Free Fields Research Articles

Operator product expansions and recoil

Some issues of recoil effects in AdS/CFT are studied from the point of view of OPE expansions for generalized free fields. We show that the conformal group structure encodes the relative energies and momenta at a collision center. This is done by being careful with the analysis of Clebsch-Gordan coefficients for an $SL(2)$ subalgebra of the conformal group. The collision fraction of kinetic energy carried by the particles is derived from a probability distribution that arises from these coefficients. We specifically identify a precise statement of when recoil of a heavy particle in AdS can be ignored: the maximum probability is for the heavy particle to be in its ground state. We also argue how a notion of reduced mass appears in these collisions, in the limit where the particles are moving slowly with respect to each other. This controls the notion of the impact parameter of the collision.

Continuous gaussian measurements of the free boson CFT: A model for exactly solvable and detectable measurement-induced dynamics

Hybrid evolution protocols, composed of unitary dynamics and repeated, weak or projective measurements, give rise to new, intriguing quantum phenomena, including entanglement phase transitions and unconventional conformal invariance. Defying the complications imposed by the non-linear and stochastic nature of the measurement process, we introduce a scenario of measurement-induced many body evolution, which possesses an exact analytical solution: bosonic Gaussian measurements. The evolution features a competition between the continuous observation of linear boson operators and a free Hamiltonian, and it is characterized by a unique and exactly solvable covariance matrix. Within this framework, we then consider an elementary model for quantum criticality, the free boson conformal field theory, and investigate in which way criticality is modified under measurements. Depending on the measurement protocol, we distinguish three fundamental scenarios (a) enriched quantum criticality, characterized by a logarithmic entanglement growth with a floating prefactor, or the loss of criticality, indicated by an entanglement growth with either (b) an area-law or (c) a volume-law. For each scenario, we discuss the impact of imperfect measurements, which reduce the purity of the wavefunction and are equivalent to Markovian decoherence, and present a set of observables, e.g., real-space correlations, the relaxation time, and the entanglement structure, to classify the measurement-induced dynamics for both pure and mixed states. Finally, we present an experimental tomography scheme, which grants access to the density operator of the system by using the continuous measurement record only.

Compact QED: the photon propagator, confinement and positivity violation for the pure gauge theory

The lattice Landau gauge photon propagator for the pure gauge theory is revisited by using large lattices. For the confined case we show that it has an associated linearly growing potential, it has a mass gap, that is related to the presence of monopoles, and its spectral function violates positivity. In the deconfined phase, our simulations suggest that a free field theory is recovered in the thermodynamic limit.

Relativistic free electrons based quantum physics

The light-matter interaction is one of the fundamental research fields in physics. The electron is the first discovered elementary particle that makes up matter. Therefore, the interaction between electron and light field has long been the research interest of physicists. Electrons are divided into two kinds, i.e. bounded electrons and free electrons. The quantum transition of bounded electron system is constrained by the selection rules with the discrete energy levels, while the free electron systems are not. In the last decade, the experiments of photon-induced near-field electron microscopy (PINEM) have been demonstrated. The experimental setup of PINEM is based on ultrafast electron transmission microscopy (UTEM). The thoeritcal framworks have also been developed to describe the interaction between quantum free electrons and optical fields. Within macroscopic quantum electrodynamics, the concept of photon is extended to photonic quasi-particles. Solutions of maxwell's equations in medium that satisfy certain boundary conditions are called photonic quasiparticles, such as surface plasmon polaritons, phonon polaritons, or even magnetic field. The different dispersion relations of photonic quasi-particles produce abundant phenomena in the interaction between light and matter. The underlying information about the PINEM interaction can be inferred from the electron energy loss spectrum (EELS). It has been used for implementing the near-field imaging in its infancy. By now it is capable of not only realizing time-resolved dynamic imaging, reconstructing the dispersion relation of photonics crystal and its Bloch mode, but also measuring the mode lifetime directly. The PINEM has also been used to study free electron wavepacket reshaping, free electron comb, free electron attosecond pulse train, etc. Recently, this field has entered into the era of quantum optics, and people use PINEM to study novel phenomena in quantum optics, such as entanglement between free electrons and cavity photons, entanglement between free electrons and free electrons, free electron qubits, and preparation of novel light quantum states. In this paper, the theoretical and experimental development of free-electron quantum physics are reviewed. We have disscussed the application scenarios of quantum free electron system. The current difficulties and future development are envisaged.

RESILIENCIA: ABORDAJE PSICOSOCIAL, ESPIRITUAL Y EDUCATIVO EN EL TRATAMIENTO DEL PACIENTE ADULTO CON OBESIDAD

Introduction: The resilience construct is a dynamic process that can be approached by every human being if they have the resources or are accompanied in the search for those resources to build it. Connecting with sensoriality and body awareness helps to promote the different laws of nutrition enunciated by Professor Escudero. The body trains itself to better perceive the stimuli which are important when it comes to nourishing itself. Objectives: To explore studies carried out on the resilience approach for the treatment of chronic disease; describe the multidisciplinary psychosocial, spiritual and educational approach proposed by resilience for the treatment of adult patients with obesity, identify which resources involve body work and movement in the treatment of obese adult patients. Methods: Literature review design. 44 documents were found. Electronic databases were consulted and citations identified in additional searches were added. Free term, descriptors and search fields were used according to inclusion criteria. Results: The evidence found fundamentally relates chronic diseases with the approach from resilience and subsequently narrates the association of obesity in relation to the therapeutic approach from resilience. From psychosocial intervention, it has been shown that the techniques proposed by the transtheoretical model of Prochaska and Di Clemente, associating them with motivational interviewing, are effective. Cognitive-behavioral treatment also demonstrated efficacy. With respect to spirituality as an approach from resilience, the results are disparate. Regarding the educational approach, favorable results have been found, especially focused on therapeutic education provided by health teams. The practice of movement and bodywork has shown positive results when integrated into therapeutic education workshops. Conclusion: There is evidence of great potential when working from resilience, including dance-therapy practices, for the treatment of adults with obesity. Keywords: resilience; obesity; dance-therapy; psychosocial; spirituality; educational.

Factorization algebras and abelian CS/WZW-type correspondences

We develop a method of quantization for free field theories on manifolds with boundary where the bulk theory is topological in the direction normal to the boundary and a local boundary condition is imposed. Our approach is within the Batalin-Vilkovisky formalism. At the level of observables, the construction produces a stratified factorization algebra that in the bulk recovers the factorization algebra developed by Costello and Gwilliam. The factorization algebra on the boundary stratum enjoys a perturbative bulk-boundary correspondence with this bulk factorization algebra. A central example is the factorization algebra version of the abelian Chern-Simons/Wess-Zumino-Witten correspondence, but we examine higher dimensional generalizations that are related to holomorphic truncations of string theory and $M$-theory and involve intermediate Jacobians.

Machine learning statistical gravity from multi-region entanglement entropy

The Ryu-Takayanagi formula directly connects quantum entanglement and geometry. Yet the assumption of static geometry lead to an exponentially small mutual information between far-separated disjoint regions, which does not hold in many systems such as free fermion conformal field theories. In this paper, we proposed a microscopic model by superimposing entanglement features of an ensemble of random tensor networks of different bond dimensions, which can be mapped to a statistical gravity model consisting of a massive scalar field on a fluctuating background geometry. We propose a machine-learning algorithm that recovers the underlying geometry fluctuation from multi-region entanglement entropy data by modeling the bulk geometry distribution via a generative neural network. To demonstrate its effectiveness, we tested the model on a free fermion system and showed mutual information can be mediated effectively by geometric fluctuation. Remarkably, locality emerged from the learned distribution of bulk geometries, pointing to a local statistical gravity theory in the holographic bulk.

Cluster capacity functionals and isomorphism theorems for Gaussian free fields

We investigate level sets of the Gaussian free field on continuous transient metric graphs widetilde{{mathcal {G}}} and study the capacity of its level set clusters. We prove, without any further assumption on the base graph {mathcal {G}}, that the capacity of sign clusters on widetilde{{mathcal {G}}} is finite almost surely. This leads to a new and effective criterion to determine whether the sign clusters of the free field on widetilde{{mathcal {G}}} are bounded or not. It also elucidates why the critical parameter for percolation of level sets on widetilde{{mathcal {G}}} vanishes in most instances in the massless case and establishes the continuity of this phase transition in a wide range of cases, including all vertex-transitive graphs. When the sign clusters on widetilde{{mathcal {G}}} do not percolate, we further determine by means of isomorphism theory the exact law of the capacity of compact clusters at any height. Specifically, we derive this law from an extension of Sznitman’s refinement of Lupu’s recent isomorphism theorem relating the free field and random interlacements, proved along the way, and which holds under the sole assumption that sign clusters on widetilde{{mathcal {G}}} are bounded. Finally, we show that the law of the cluster capacity functionals obtained in this way actually characterizes the isomorphism theorem, i.e. the two are equivalent.

AdS from CFT for scalar QED

We construct an explicit bulk dual in anti--de Sitter space, with couplings of order $1/N$, for the $SU(N)$-singlet sector of QED in $d$ space-time dimensions ($2<d<4$) coupled to $N$ scalar fields. We begin from the bulk dual for the theory of $N$ complex free scalar fields that we constructed in our previous work, and couple this to $U(1)$ gauge fields living on the boundary in order to get the bulk dual of scalar QED (in which the $U(1)$ gauge fields become the boundary value of the bulk vector fields). As in our previous work, the bulk dual is nonlocal but we can write down an explicit action for it. We focus on the CFTs arising at low energies (or, equivalently, when the $U(1)$ gauge coupling goes to infinity). For $d=3$ we discuss also the addition of a Chern-Simons term for $U(1)$, modifying the boundary conditions for the bulk gauge field. We also discuss the generalization to QCD, with $U({N}_{c})$ gauge fields coupled to $N$ scalar fields in the fundamental representation (in the large $N$ limit with fixed ${N}_{c}$).

ISPH Simulation of Solitary Waves Propagating Over a Bottom-Mounted Barrier With k–ε Turbulence Model

Solitary wave propagating over a bottom-mounted barrier is simulated using the Incompressible Smoothed Particle Hydrodynamics (ISPH) method in order to study the generation and transport of turbulence associated with flow separation around submerged structures. For an accurate capture of turbulence characteristics during the wave propagation, rather than employing the standard sub-particle scale (SPS) model, the k-ε turbulence model is coupled with the numerical scheme. The results of the numerical model are compared with experimental data, and good agreement is observed in terms of mean velocity, free surface elevation, vorticity fields and turbulent kinetic energy. The numerical model is then employed to investigate the effects of wave non-linearity and geometrical size of the submerged barrier on the flow separation; and calculate the reflection, dissipation and transmission coefficients to evaluate the importance of energy dissipation due to the generation of vortices. The results of this study show that the developed ISPH method with the k-ε turbulence closure model is capable of reproducing the velocity fields and the turbulence characteristics accurately, and thus can be used to perform predictions of comprehensive hydrodynamics of flow-structure interactions in the urban hydro-environment systems.

Free scalar correlators in de Sitter space via the stochastic approach beyond the slow-roll approximation

The stochastic approach to calculating scalar correlation functions in de Sitter spacetime is extended beyond the overdamped "slow roll" approximation. We show that with the correct noise term, it reproduces the exact asymptotic long-distance behaviour of field correlators in free field theory, thereby demonstrating the viability of the technique. However, we also show that the na\"ive way of calculating the noise term by introducing a cut-off at the horizon does not give the correct answer unless the cut-off is chosen specifically to give the required result. We discuss the implications of this for interacting theories.

Relative entropy and curved spacetimes

Given any half-sided modular inclusion of standard subspaces, we show that the entropy function associated with the decreasing one-parameter family of translated standard subspaces is convex for any given (not necessarily smooth) vector in the underlying Hilbert space. In second quantisation, this infers the convexity of the vacuum relative entropy with respect to the translation parameter of the modular tunnel of von Neumann algebras. This result allows us to study the QNEC inequality for coherent states in a free Quantum Field Theory on a stationary curved spacetime, given a KMS state. To this end, we define wedge regions and appropriate (deformed) subregions. Examples are given by the Schwarzschild spacetime and null translated subregions with respect to the time translation Killing flow. More generally, we define wedge and strip regions on a globally hyperbolic spacetime, so to have non trivial modular inclusions of von Neumann algebras, and make our analysis in this context.

Dosimetric Impact of Systematic and Random Errors With Multi-Leaf Collimator Leaf Positioning in Intracranial Stereotactic Radiosurgery

Modern medical Linac equipped with multileaf collimators (MLC) are widely used for intracranial stereotactic radiosurgery (SRS). This study aimed to evaluate dosimetric impact of systematic and random positioning errors with MLC leaves and to establish practical limits on MLC leaf positioning uncertainties in SRS treatments.A single institution retrospective review identified 10 clinical single-target conformal arc SRS plans and 7 single- or multiple-target VMAT SRS plans treating a total of 15 PTVs. Each conformal arc SRS plan was prescribed 20 Gy in one fraction to a PTV using 2-5 arc fields with PTV volume ranging from 0.10 to 2.48 cc, and each volumetric modulated arc therapy (VMAT) SRS plan was prescribed 20 - 27 Gy in 1 - 5 fractions to 1 - 4 PTVs, with PTV volume ranging from 0.11 to 7.73 cc. 6-MV flattening-filter free photon fields were used in all the plans. A 120-leaf MLC was used for beam modulation with a leaf width of 2.5 mm for the central 32 leaf-pairs and 5.0 mm for the peripheral 28 leaf-pairs. Systematic or random leaf positioning errors ranging from 0.1 to 1.0 mm at 0.1-mm intervals were introduced to each SRS plan. Plan dose was re-calculated with original field MUs with a 1.0 mm calculation resolution using a linear Boltzmann transport algorithm and was verified using another dose calculation engine with a convolution superposition algorithm. Variations in PTV dosimetric parameters including mean dose and D(95%) due to systematic and random leaf positioning errors were analyzed. PTV dose variation was also verified with measurement using an ion chamber in water equivalent phantom.Both the PTV mean dose and D(95%) decreased linearly with increasing systematic and random positioning errors in all the SRS plans. In systematic leaf positioning errors with a 1-mm shift towards the isocenter for all MLC leaves, the PTV mean dose and D(95%) decreased by an average of 8.7% (range: 5.1 - 12.4%) and 15.2% (range: 10.4 - 20.1%) respectively in the conformal arc plans; the PTV mean dose and D(95%) decreased by an average of 18.2% (range: 11.6 - 25.0%) and 21.8% (range: 15.1 - 27.3%) respectively in the VMAT plans. The PTV volume positively correlated with the declining rate of mean PTV dose (correlation coefficient: 0.80, P-value = 0.01) with the conformal arc SRS plans. In random leaf positioning errors, with a standard deviation of up to 1 mm, the decrease of PTV mean dose and D(95%) was up to 2.4% and 3.3% respectively in the conformal arc plans, and decreased up to 2.7% and 2.8% respectively in the VMAT plans.Manufacturers' specifications for MLC leaf positioning accuracy are not adequate for accurate intracranial SRS dose delivery. To ensure that both the PTV mean dose and D(95%) are within 5% from plan dose, the systematic MLC leaf positioning error needs to be < 0.3 mm for conformal arc SRS plans and < 0.2 mm for VMAT SRS plans. On the other hand, random leaf positioning errors have smaller impact on dose delivery accuracy within the limits specified by manufacturers.C. Han: None. J.R. Liu: None. D. Du: None. J. Liang: None. K. Qing: None. W.T. Watkins: None. S. Zhang: None. A. Liu: None.

Scattering of plane waves by a 3D canyon in a transversely isotropic fluid-saturated layered half-space

Scattering of plane waves by a three-dimensional (3D) irregularity in a transversely isotropic (TI) fluid-saturated layered half-space is investigated for the first time. The derived exact stiffness matrix is applied to solve the dynamic response of free fields. The scattered fields, which arise from the presence of canyon irregularity, are described by applying dynamic Green's functions for uniformly distributed loads and pore pressure acting on an inclined plane, that is, the special indirect boundary element method (IBEM). The accuracy of the proposed method is verified via the comparison between the calculated results and those of published literature. By taking a semi-spherical canyon cut in a homogeneous, single-layered, and three-layered TI saturated half-space as examples, the influences of material anisotropy, boundary drainage condition, and sedimentary sequence on dynamic response are investigated. The results show that the material anisotropy and boundary drainage conditions all have a significant impact on the seismic responses, which is highly dependent on the waves type, incident angle, and frequency. For the layered medium, the displacement amplification is affected by the soil layer properties and sedimentary sequence.

Odd entanglement entropy and logarithmic negativity for thermofield double states

We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zero-mode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times t < β/2 (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times t < d/2 (half of the distance between intervals). We also find a similar delay to see linear growth of ∆S = SOEE− SEE. All these results show that the dynamics of these measures are consistent with the quasi-particle picture, of course apart from the logarithmic growth.

Mellin amplitudes for 1d CFT

We define a Mellin amplitude for CFT1 four-point functions. Its analytical properties are inferred from physical requirements on the correlator. We discuss the analytic continuation that is necessary for a fully nonperturbative definition of the Mellin transform. The resulting bounded, meromorphic function of a single complex variable is used to derive an infinite set of nonperturbative sum rules for CFT data of exchanged operators, which we test on known examples. We then consider the perturbative setup produced by quartic interactions with an arbitrary number of derivatives in a bulk AdS2 field theory. With our formalism, we obtain a closed-form expression for the Mellin transform of tree-level contact interactions and for the first correction to the scaling dimension of “two-particle” operators exchanged in the generalized free field theory correlator.

Disks globally maximize the entanglement entropy in 2 + 1 dimensions

The entanglement entropy corresponding to a smooth region in general three-dimensional CFTs contains a constant universal term, −F ⊂ SEE. For a disk region, F|disk ≡ F0 coincides with the free energy on \U0001d54a3 and provides an RG-monotone for general theories. As opposed to the analogous quantity in four dimensions, the value of F generally depends in a complicated (and non-local) way on the geometry of the region and the theory under consideration. For small geometric deformations of the disk in general CFTs as well as for arbitrary regions in holographic theories, it has been argued that F is precisely minimized by disks. Here, we argue that F is globally minimized by disks with respect to arbitrary regions and for general theories. The proof makes use of the strong subadditivity of entanglement entropy and the geometric fact that one can always place an osculating circle within a given smooth entangling region. For topologically non-trivial entangling regions with nB boundaries, the general bound can be improved to F ≥ nBF0. In addition, we provide accurate approximations to F valid for general CFTs in the case of elliptic regions for arbitrary values of the eccentricity which we check against lattice calculations for free fields. We also evaluate F numerically for more general shapes in the so-called “Extensive Mutual Information model”, verifying the general bound.

Charging up the functional bootstrap

We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on the line. The first, which we call “simple”, is essentially a direct sum of analytic functionals for the uncharged case. We use it to establish very general bounds on the OPE density appearing in charged correlators. The second basis is dual to generalized free fields and we explain how it is related to a charged version of the Polyakov bootstrap. We apply these functionals to map out the space of correlators and obtain new improved bounds on the 3d Ising twist defect.

From quantum field theory to quantum mechanics

The purpose of this article is to construct an explicit relation between the field operators in Quantum Field Theory and the relevant operators in Quantum Mechanics for a system of N identical particles, which are the symmetrised functions of the canonical operators of position and momentum, thus providing a clear relation between Quantum Field Theory and Quantum Mechanics. This is achieved in the context of the non-interacting Klein–Gordon field. Though this procedure may not be extendible to interacting field theories, since it relies crucially on particle number conservation, we find it nevertheless important that such an explicit relation can be found at least for free fields. It also comes out that whatever statistics the field operators obey (either commuting or anticommuting), the position and momentum operators obey commutation relations. The construction of position operators raises the issue of localizability of particles in Relativistic Quantum Mechanics, as the position operator for a single particle turns out to be the Newton–Wigner position operator. We make some clarifications on the interpretation of Newton–Wigner localized states and we consider the transformation properties of position operators under Lorentz transformations, showing that they do not transform as tensors, rather in a manner that preserves the canonical commutation relations. From a complex Klein–Gordon field, position and momentum operators can be constructed for both particles and antiparticles.

Long Distance Entanglement of Purification and Reflected Entropy in Conformal Field Theory.

Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both the entanglement of purification and reflected entropy is enhanced with respect to the mutual information behavior by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest.