Classical Background Field Research Articles

Measuring inflaton couplings via primordial gravitational waves

We investigate the reach of future gravitational wave (GW) detectors in probing inflaton couplings with visible sector particles that can either be bosonic or fermionic in nature. Assuming reheating takes place through perturbative quantum production from vacuum in presence of classical inflaton background field, we find that the spectral energy density of the primordial GW generated during inflation becomes sensitive to inflaton-matter coupling. We conclude, obeying bounds from Big Bang Nucleosysthesis and Cosmic Microwave Background, that, e.g., inflaton-scalar couplings of the order of ~ \U0001d4aa(10−20) GeV fall within the sensitivity range of several proposed GW detector facilities. However, this prediction is sensitive to the size of the inflationary scale, nature of the inflaton-matter interaction and shape of the potential during reheating. Having found the time-dependent effective inflaton decay width, we also discuss its implications for dark matter (DM) production from the thermal plasma via UV freeze-in during reheating. It is shown, that one can reproduce the observed DM abundance for its mass up to several PeVs, depending on the dimension of the operator connecting DM with the thermal bath and the associated scale of the UV physics. Thus we promote primordial GW to observables sensitive to feebly coupled inflaton, which is very challenging if not impossible to test in conventional particle physics laboratories or astrophysical measurements.

The Variational Problem and Background Field in the Renormalization Group Method for Nonlinear Sigma Models

We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in d=3,4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d = 3, 4$$\\end{document} and adapt it to a class of nonlinear sigma models in d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document}. The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis.

Strongly coupled QFT dynamics via TQFT coupling

We consider a class of quantum field theories and quantum mechanics, which we couple to ℤN topological QFTs, in order to classify non-perturbative effects in the original theory. The ℤN TQFT structure arises naturally from turning on a classical background field for a ℤN 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to ℤN TQFT, the non-perturbative expansion parameter is exp[−SI/N] = exp[−8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 × {S}_L^1 can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in mathbbm{CP} 1 model, and mass gap for arbitrary θ in mathbbm{CP} N−1, N ≥ 3 on ℝ2.

Entanglement of classical and quantum short-range dynamics in mean-field systems

The relationship between classical and quantum mechanics is usually understood via the limit ħ→0. This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed (Bru and de Siqueira Pedra, 0000; Bru and de Siqueira Pedra, 2021 [46,47]) the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.

One-dimensional long-range Falikov-Kimball model: Thermal phase transition and disorder-free localization

Disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimball model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogenous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised Falikov-Kimball model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov Chain Monte Carlo method to map the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.

Axion assisted Schwinger effect

We point out an enhancement of the pair production rate of charged fermions in a strong electric field in the presence of time dependent classical axion-like background field, which we call axion assisted Schwinger effect. While the standard Schwinger production rate is proportional to exp left(-pi left({m}^2+{p}_T^2right)/Eright) , with m and pT denoting the fermion mass and its momentum transverse to the electric field E, the axion assisted Schwinger effect can be enhanced at large momenta to exp(−πm2/E). The origin of this enhancement is a coupling between the fermion spin and its momentum, induced by the axion velocity. As a non-trivial validation of our result, we show its invariance under field redefinitions associated with a chiral rotation and successfully reproduce the chiral anomaly equation in the presence of helical electric and magnetic fields. We comment on implications of this result for axion cosmology, focussing on axion inflation and axion dark matter detection.

Scalar field theory description of the running vacuum model: the vacuumon

We investigate the running vacuum model (RVM) in the framework of scalar field theory. This dynamical vacuum model provides an elegant global explanation of the cosmic history, namely the universe starts from a non-singular initial de Sitter vacuum stage, it passes smoothly from an early inflationary era to a radiation epoch (“graceful exit”) and finally it enters the dark matter and dark energy (DE) dominated epochs, where it can explain the large entropy problem and predicts a mild dynamical evolution of the DE. Within this phenomenologically appealing context, we formulate an effective classical scalar field description of the RVM through a field ϕ, called the vacuumon, which turns out to be very helpful for an understanding and practical implementation of the physical mechanisms of the running vacuum during both the early universe and the late time cosmic acceleration. In the early universe the potential for the vacuumon may be mapped to a potential that behaves similarly to that of the scalaron field of Starobinsky-type inflation at the classical level, whilst in the late universe it provides an effective scalar field description of DE. The two representations, however, are not physically equivalent since the mechanisms of inflation are entirely different. Moreover, unlike the scalaron, vacuumon is treated as a classical background field, and not a fully fledged quantum field, hence cosmological perturbations will be different between the two pictures of inflation.

Formulating the Kramers problem in field theory

The escape problem is defined in the context of quantum field theory. The escape rate is explicitly derived for a scalar field governed by fluctuation-dissipation dynamics, through generalizing the standard Kramers problem. In the presence of thermal fluctuations, there is a nonvanishing probability for a classical background field, initially located at a minimum of its potential in a homogeneous configuration, to escape from the well. The simple and well-known related problem of the escape of a classical point particle due to random forces is first reviewed. We then discuss the difficulties associated with a well-defined formulation of an escape rate for a scalar field and how these can be overcome. A definition of the Kramers problem for a scalar field and a method to obtain the rate are provided. Finally, we discuss some of the potential applications of our results, which can range from condensed matter systems, i.e., nonrelativistic fields, to applications in high-energy physics, like for cosmological phase transitions.

On Wick Polynomials of Boson Fields in Locally Covariant Algebraic QFT

This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fields are pictured as sections of natural vector bundles over globally hyperbolic spacetimes and quantized through the known functorial machinery in terms of local $^*$-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles, in addition to the Lorentzian metric. The mass and the coupling constants are in particular viewed as background fields. Wick powers of the quantized vector field are axiomatically defined imposing in particular local covariance, scaling properties and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is specialized to the case of general tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields. The notion of local smooth dependence on polynomial scalar invariants is made precise in the text.

Quark and gluon production from a boost-invariantly expanding color electric field

Particle production from an expanding classical color electromagnetic field is extensively studied, motivated by the early stage dynamics of ultra-relativistic heavy ion collisions. We develop a formalism at one-loop order to compute the particle spectra by canonically quantizing quark, gluon and ghost fluctuations under the presence of such an expanding classical color background field; the canonical quantization is done in the $\tau$-$\eta$ coordinates in order to take into account manifestly the expanding geometry. As a demonstration, we model the expanding classical color background field by a boost-invariantly expanding homogeneous color electric field with lifetime $T$, for which we obtain analytically the quark and gluon production spectra by solving the equations of motion of QCD non-perturbatively with respect to the color electric field. In this paper we study (i) finite lifetime effect which is found to modify significantly the particle spectra from those expected from the Schwinger formula; (ii) the difference between the quark and gluon production; and (iii) the quark mass dependence of the production spectra. Implications of these results to ultra-relativistic heavy ion collisions are also discussed.

Multiple Scattering with fully coherent scattering in pA and AA collisions

A new energy loss mechanism model is presented. Medium multiple scattering is modified by the interaction with a classical non-abelian background field. It is shown that the obtained gluon radiation spectrum has a symmetric structure in x (the outgoing radiation energy over incident parton energy) and (1 − x) and the appropriate sign.

Quantum field theory treatment of magnetic effects on the spin and orbital angular momentum of a free electron

We consider in a quantum field theory framework the effects of a classical magnetic field on the spin and orbital angular momentum (OAM) of a free electron. We derive formulae for the changes in the spin and OAM due to the introduction of a general classical background field. We consider then a constant magnetic field, in which case the relevant expressions of the effects become much simpler and conversions between spin and OAM become readily apparent. An estimate of the expectation values for a realistic electron state is also given. Our findings may be of interest to researchers in spintronics and the field of quantum biology, where electron spin has been implicated on macroscopic time and energy scales.

Virasoro conformal blocks and thermality from classical background fields

We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in $AdS_3$, or equivalently, the eigenstate thermalization hypothesis for $CFT_2$ at large central charge.

Generalized global symmetries

A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.

Classical Field Approach to Quantum Weak Measurements

By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and postselection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and postselected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.

Does Planck really rule out monomial inflation?

We consider the modifications of monomial chaotic inflation modelsdue to radiative corrections induced by inflaton couplings to bosonsand/or fermions necessary for reheating. To the lowest order, ignoringgravitational corrections and treating the inflaton as a classicalbackground field, they are of the Coleman-Weinberg type and parametrizedby the renormalization scale μ. In cosmology, there are not enoughmeasurements to fix μ so that we end up with a family of models,each having a slightly different slope of the potential. We demonstrateby explicit calculation that within the family of chaotic ϕ2models, some may be ruled out by Planck whereas some remain perfectlyviable. In contrast, radiative corrections do not seem to help chaoticϕ4 models to meet the Planck constraints.

Fluctuations of the initial color fields in high-energy heavy-ion collisions

In the Color Glass Condensate approach to the description of high energy heavy ion collisions, one needs to superimpose small random Gaussian distributed fluctuations to the classical background field, in order to resum the leading secular terms that result from the Weibel instability, that would otherwise lead to pathological results beyond leading order. In practical numerical simulations, one needs to know this spectrum of fluctuations at a proper time $\tau \ll Q_s^{-1}$ shortly after the collision, in the Fock-Schwinger gauge $A^\tau=0$. In this paper, we derive these fluctuations from first principles, by solving the Yang-Mills equations linearized around the classical background, with plane wave initial conditions in the remote past. We perform the intermediate steps in light-cone gauge, and we convert the results to the Fock-Schwinger gauge at the end. We obtain simple and explicit formulas for the fluctuation modes.

An Improved Quasi-particle Model Framework for Quark-Gluon Plasma from the Path Integral Formalism

An improved framework for the quasi-particle model is presented. Unlike the previous approach of establishing the quasi-particle model, we introduce a classical background field (it is allowed to depend on temperature) to deal with the infinity of thermal vacuum energy which exists in previous quasi-particle models. After taking into account the effect of this classical background field, the partition function of the quasi-particle system can be well defined. Based on this and following the standard ensemble theory, we construct a thermodynamically consistent quasi-particle model without the need to reformulate the statistical mechanics or the thermodynamic consistency relation. It is shown that our method is general and can be generalized to the case in which the effective mass depends not only on the temperature but also on the chemical potential.

Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a “classical measurement process” in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

A thermodynamically consistent quasi-particle model without temperature-dependent infinity of the vacuum zero point energy

In this Letter, an improved quasi-particle model is presented. Unlike the previous approach of establishing quasi-particle model, we introduce a classical background field (it is allowed to depend on the temperature) to deal with the infinity of thermal vacuum energy which exists in previous quasi-particle models. After taking into account the effect of this classical background field, the partition function of quasi-particle system can be made well-defined. Based on this and following the standard ensemble theory, we construct a thermodynamically consistent quasi-particle model without the need of any reformulation of statistical mechanics or thermodynamical consistency relation. As an application of our model, we employ it to the case of (2+1) flavor QGP at zero chemical potential and finite temperature and obtain a good fit to the recent lattice simulation results of Borsányi et al. A comparison of the result of our model with early calculations using other models is also presented. It is shown that our method is general and can be generalized to the case where the effective mass depends not only on the temperature but also on the chemical potential.