Scalar Field Theory Research Articles

The discreet charm of the discrete series in dS2

We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS2) with an eye on the group-theoretic organization of single and multi-particle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realize these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén–Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories with SL(N,R) gauge group in dS2 and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to the SL(N,R) BF theory in the large-N limit.

Wobbling kinks and shape mode interactions in a coupled two-component [formula omitted] theory

The dynamics of a wobbling kink in a two-component coupled ϕ4 scalar field theory (with an excited orthogonal shape mode) is addressed. For this purpose, the vibration spectrum of the second order small kink fluctuation is studied in order to find the corresponding vibration modes associated to the first (longitudinal) and second (orthogonal) field components. By means of this analysis, it was found that the number of possible shape modes depends on the value of the coupling constant. It is notable that when one of the orthogonal field shape modes is initially triggered, the unique shape mode of the longitudinal field is also activated. This coupling causes the kink to emit radiation with twice the frequency of excited mode in the first field component. Meanwhile, in the orthogonal channel we find radiation with two different frequencies: one is three times the frequency of the orthogonal wobbling mode and another is the sum of the frequencies of the longitudinal shape mode and the triggered mode. All the analytical results obtained in this study have been successfully contrasted with those obtained through numerical simulations.

A coherent state approach to the Casimir effect for a massive scalar field in a noncommutative spacetime

In this paper we investigate the Casimir effect in the classical geometry of two parallel conducting plates, separated by a distance L, for a massive scalar field in a noncommutative spacetime within a coherent state approach. Noncommutative geometry is implemented by means of modified commutation relations for the spacetime coordinates, thus introducing a fundamental length scale l in the theory. Following a coordinate coherent states approach, we define mean values over the noncommutative spacetime and introduce the massive scalar field theory. We derive an expression for the zero-point energy which we evaluate by means of a dimensional regularization process. We express the Casimir energy in terms of powers of the ratios (l/L)2n in the massless case and (ml2/L)2n in the massive case. Our results are discussed both, theoretically and numerically. We finally estimate boundary effects by introducing an specific model for the plates.

Scaled affine quantization of φ312 is nontrivial

We prove through path integral Monte Carlo that the covariant Euclidean scalar field theory, [Formula: see text], where [Formula: see text] denotes the power of the interaction term and [Formula: see text] with [Formula: see text] as the spatial dimension and 1 adds imaginary time, such that [Formula: see text], [Formula: see text] can be acceptably quantized using scaled affine quantization (AQ) and the resulting theory is nontrivial, unlike what happens using canonical quantization which finds it trivial.

Coarsening and wavelength selection far from equilibrium: A unifying framework based on singular perturbation theory.

Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory exists for the dynamics of fully nonlinear patterns. We develop a unifying theory for nonlinear wavelength-selection dynamics in (nearly) mass-conserving two-component reaction-diffusion systems independent of the specific mathematical model chosen. Previous work has shown that these systems support an extremely broad band of stable wavelengths, but the mechanism by which a specific wavelength is selected has remained unclear. We show that an interrupted coarsening process selects the wavelength at the threshold to stability. Based on the physical intuition that coarsening is driven by competition for mass and interrupted by weak source terms that break strict mass conservation, we develop a singular perturbation theory for the stability of stationary patterns. The resulting closed-form analytical expressions enable us to quantitatively predict the coarsening dynamics and the final pattern wavelength. We find excellent agreement with numerical results throughout the diffusion- and reaction-limited regimes of the dynamics, including the crossover region. Further, we show how, in these limits, the two-component reaction-diffusion systems map to generalized Cahn-Hilliard and conserved Allen-Cahn dynamics, therefore providing a link to these two fundamental scalar field theories. The systematic understanding of the length-scale dynamics of fully nonlinear patterns in two-component systems provided here builds the basis to reveal the mechanisms underlying wavelength selection in multicomponent systems with potentially several conservation laws.

Constructing Carrollian field theories from null reduction

In this paper, we propose a novel way to construct off-shell actions of d-dimensional Carrollian field theories by considering the null-reduction of the Bargmann invariant actions in d +1 dimensions. This is based on the fact that d-dimensional Carrollian symmetry is the restriction of the (d + 1)-dimensional Bargmann symmetry to a null hypersurface. We focus on free scalar field theory and electromagnetic field theory, and show that the electric sectors and the magnetic sectors of these theories originate from different Bargmann invariant actions in one higher dimension. In the cases of massless free scalar field and d = 4 electromagnetic field, we verify the Carrollian conformal invariance of the resulting theories, and find that there appear naturally chain representations and staggered modules of Carrollian conformal algebra.

Higher-Order Corrections to the Effective Field Theory of Low-Energy Axions

Dark matter (DM) can be composed of a collection of axions, or axion-like particles (ALPs), whose existence is due to the spontaneous breaking of the Peccei–Quinn U(1) symmetry, which is the most compelling solution of the strong CP-problem of quantum chromodynamics (QCD). Axions must be spin-0 particles with very small masses and extremely weak interactions with themselves as well as with the particles that constitute the Standard Model. In general, the physics of axions is detailed by a quantum field theory of a real scalar field, ϕ. Nevertheless, it is more convenient to implement a nonrelativistic effective field theory with a complex scalar field, ψ, to characterize the mentioned axions in the low-energy regime. A possible application of this equivalent description is for studying the collapse of cold dark matter into more complex structures. There have been a few derivations of effective Lagrangians for the complex field ψ, which were all equivalent after a nonlocal space transformation between ϕ and ψ was found, and some other corrections were introduced. Our contribution herein is to further provide higher-order corrections; in particular, we compute the effective field theory Lagrangian up to order (ψ*ψ)5, also incorporating the fast-oscillating field fluctuations into the dominant slowly varying nonrelativistic field.

Quantum flux operators for Carrollian diffeomorphism in general dimensions

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a central charge, respectively. At future/past null infinity, the fluxes are physically observable and encode rich information of the radiation. The central charge may be regularized to be finite by the spectral zeta function or heat kernel method on the unit sphere. For the theory at the Rindler horizon, the effective central charge is proportional to the area of the bifurcation surface after regularization. Moreover, the zero mode of supertranslation is identified as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum information theory. Our results may hold for general null hypersurfaces and provide new insight in the study of the Carrollian field theory, asymptotic symmetry group and entanglement entropy.

Noncommutative scalar field theory in a curved background: Duality between noncommutative and effective commutative description

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner–Nordström-like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed [Formula: see text] gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call “duality between formal and effective approach”. We also show that a NC deformation via semi-Killing twist operator cannot be rewritten in terms of an effective metric. There is dual description for those particular deformations.

Multisoliton complex systems with explicit superpotential interactions

We consider scalar field theories in dimensions with N fields which interact through a potential , which is defined in terms of an explicit superpotential W. We construct W for any N in terms of a known superpotential w for a single-scalar model, such as that for the sine-Gordon equation or the ϕ 4 model, leading to an expression for V which has multiple minima that supports solitons. Static solitons which minimize the total energy in each soliton sector appear as solutions of first-order Bogomolny equations, which have a gradient structure. These are identical in form to equations which arise in the context of synchronization phenomena in complex systems, with the space and time variables interchanged. The sine-Gordon superpotential, for example, leads to an explicit periodic superpotential W for N scalar fields, with associated Bogomolny equations that are equivalent to the well-known Kuramoto equations which describe the synchronization of identical phase oscillators on the unit circle. The known asymptotic properties of the Kuramoto system, for both positive and negative coupling constants, ensure that finite-energy solitons exist for any given set of intermediate values imposed at the origin. Besides the models derived from the sine-Gordon equation, we investigate ϕ 4 and ϕ 6 models with N scalar fields and show numerically that solitons again exist over a wide range of parameters. We also derive general properties of the elementary meson excitations of the system, in particular we show that meson-soliton bound states exist over a restricted range of mass parameters with respect to an exact solution of the ϕ 6 system for N = 3.

Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime

Asymptotic behavior of solutions and spectrum of states in the quantum scalar field theory in the Schwarzschild spacetime

Effective field theories as Lagrange spaces

We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry.

Towards a bound on the Higgs mass in causal set quantum gravity

In the Standard Model of particle physics, the mass of the Higgs particle can be linked to the scale at which the Standard Model breaks down due to a Landau pole/triviality problem: for a Higgs mass somewhat higher than the measured value, the Standard Model breaks down before the Planck scale. We take a first step towards investigating this relation in the context of causal set quantum gravity. We use a scalar-field propagator that carries the imprints of spacetime discreteness in a modified ultraviolet behavior that depends on a nonlocality scale. We investigate whether the modification can shift the scale of the Landau pole in a scalar field theory with quartic interaction. We discover that the modifications speed up the onset of the Landau pole considerably, so that the scale of new physics occurs roughly at the nonlocality scale. Our results call into question, whether a separation between the nonlocality scale and the discreteness scale, which is postulated within causal set quantum gravity, and which has been argued to give rise to phenomenological consequences, is in fact achievable. Methodologically, our paper is the first to apply continuum functional Renormalization Group techniques in the context of a causal-set inspired setting.

Quantum computation of phase transition in interacting scalar quantum field theory

Quantum computation of phase transition in interacting scalar quantum field theory

Estimating truncation effects of quantum bosonic systems using sampling algorithms

To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations.

What if ϕ4 theory in 4 dimensions is non-trivial in the continuum?

Traditionally, scalar ϕ4 theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and mathematical proofs. Digging into the proofs one finds that they do not actually cover all physically meaningful situations, in particular the case of multi-component fields and non-polynomial action. In this work, I study multi-component scalar field theories in four dimensions in the continuum and show that they do evade the apparently foregone conclusion of triviality. Instead, one finds a non-trivial interacting theory that has two phases, bound states and non-trivial scattering amplitudes in the limit of many components. This has potentially broad implications, both for the foundations of quantum field theory as well as for the experimentally accessible Higgs sector of the Standard Model.

Entanglement of harmonic systems in squeezed states

The entanglement entropy of a free scalar field in its ground state is dominated by an area law term. It is noteworthy, however, that the study of entanglement in scalar field theory has not advanced far beyond the ground state. In this paper, we extend the study of entanglement of harmonic systems, which include free scalar field theory as a continuum limit, to the case of the most general Gaussian states, namely the squeezed states. We find the eigenstates and the spectrum of the reduced density matrix and we calculate the entanglement entropy. We show that our method is equivalent to the correlation matrix method. Finally, we apply our method to free scalar field theory in 1+1 dimensions and show that, for very squeezed states, the entanglement entropy is dominated by a volume term, unlike the ground-state case. Even though the state of the system is time-dependent in a non-trivial manner, this volume term is time-independent. We expect this behaviour to hold in higher dimensions as well, as it emerges in a large-squeezing expansion of the entanglement entropy for a general harmonic system.

Weak vs. strong breaking of integrability in interacting scalar quantum field theories

The recently proposed classification of integrability-breaking perturbations according to their strength is studied in the context of quantum field theories. Using random matrix methods to diagnose the resulting quantum chaotic behaviour, we investigate the \phi^4ϕ4 and \phi^6ϕ6 interactions of a massive scalar, by considering the crossover between Poissonian and Wigner-Dyson distributions in systems truncated to a finite-dimensional Hilbert space. We find that a naive extension of the scaling of crossover coupling with the volume observed in spin chains does not give satisfactory results for quantum field theory. Instead, we demonstrate that considering the scaling of the crossover coupling with the number of particles yields robust signatures, and is able to distinguish between the strengths of integrability breaking in the \phi^4ϕ4 and \phi^6ϕ6 quantum field theories.

Mechanization of a scalar field theory in 1+1 dimensions: Bogomol'nyi-Prasad-Sommerfeld mechanical kinks and their scattering.

We present an updated version of a general-purpose collective coordinate model that aims to fully map out the dynamics of a single scalar field in 1+1 dimensions. This is achieved by a procedure that we call a mechanization, in which we reduce the infinite number of degrees of freedom down to a finite and controllable number by chopping the field into flat segments connected via joints. In this paper we introduce two new ingredients to our procedure. The first is a manifestly Bogomol'nyi-Prasad-Sommerfeld (BPS) mechanization in which BPS mechanical kinks saturate the same bound on energy as their field-theoretic progenitors. The second is allowing the joints to switch, leading to an extended concept of the effective Lagrangian, through which we describe direct collisions of mechanical kinks and antikinks.

Scaling violation and the appearance of mass in scalar quantum field theories

В безмассовых квантово-полевых теориях в логарифмических размерностях нарушается скейлинг. Рассматривается возможность интерпретации этого эффекта как спонтанного появления массы в рамках скелетных уравнений самосогласования с полным пропагатором в моделях с взаимодействиями $\varphi^3$, $\varphi^4$, $\varphi^6$ скалярного поля $\varphi$.