Modified microcausality from perturbation theory

Higher derivative field theories with interactions raise serious doubts about their validity due to severe energy instabilities. In many cases the implementation of a direct perturbation treatment to excise the dangerous negative-energies from a higher derivative field theory may lead to violations of Lorentz and other symmetries. In this work we study a perturbative formulation for higher derivative field theories that allows the construction of a low-energy effective field theory being a genuine perturbations over the ordinary-derivative theory and having a positive-defined Hamiltonian. We show that some discrete symmetries are recovered in the low-energy effective theory when the perturbative method to reduce the negative-energy degrees of freedom from the higher derivative theory is applied. In particular, we focus on the higher derivative Maxwell-Chern-Simons model which is a Lorentz invariant and parity-odd theory in $2+1$ dimensions. The parity violation arises in the effective action of ${\mathrm{QED}}_{3}$ as a quantum correction from the massive fermionic sector. We obtain the effective field theory which remains Lorentz invariant, but parity invariant to the order considered in the perturbative expansion.

From the Hubbard model to a systematic low-energy effective field theory for magnons and holes in an antiferromagnet

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute -- given a many-body state, $\mathcal{O}_x(t) \mathcal{O}_y |\psi\rangle \approx \mathcal{O}_y\mathcal{O}_x(t) |\psi\rangle$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance $r$ interact with potential energy $V(r) \propto 1/r^{\alpha}$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, this linear light cone exists for every many-body state when $\alpha>3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $\alpha>\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $\alpha>2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones -- and their tightness -- also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

On the nonlinear properties of retarded products

The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which seems difficult to remove. We solve this problem here by another strategy: the fields at a point in the interaction Lagrangian are replaced by the fields at a quantum point, described by an optimally localized state on QST; the resulting Lagrangian density agrees with the previous one after spacetime integration, but gives rise to a different interaction hamiltonian. But now the methods of perturbative Algebraic Quantum Field Theory can be applied, and produce an ultraviolet finite perturbation expansion of the interacting observables. If the obtained theory is tested in an equilibrium state at finite temperature the adiabatic cutoff in time becomes immaterial, namely it has no effect on the correlation function at any order in perturbation theory. Moreover, the interacting vacuum state can be obtained in the vanishing temperature limit. It is nevertheless important to stress that the use of states which are optimally localized for a given observer brakes Lorentz invariance at the very beginning.

The rotational g factors of the hydrogen halides, HX (X=F,Cl,Br,I), and noble gas hydride cations, XH+ (X=Ne,Ar,Kr,Xe), have been calculated at the level of the random phase approximation (RPA) as relativistic four-component linear response functions as well as nonrelativistic linear response functions. In addition, using perturbation theory with the mass-velocity and Darwin operators as perturbations, the relativistic corrections have been estimated as quadratic response functions. It was found that the four-component relativistic calculations give in general a more negative electronic contribution to the rotational g factor than the nonrelativistic calculations with relativistic corrections ranging from 0.2% for HF and NeH+ to 2.9% for XeH+ and 3.5% for HI. The estimates of the relativistic corrections obtained by perturbation theory with the mass-velocity and Darwin operators are in good agreement with the four-component results for HF, HCl, NeH+, and ArH+, whereas for HI, KrH+, and XeH+ they have the wrong sign.

In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interaction which includes fully the retardation effect in it. This term plus the linear confining potential are chosen to be the interaction Hamiltonian and employed in the practical calculation. With the integrals containing three and four spherical Bessel functions in the QCD vertices being analytically calculated, the interaction Hamiltonian is given an explicit expression in the angular momentum representation. Numerically solving the relativistic equation with taking the contributions arising from the retardation effect and the longitudinal mode of gluon fields into account, a set of masses for the ${0}^{++}{,0}^{\ensuremath{-}+}{,1}^{++}{,1}^{\ensuremath{-}+}{,2}^{++},$ and ${2}^{\ensuremath{-}+}$ glueball states are obtained and are in fairly good agreement with the predictions given by the lattice simulation. In addition, some new glueball states are predicted.

The standard approaches of phenomenology of Quantum Gravity have usually explicitly violated Lorentz invariance, either in the dispersion relation or in the addition rule for momenta. We investigate whether it is possible in 3+1 dimensions to have a non local deformation that preserves fully Lorentz invariance, as it is the case in 2+1D Quantum Gravity. We answer positively to this question and show for the first time how to construct a homogeneously curved momentum space preserving the full action of the Lorentz group in dimension 4 and higher, despite relaxing locality. We study the property of this relative locality deformation and show that this space leads to a noncommutativity related to Snyder spacetime.

From a geometric point of view, massless spinors in 3+1 dimensions are composed of primary fields of weights [Formula: see text] and [Formula: see text], where the weights are defined with respect to diffeomorphisms of a sphere in momentum space. The Weyl equation thus appears as a consequence of the transformation behavior of local sections of half-canonical bundles under a change of charts. As a consequence, it is possible to impose covariant constraints on spinors of negative (positive) helicity in terms of (anti-)holomorphy conditions. Furthermore, the identification with half-differentials is employed to determine possible extensions of fermion propagators compatible with Lorentz covariance.

In spontaneously broken non-Abelian gauge theories which admit gauge hierarchy at the tree level, we show, to all orders in perturbation theory, that (i) the superheavy particles decouple from the light sector at low energies, (ii) an effective low-energy renormalizable theory emerges together with appropriate counterterms, and (iii) the gauge hierarchy can be consistently maintained in the presence of radiative corrections. These assertions are explicitly demonstrated for O(3) gauge theory with two triplets of Higgs particles in a manner easily applicable to more realistic grand unified theories. Furthermore, as a byproduct of our analysis, we obtain a systematic method of computing the parameters of the effective low-energy theory via renormalization-group equations to any desired accuracy.

Non-radiative bound states in the continuum (BICs) allow construction of resonant cavities with confined electromagnetic energy and high-quality (Q) factors. However, the sharp decay of the Q factor in the momentum space limits their usefulness for device applications. Here we demonstrate an approach to achieve sustainable ultrahigh Q factors by engineering Brillouin zone folding-induced BICs (BZF-BICs). All the guided modes are folded into the light cone through periodic perturbation that leads to the emergence of BZF-BICs possessing ultrahigh Q factors throughout the large, tunable momentum space. Unlike conventional BICs, BZF-BICs show perturbation-dependent dramatic enhancement of the Q factor in the entire momentum space and are robust against structural disorders. Our work provides a unique design path for BZF-BIC-based silicon metasurface cavities with extreme robustness against disorder while sustaining ultrahigh Q factors, offering potential applications in terahertz devices, nonlinear optics, quantum computing, and photonic integrated circuits.

Finite model of four-fermion interactions with indefinite metric

We consider the light-cone (LC) gauge and LC quantization of the dimensional reduction of super Yang Mills theory from four to two dimensions. After integrating out all unphysical degrees of freedom, then on-local LC Hamiltonian exhibits an explicit \( \mathcal{N} = \left( {2,2} \right) \) supersymmetry. A further SUSY-preserving compactification of LC-space on a torus of radius R, allows for a large-N numerical study where the smooth large-R limit of physical quantities can be checked. As a first step, we consider a simple, yet quite rich, “Coulomb approximation” that maintains an \( \mathcal{N} = \left( {1,1} \right) \) subgroup of the original supersymmetry and leads to a non-trivial generalization of ’t Hooft’s model with an arbitrary –but conserved– number of partons. We compute numerically the eigenvalues and eigenvectors both in momentum and in position space. Our results, so far limited to the sectors with 2, 3 and 4 partons, directly and quantitatively confirm a simple physical picture in terms of a string-like interaction with the expected tension among pairs of nearest-neighbours along the single-trace characterizing the large-N limit. Although broken by our approximation, traces of the full \( \mathcal{N} = \left( {2,2} \right) \) supersymmetry are still visible in the low-lying spectrum.

Crossing symmetry asserts that particles are indistinguishable from antiparticles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios in a scattering experiment are described by one and the same function. Why could we expect it to be true? In this work we examine this question in a simplified setup and take steps towards illuminating a possible physical interpretation of crossing symmetry. To be more concrete, we consider planar scattering amplitudes involving any number of particles with arbitrary spins and masses to all loop orders in perturbation theory. We show that by deformations of the external momenta one can smoothly interpolate between pairs of crossing channels without encountering singularities or violating mass-shell conditions and momentum conservation. The analytic continuation can be realized using two types of moves. The first one makes use of an iϵ prescription for avoiding singularities near the physical kinematics and allows us to adjust the momenta of the external particles relative to one another within their light cones. The second, more violent, step involves a rotation of subsets of particle momenta via their complexified light cones from the future to the past and vice versa. We show that any singularity along such a deformation would have to correspond to two beams of particles scattering off each other. For planar Feynman diagrams, these kinds of singularities are absent because of the particular flow of energies through their propagators. We prescribe a five-step sequence of such moves that combined together proves crossing symmetry for planar scattering amplitudes in perturbation theory, paving a way towards settling this question for more general scattering processes in quantum field theories.

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function [1]. Analyticity of the formula in s implies that the scaling dimensions of the defect operators are aligned in Regge trajectories widehat{Delta}(s) . These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large s spectrum in the spirit of the work of Alday and Maldacena [2].