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Carmen Molina-Paris

Publications and source records attributed to Carmen Molina-Paris.

36 records · Page 2Linked to original sources
arXiv2000

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations

The presence of fluctuations and non-linear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop {\emph{effective action}} and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop {\emph{finite}} in $d=0$ and $d=1$, and is one-loop renormalizable in $d=2$ and $d=3$ space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in $d=2$.

cond-mat.stat-mech↗
arXiv2000

Geometrodynamics of Variable-Speed-of-Light Cosmologies

This paper is dedicated to the memory of Dennis Sciama. Variable-Speed-of-Light (VSL) cosmologies are currently attracting interest as an alternative to inflation. We investigate the fundamental geometrodynamic aspects of VSL cosmologies and provide several implementations which do not explicitly break Lorentz invariance (no "hard" breaking). These "soft" implementations of Lorentz symmetry breaking provide particularly clean answers to the question "VSL with respect to what?". The class of VSL cosmologies we consider are compatible with both classical Einstein gravity and low-energy particle physics. These models solve the "kinematic" puzzles of cosmology as well as inflation does, but cannot by themselves solve the flatness problem, since in their purest form no violation of the strong energy condition occurs. We also consider a heterotic model (VSL plus inflation) which provides a number of observational implications for the low-redshift universe if chi contributes to the "dark energy" either as CDM or quintessence. These implications include modified gravitational lensing, birefringence, variation of fundamental constants and rotation of the plane of polarization of light from distant sources.

astro-ph↗
arXiv2000

Attractor states and infrared scaling in de Sitter space

The renormalized expectation value of the energy-momentum tensor for a scalar field with any mass m and curvature coupling xi is studied for an arbitrary homogeneous and isotropic physical initial state in de Sitter spacetime. We prove quite generally that has a fixed point attractor behavior at late times, which depends only on m and xi, for any fourth order adiabatic state that is infrared finite. Specifically, when m^2 + xi R > 0, approaches the Bunch-Davies de Sitter invariant value at late times, independently of the initial state. When m = xi = 0, it approaches instead the de Sitter invariant Allen-Folacci value. When m = 0 and xi \ge 0 we show that this state independent asymptotic value of the energy-momentum tensor is proportional to the conserved geometrical tensor (3)H_{ab}, which is related to the behavior of the quantum effective action of the scalar field under global Weyl rescaling. This relationship serves to generalize the definition of the trace anomaly in the infrared for massless, non-conformal fields. In the case m^2 + xi R = 0, but m and xi separately different from zero, grows linearly with cosmic time at late times. For most values of m and xi in the tachyonic cases, m^2 + xi R < 0, grows exponentially at late cosmic times for all physically admissable initial states.

gr-qc↗
arXiv2000

Chi-Variable-Speed-of-Light Cosmologies

Variable-Speed-of-Light (VSL) cosmologies are currently attracting much interest as a possible alternative to cosmological inflation. We discuss the fundamental geometrodynamic aspects of VSL cosmologies, and provide several alternative implementations. These implementations provide a large class of VSL cosmologies that pass the zeroth-order consistency tests of being compatible with both classical Einstein gravity and low-energy particle physics. While they solve the ``kinematic'' puzzles as well as inflation does, VSL cosmologies typically do not solve the flatness problem since in their purest form no violation of the strong energy condition occurs. Nevertheless, these models are easy to unify with inflation.

astro-ph↗
arXiv1999

Effective potential for the reaction-diffusion-decay system

In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.

cond-mat.stat-mech↗
arXiv1999

Effective action for stochastic partial differential equations

Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. In this paper we set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these non-quantum field theories are fully interacting. Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues, and furthermore offers marked technical advantages: We can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the BRST formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ``direct approach'' is the SPDE analog of canonical quantization using physical fields.) We show how to define the effective action to all loops, and then focus on the one-loop effective action, and its specialization to constant fields: the effective potential. An important result is that the amplitude of the two-point function governing the noise acts as the loop-counting parameter and is the analog of Planck's constant hbar in this SPDE context. We derive a general expression for the one-loop effective potential of an arbitrary SPDE subject to translation-invariant Gaussian noise, and compare this with the one-loop potential for QFT.

cond-mat.stat-mech↗
arXiv1999

One-loop $λϕ^4$ theory in Robertson-Walker spacetimes: adiabatic regularization and analytic approximation

The renormalization of a scalar field theory with a quartic self-coupling (a $λϕ^4$ theory) via adiabatic regularization in a general Robertson-Walker spacetime is discussed. The adiabatic counterterms are presented in a way that is most conducive to numerical computations. A variation of the adiabatic regularization method is presented which leads to analytic approximations for the energy-momentum tensor of the field and the quantum contribution to the effective mass of the mean field. Conservation of the energy-momentum tensor for the field is discussed and it is shown that the part of the energy-momentum tensor which depends only on the mean field is not conserved but the full renormalized energy-momentum tensor is conserved as expected and required by the semiclassical Einstein's equation. It is also shown that if the analytic approximations are used then the resulting approximate energy-momentum tensor is conserved. This allows a self-consistent backreaction calculation to be performed using the analytic approximations. The usefulness of the approximations is discussed.

gr-qc↗
arXiv1999

Energy-Momentum Tensor of Particles Created in an Expanding Universe

We present a general formulation of the time-dependent initial value problem for a quantum scalar field of arbitrary mass and curvature coupling in a FRW cosmological model. We introduce an adiabatic number basis which has the virtue that the divergent parts of the quantum expectation value of the energy-momentum tensor are isolated in the vacuum piece of , and may be removed using adiabatic subtraction. The resulting renormalized is conserved, independent of the cutoff, and has a physically transparent, quasiclassical form in terms of the average number of created adiabatic `particles'. By analyzing the evolution of the adiabatic particle number in de Sitter spacetime we exhibit the time structure of the particle creation process, which can be understood in terms of the time at which different momentum scales enter the horizon. A numerical scheme to compute as a function of time with arbitrary adiabatic initial states (not necessarily de Sitter invariant) is described. For minimally coupled, massless fields, at late times the renormalized goes asymptotically to the de Sitter invariant state previously found by Allen and Folacci, and not to the zero mass limit of the Bunch-Davies vacuum. If the mass m and the curvature coupling xi differ from zero, but satisfy m^2+xi R=0, the energy density and pressure of the scalar field grow linearly in cosmic time demonstrating that, at least in this case, backreaction effects become significant and cannot be neglected in de Sitter spacetime.

gr-qc↗
arXiv1999

Effective potential for the massless KPZ equation

In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation--SPDE) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the one-loop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy vorticity-free Burgers equation), and analyze its behaviour in the ultraviolet (short-distance) regime. When this field theory is subject to white noise we can calculate the one-loop effective potential and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the one-loop effective potential for the massless KPZ equation is closely related to that for lambda phi^4 QFT. In particular we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman-Weinberg mechanism) in 1 and 2 space dimensions, and that this behaviour does not persist in 3 space dimensions.

cond-mat.stat-mech↗
arXiv1998

Tolman wormholes violate the strong energy condition

For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define the bounce in terms of a three-dimensional edgeless achronal spacelike hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at and near the bounce and to derive general theorems regarding violations of the energy conditions--theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the highly symmetric FRW-based subclass of Tolman wormholes. [For example: even under the mildest of hypotheses, the strong energy condition (SEC) must be violated.] Alternatively, one can dispense with the minimal volume condition and define a generic bounce entirely in terms of the motion of test particles (future-pointing timelike geodesics), by looking at the expansion of their timelike geodesic congruences. One re-confirms that the SEC must be violated at or near the bounce. In contrast, it is easy to arrange for all the other standard energy conditions to be satisfied.

gr-qc↗
arXiv1998

Minimal conditions for the creation of a Friedman-Robertson-Walker universe from a "bounce"

We investigate the minimal conditions under which the creation of our universe might arise due to a "bounce" from a previous collapse, rather than an explosion from a big-bang singularity. Such a bounce is sometimes referred to as a Tolman wormhole. We subject the bounce to a general model-independent analysis along the lines of that applied to the Morris-Thorne traversable wormholes, and show that there is always an open temporal region surrounding the bounce over which the strong energy condition (SEC) must be violated. On the other hand, all the other energy conditions can easily be satisfied. In particular, we exhibit an inflation-inspired model in which a big bounce is "natural".

gr-qc↗
arXiv1998

Zeta functions, renormalization group equations, and the effective action

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories.

hep-th↗
arXiv1998

Renormalization Group Improving the Effective Action

The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of thermal or statistical nature. In both cases the effects of these fluctuations can be accounted for by solutions of the corresponding renormalization group equations. We show how the renormalization group equations are intimately connected with the effective action: given the effective action we can extract the renormalization group equations; given the renormalization group equations the effects of these fluctuations can be included in the classical action by using what is known as improved perturbation theory (wherein the bare parameters appearing in tree-level expressions are replaced by their scale-dependent running forms). The improved action can then be used to reconstruct the effective action, up to finite renormalizations, and gradient terms.

hep-th↗
arXiv1998

Quantum Gravity Without Ghosts

An outline is given of a recently discovered technique for building a quantum effective action that is completely independent of gauge-fixing choices and ghost determinants. One makes maximum use of the geometry and fibre-bundle structure of the space of field histories and introduces a set of nonlocal composite fields: the geodesic normal fields based on Vilkovisky's connection on the space of histories. The closed-time-path formalism of Schwinger, Bakshi, Mahantappa {\it et al} can be adapted for these fields, and a set of gauge-fixing-independent dynamical equations for their expectation values (starting from given initial conditions) can be computed. An obvious application for such equations is to the study of the formation and radiative decay of black holes, and to other back-reaction problems.

hep-th↗
arXiv1997

Effective equation of state for a spherically expanding pion plasma

Following a relativistic heavy ion collision, the quark-gluon plasma produced eventually undergoes a chiral phase transition. We assume that during this phase transition one can describe the dynamics of the system by the linear $σ$ model and that the expansion can be thought of as mostly radial. Because the $σ$ model is an effective field theory there is an actual momentum cutoff (Landau pole) in the theory at around 1 GeV. Thus it is necessary to find ways of obtaining a covariantly conserved, renormalized energy-momentum tensor when there is a cutoff present (which breaks covariance), in order to identify the effective equation of state of this time evolving system. We show how to solve this technical problem and then determine the energy density and pressure of the system as a function of the proper time. We consider different initial conditions and search for instabilities which can lead to the formation of disoriented chiral condensates (DCCs). We find that the energy density and pressure both decrease quickly, as is appropriate for a rapidly cooling system, and that the energy is numerically conserved.

hep-ph↗
arXiv1997

Casimir effect in dielectrics: Surface area contribution

In this paper we take a deeper look at the technically elementary but physically robust viewpoint in which the Casimir energy in dielectric media is interpreted as the change in the total zero point energy of the electromagnetic vacuum summed over all states. Extending results presented in previous papers [hep-th/9609195; hep-th/9702007] we approximate the sum over states by an integral over the density of states including finite volume corrections. For an arbitrarily-shaped finite dielectric, the first finite-volume correction to the density of states is shown to be proportional to the surface area of the dielectric interface and is explicitly evaluated as a function of the permeability and permitivity. Since these calculations are founded in an elementary and straightforward way on the underlying physics of the Casimir effect they serve as an important consistency check on field-theoretic calculations. As a concrete example we discuss Schwinger's suggestion that the Casimir effect might be the underlying physical basis behind sonoluminescence}. The recent controversy concerning the relative importance of volume and surface contributions is discussed. For sufficiently large bubbles the volume effect is always dominant. Furthermore we can explicitly calculate the surface area contribution as a function of refractive index.

hep-th↗
arXiv1995

Gauge Theory Without Ghosts

A quantum effective action for gauge field theories is constructed that is gauge invariant and independent of the choice of gauge breaking terms and the ghost determinant.

hep-th↗