eigenvalues and 〈x ²〉 _n for the oscillators having potential energyV(x)=(ω ² x ²/2)+λ<x ^2r >x ^2s have been determined for various values ofλ, r, s andn using renormalized hypervirial-Padé scheme. In general, the results show an improvement over the findings of earlier workers. Variation of the evaluated quantities and of the renormalization parameter withλ, r, s andn has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative formalism of perturbation theory developed by Kim and Sukhatme (J. Phys. A25 647 (1992)).     

Localized fields on scalar global defects

We investigate the localization of modes on the worldvolume of a p  -brane embedded in (p+d+1$p+d+1$)-dimensional spacetime. The p  -brane here is such that its profile is regarded as a scalar global defect and the localized modes are scalar modes that come from the fluctuations around such defect. The effective action on the brane is computed and the induced potentials are typically ?⁴${?}^4$-type potentials that are flatter for lower d-dimensions. We also make a connection of such scalar global defects with black p-branes in certain limits.     

The existence of scalar Lie fields

It is shown that the existence of nontrivial scalar Lie fields (i. e. fields whose commutator is linear in the field itself) is not precluded by algebraic consistency arguments. A partial characterization of the simplest algebraic Lie field structures is given. Several examples are presented, one of which may be represented by Hermitian operators in a Hilbert space having a unitary representation of the Poincaré group.     

Flavour dynamics with general scalar fields

We consider a spontaneously broken gauge theory based on the standard model (SM) group with scalar fields that carry arbitrary representations of G, and we investigate some general properties of the charged and neutral current involving these fields. In particular we derive the conditions for having real or complex couplings of the Z boson to two different neutral or charged scalar fields, and for the existence of CP-violating Z-scalar-scalar couplings. Moreover, we study models with the same fermion content as in the SM, with one SU(2) Higgs singlet, and an arbitrary number of Higgs doublets. We show that the structure of the Z-Higgs boson and of the Yukawa couplings in these models can be such that CP-violating form factors which conserve chirality are induced at the one-loop level. Received: 18 December 1998 / Published online: 22 March 1999     

Class restrictions and massive scalar fields

It has been extablished that no gravitational interaction is possible with a massive scalar field for a special class one metric.     

Energy conditions and classical scalar fields

Attention has been recently called upon the fact that the weak and null energy conditions are violated in wormhole solutions of Einstein's theory with classical, nonminimally coupled, scalar fields as material source. It is shown that the discussion is only meaningful when ambiguities in the definitions of stress-energy tensor and energy density of a nonminimally coupled scalar are resolved. The three possible approaches are discussed with emphasis on the positivity of the respective energy densities and covariant conservation laws. The root of the ambiguities is traced to the energy localization problem for the gravitational field.     

Perturbation theory and non-renormalizable scalar fields

We study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of :P(): _d when one does not allow any renormalization besides the usual coupling constants, mass and wave function renormalizations.Supported in part by NSF grant PHY-8342570. Address after March 1985: Theoretische Physik, ETH-Hönggerberg, CH-8093 Zürich, SwitzerlandSupported in part by NSF grant MCS-8108814 (A03)     

Field-dependent coupling strength for scalar fields

Effective Lagrangians with a nonlinear coupling between the scalar density of the nucleons and the scalar meson field are investigated within the framework of relativistic mean-field theories. This phenomenological coupling acts as a field-dependent coupling strength and is supposed to take into account renormalization effects within a mean-field picture. The parameters of the model are adjusted to saturation properties of nuclear matter and predictions for the real part of the optical potential are compared with experimental data. For that relativistic and nonrelativistic optical model fits are examined and an experimental standard is deduced which covers the energy range from ? 50 MeV to 1000 MeV. A definition for the real part of the optical potential is given which is not linear in the energy but has the proper limits for momentum zero and infinity. It is shown that for a special choice of the field-dependent coupling strength the meanfield theory can describe the nuclear equation of state and the momentum dependence of the single particle energy without further parameters up to momenta where the intrinsic structure of nucleon becomes relevant.     

Gravitational collapse of charged scalar fields

In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell–Klein–Gordon sector are derived in the \(3+1\) formalism, and coupled to gravity by means of the stress–energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte–Shapiro–Shibata–Nakamura formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn’t disperse and approaches a final state corresponding to a sub-extremal Reissner–Nördstrom black hole with \(|Q| . By increasing the fundamental charge of the scalar field \(q\) we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.     

Gauging universe expansion via scalar fields

In this study, we investigate the expansion of the FRLW universe in the open, closed, and flat geometries. The universe is dominated by a scalar field (spatially homogeneous) as a source of dark energy. We consider the three different classes of scalar fields – quintessence, tachyonic, and phantom field – for our analysis. A mathematical analysis is carried out by considering these three scalar fields with exponential and power-law potentials. Both potentials give exponential expansion in the open, closed, and flat FRLW universes. It is found that quintessence, tachyonic, and phantom scalar fields are indistinguishable under the slow roll approximation.     

No scalar hair behaviors of static massive scalar fields with nodes

The European Physical Journal C - We present a C++ software package called PhaseTracer for mapping out cosmological phases, and potential transitions between them, for Standard Model extensions...     

Linear spin-zero quantum fields in external gravitational and scalar fields

The quantum theory of both linear, and interacting fields on curved space-times is discussed. It is argued that generic curved space-time situations force the adoption of the algebraic approach to quantum field theory: and a suitable formalism is presented for handling an arbitrary quasi-free state in an arbitrary globally hyperbolic space-time.For the interacting case, these quasi-free states are taken as suitable starting points, in terms of which expectation values of field operator products may be calculated to arbitrary order in perturbation theory. The formal treatment of interacting fields in perturbation theory is reduced to a treatment of free quantum fields interacting with external sources.Central to the approach is the so-called two-current operator, which characterises the effect of external sources in terms of purely algebraic (i.e. representation free) properties of the source-free theory.The paper ends with a set of Feynman rules which seems particularly appropriate to curved space-times in that it takes care of those aspects of the problem which are specific to curved space-times (and independent of interaction). Heuristically, the scheme calculates in-in rather than in-out matrix elements. Renormalization problems are discussed but not treated.Work partly supported by the Schweizerische Nationalfonds     

Linear spin-zero quantum fields in external gravitational and scalar fields

We give mathematically rigorous results on the quantization of the covariant Klein Gordon field with an external stationary scalar interaction in a stationary curved space-time. We show how, following Segal, Weinless etc., the problem reduces to finding a “one particle structure” for the corresponding classical system. Our main result is an existence theorem for such a one-particle structure for a precisely specified class of stationary space-times. Byproducts of our approach are:

1. A discussion of when a given “equal-time” surface in a given stationary space-time is Cauchy.
2. A modification and extension of the methods of Chernoff [3] for proving the essential self-adjointness of certain partial differential operators.

     

Dynamics of scalar fields in an expanding/contracting cosmos at finite temperature

This study extends the investigation of quantum dissipative effects of a cosmological scalar field by taking into account cosmic expansion and contraction.Cheung,Drewes,Kang,and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field in a recent work,where analytical expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interactions,and the work was conducted using Minkowski-space propagators in loop diagrams.In this work,we incorporate the Hubble expansion and contraction of the cosmic background and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly.Given that the Hubble parameter,H,attains a small but non-zero value,we carry out calculations to the first order in H.If we set H=0,all results match those in flat spacetime.Interestingly,we must integrate over the resonances,which in turn leads to an amplification of the effects of a non-zero H.This is an intriguing phenomenon,which cannot be uncovered in flat spacetime.The implications on particle creations in the early universe will be studied in a forthcoming study.