Invariant Scalar Field Research Articles

Implementing Mach’s principle using gauge theory

We reformulate an approach fist given by Barbour and Bertotti (BB) for implementing Mach's principle for nonrelativistic particles. This reformulation can deal with arbitrary symmetry groups and finite group elements. Applying these techniques to U(1) and SU(N) invariant scalar field theories, we show that BB's proposal is nearly equivalent to defining a covariant derivative using a dynamical connection. We then propose a modified version of the BB method which implements Mach's principle using gauge theory techniques and argue that this modified method is equivalent to the original. Given this connection between the particle models and Yang-Mills theories, we consider the effect of dynamic curvature as a possible generalization of the BB scheme. Since the BB method can be used as a novel way of deriving geometrodynamics, the connection with gauge theory may shed new light on the gauge properties of the gravitational field.

Relativistic calculation of the pion loop correlation energy in nuclear matter in a theory including confinement

We present a relativistic calculation of the saturation properties of nuclear matter which contains the correlation energy. Pion loops are incorporated on top of a relativistic Hartree-Fock (RHF) approach based on a chiral theory. It includes the effect of nucleon structure through its response to the background chiral invariant scalar field. All the parameters which enter the RHF calculation are fixed or strongly constrained by hadron phenomenology or lattice data. The new input for the correlation energy is the Landau-Migdal parameter ${g}^{'}$ governing the short-range part of the spin-isospin interaction. We find that the inclusion of the correlation energy improves the description of the saturation properties of nuclear matter.

Gravitational wave background from superinflation in loop quantum cosmology

We investigate the behavior of tensor fluctuations in Loop Quantum Cosmology, focusing on a class of scaling solutions which admit a near scale-invariant scalar field power spectrum. We obtain the spectral index of the gravitational field perturbations, and find a strong blue tilt in the power spectrum with ${n}_{t}\ensuremath{\approx}2$. The amplitude of tensor modes are, therefore, suppressed by many orders of magnitude on large scales compared to those predicted by the standard inflationary scenario where ${n}_{t}\ensuremath{\approx}0$.

Three-algebras andN=6Chern-Simons gauge theories

We derive the general form for a three-dimensional scale-invariant field theory with N=6 supersymmetry, SU(4) R-symmetry and a U(1) global symmetry. The results can be written in terms of a 3-algebra in which the triple product is not antisymmetric. For a specific choice of 3-algebra we obtain the N=6 theories that have been recently proposed as models for M2-branes in an R^8/Z_k orbifold background.

Conformal invariance and apparent universality of semiclassical gravity

In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike what happens in the case where the coupling to the curvature $\ensuremath{\xi}$ is generic, for the special cases $\ensuremath{\xi}=0$ and $\ensuremath{\xi}=1/6$ the large distance behavior of the expectation value $⟨T^{\ensuremath{\mu}}{}_{\ensuremath{\nu}}⟩$ turns out to be independent of the internal structure of the gravitational source. Here, we address a higher dimensional generalization of this result: We first compute the difference between a black hole and a static spherically symmetric star for the observables $⟨{\ensuremath{\phi}}^{2}⟩$ and $⟨T^{\ensuremath{\mu}}{}_{\ensuremath{\nu}}⟩$ in the far field limit. Thus, we show that the conformally invariant massless scalar field theory in a static spherically symmetric background exhibits such a universality phenomenon in $D\ensuremath{\ge}4$ dimensions. Also, using the one-loop effective action, we compute $⟨T^{\ensuremath{\mu}}{}_{\ensuremath{\nu}}⟩$ for a weakly gravitating object. These results lead to the explicit expression of the expectation value $⟨T^{\ensuremath{\mu}}{}_{\ensuremath{\nu}}⟩$ for a Schwarzschild-Tangherlini black hole in the far field limit. As an application, we obtain quantum corrections to the gravitational potential in $D$ dimensions, which for $D=4$ are shown to agree with the one-loop correction to the graviton propagator previously found in the literature.

Dangerous Liouville wave—exactly marginal but non-conformal deformation

We give a non-trivially interacting field theory example of scale invariant but non-conformal field theory. The model is based on the exactly solvable Liouville field theory coupled with free scalars deformed by an exactly marginal operator. We show non-vanishing of the trace of the energy-momentum tensor by using the quantum Schwinger-Dyson equation for the Liouville field theory, which is a sophistication of the quantum higher equations of motion for the Liouville field theory introduced by Alyosha Zamolodchikov. Possibly dangerous implications for the super-critical string theory will be discussed.

Relativistic chiral Hartree-Fock description of nuclear matter with constraints from nucleon structure and confinement

We present a relativistic chiral effective theory for symmetric and asymmetric nuclear matter taken in the Hartree-Fock scheme. The nuclear binding is ensured by a background chiral invariant scalar field associated with the radial fluctuations of the chiral quark condensate. Nuclear matter saturation is obtained once the scalar response of the nucleon-generating three-body repulsive forces is incorporated. For those parameters related to the scalar sector and quark confinement mechanism inside the nucleon we make use of an analysis of lattice results on nucleon mass evolution with quark mass. The other parameters are constrained as much as possible by standard hadron and nuclear phenomenology. Special attention is paid to the treatment of the propagation of the scalar fluctuations. The rearrangement terms associated with in-medium modified mass and coupling constants are explicitly included to satisfy the Hugenholtz-Van Hove theorem. We point out the important role of the tensor piece of the rho exchange Fock term to reproduce the asymmetry energy of nuclear matter. We also discuss the isospin dependence of the Landau nucleon effective mass.

On resumming inflationary perturbations beyond one-loop

It is well known that the correlation functions of a scalar field in a quasi-de Sitter space exhibitat the loop level cumulative infrared effects proportional to the total number of e-foldings ofinflation. Using the in–in formalism, we explore the behavior of these infrared effects in the largeN limitof an O(N)-invariant scalar field theory with quartic self-interactions. By resumming all higher-orderloop diagrams non-perturbatively, we show that the connected four-point correlationfunction, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respectto its tree-level value.

Harmonic Bilocal Fields Generated by Globally Conformal Invariant Scalar Fields

The twist two contribution in the operator product expansion of \(\phi_{1} ({\rm x}_{1})\phi_{2}({\rm x}_{2})\) for a pair of globally conformal invariant, scalar fields of equal scaling dimension d in four space–time dimensions is a field V 1 (x1, x2) which is harmonic in both variables. It is demonstrated that the Huygens bilocality of V 1 can be equivalently characterized by a “single–pole property” concerning the pole structure of the (rational) correlation functions involving the product \(\phi_{1}({\rm x}_{1})\phi_{2}({\rm x}_{2})\). This property is established for the dimension d = 2 of \(\phi_{1}, \phi_{2}\). As an application we prove that any system of GCI scalar fields of conformal dimension 2 (in four space–time dimensions) can be presented as a (possibly infinite) superposition of products of free massless fields.

One-dimensional solitary waves in singular deformations of SO(2) invariant two-component scalar field theory models

In this paper we study the structure of the manifold of solitary waves in some deformations of SO(2) symmetric two-component scalar field theoretical models in two-dimensional Minkowski space. The deformation is chosen in order to make the analogous mechanical system Hamilton–Jacobi separable in polar coordinates and displays a singularity at the origin of the internal plane. The existence of the singularity confers interesting and intriguing properties on the solitary waves or kink solutions.

The Casimir effect for parallel plates revisited

The Casimir effect for a massless scalar field with Dirichlet and periodic boundary conditions (bc’s) on infinite parallel plates is revisited in the local quantum field theory (lqft) framework introduced by Kay [Phys. Rev. D 20, 3052 (1979)]. The model displays a number of more realistic features than the ones he treated. In addition to local observables, as the energy density, we propose to consider intensive variables, such as the energy per unit area ε, as fundamental observables. Adopting this view, lqft rejects Dirichlet (the same result may be proved for Neumann or mixed) bc, and accepts periodic bc: in the former case ε diverges, in the latter it is finite, as is shown by an expression for the local energy density obtained from lqft through the use of the Poisson summation formula. Another way to see this uses methods from the Euler summation formula: in the proof of regularization independence of the energy per unit area, a regularization-dependent surface term arises upon use of Dirichlet bc, but not periodic bc. For the conformally invariant scalar quantum field, this surface term is absent due to the condition of zero trace of the energy momentum tensor, as remarked by De Witt [Phys. Rep. 19, 295 (1975)]. The latter property does not hold in the application to the dark energy problem in cosmology, in which we argue that periodic bc might play a distinguished role.

FUBINI VACUA AS A CLASSICAL DE SITTER VACUA

The Fubini's idea to introduce a fundamental scale of hadron phenomena by means of dilatation non-invariant vacuum state in the framework of a scale invariant Lagrangian field theory is recalled. The Fubini vacua is invariant under the de Sitter subgroup of the full conformal group. We obtain a finite entropy for the quantum state corresponding to the classical Fubini vacua in Euclidean spacetime resembling the entropy of the de Sitter vacua. In Minkowski spacetime it is shown that the Fubini vacua is mainly a bath of radiation with Rayleigh–Jeans distribution for the low energy radiation. In four dimensions, the critical scalar theory is shown to be equivalent to the Einstein field equation in the ansatz of conformally flat metrics and to the SU(2) Yang–Mills theory in the 't Hooft ansatz. In D dimensions, the Hitchin formula for the information geometry metric of the moduli space of instantons is used to obtain the information geometry of the free-parameter space of the Fubini vacua which is shown to be a (D+1)-dimensional AdS space. Considering the Fubini vacua as a de Sitter vacua, the corresponding cosmological constant is shown to be given by the coupling constant of the critical scalar theory. In Minkowski spacetime it is shown that the Fubini vacua are equivalent to an open FRW universe.

PHANTOM FIELD FROM CONFORMAL INVARIANCE

We establish a correspondence between a conformally invariant complex scalar field action (with a conformal self-interaction potential) and the action of a phantom scalar field minimally coupled to gravity (with a cosmological constant). In this correspondence, the module of the complex scalar field is used to relate conformally the metrics of both systems while its phase is identified with the phantom scalar field. At the level of the equations, the correspondence allows to map solution of the conformally nonlinear Klein–Gordon equation with vanishing energy–momentum tensor to solution of a phantom scalar field minimally coupled to gravity with cosmological constant satisfying a massless Klein–Gordon equation. The converse is also valid with the advantage that it offers more possibilities owing to the freedom of rewriting a metric as the conformal transformation of another metric. In three dimensions, the coupling of this matter action to conformal gravity is put in equivalence with topologically massive gravity with a cosmological constant and with a phantom source. Finally, we provide some examples of this correspondence.

Equations of motion for a (non-linear) scalar field model as derived from the field equations

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for thederivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a nonlinear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the $N$-body problem of the Lorentz invariant field equations.

Scopes and limits of modality in quantum mechanics

The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations.

Equations of motion for a (non‐linear) scalar field model as derived from the field equations

AbstractThe problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non‐linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N‐body problem of the Lorentz invariant field equations.

Heat equilibrium distribution in a turbulent flow

We consider a shear flow of a scale invariant Gaussian random velocity field that does not depend on the coordinates in the direction of the flow. We investigate a heat advection coming from a Gaussian random homogeneous source. We discuss a relaxation at large time of a temperature distribution determined by the forced advection-diffusion equation. We represent the temperature correlation functions by means of the Feynman-Kac formula. Jensen inequalities are applied for lower and upper bounds on the correlation functions. We show that at finite time there is no velocity dependence of long range temperature correlations (low momentum asymptotics) in the direction of the flow but the equilibrium heat distribution has large distance correlations (low momentum behavior) with an index depending on the scaling index of the random flow and of the index of the random forcing. If the velocity has correlations growing with the distance (a turbulent flow), then the large distance correlations depend in a crucial way on the scaling index of the turbulent flow. In such a case the correlations increase in the direction of the flow and decrease in the direction perpendicular to the flow, making the stream of heat more coherent.

Infrared Asymptotics of the Heat Kernel and Nonlocal Effective Action

We review recent results in the nonperturbative theory of the heat kernel and its late-time asymptotic properties responsible for the infrared behavior of the quantum effective action for massless theories. In particular, we derive a generalization of the Coleman-Weinberg potential for theories with an inhomogeneous background field. This generalization represents a new nonlocal, nonperturbative action accounting for the effects in a transition domain between the space-time interior and its infinity. In four dimensions, these effects delocalize the logarithmic Coleman-Weinberg potential, while in d > 4, they are dominated by a new powerlike, renormalization-independent nonlocal structure. We also consider the nonperturbative behavior of the heat kernel in a curved space-time with an asymptotically flat geometry. In particular, we analyze the conformal properties of the heat kernel for a conformally invariant scalar field and discuss the problem of segregating the local cosmological term from the nonlocal effective action.

Quantitative integration of hydrogeophysical data: Conditional geostatistical simulation for characterizing heterogeneous alluvial aquifers

High-resolution geophysical parameter information, as it can be provided, for example, by crosshole georadar and seismic tomography, has proven to provide useful spatial information to complement traditional hydrological methods such as core analyses, logging techniques, and tracer or pumping tests. Quantitative integration of these diverse database components is one of the major challenges in the field of high-resolution hydrogeophysics because of their different scales of measurement and the usually weak petrophysical relations among the measurements. In this study, we systematically explore the usefulness of a conditional stochastic simulation approach based on simulated annealing for this purpose. First, we generate a realistic model of an alluvial aquifer consisting of a 2D scale-invariant porosity field. On the basis of this model, we generate synthetic neutron porosity logs and crosshole georadar tomographic surveys. We then use the proposed geostatistical simulation approach to integrate this hydrogeophysical database. The effectiveness of this approach to characterize the detailed porosity distribution in heterogeneous alluvial aquifers is assessed by comparing the results for a variety of simulated porosity fields that differ fundamentally in terms of their conditioning information. Our results indicate this approach has the potential to allow for a realistic hydrogeophysical characterization in the submeter range of the porosity distribution in heterogeneous alluvial aquifers.

CONFORMAL ANOMALIES FOR INTERACTING SCALAR FIELDS ON CURVED MANIFOLDS WITH BOUNDARY

The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit calculations are given for those contributions to the conformal anomaly which emerge as a result of free scalar propagation as well as from scalar self-interactions up to second order in the scalar self-coupling. The renormalization-group behavior of the theory is, subsequently, exploited in order to advance the evaluation of the conformal anomaly to third order in the scalar self-coupling. As a direct consequence the effective action is evaluated to the same order. In effect, complete contributions to the theory's conformal anomaly and effective action are evaluated up to fourth-loop order.