arXiv subjects

Olindo Corradini

Publications and source records attributed to Olindo Corradini.

At least 19 recordsLinked to original sources

arXiv2026

An Algebraic Obstruction to Ising Criticality for Finite-BCH Entanglers in Wavelet MERA

The computational treatment of non-Gaussian entanglers could pose a significant challenge when extending the Multi-Scale Entanglement Renormalization Ansatz (MERA) to interacting quantum field theories. A natural strategy is therefore to consider polynomial entanglers for which the Baker-Campbell-Hausdorff (BCH) expansion terminates at finite order. In this work, we identify an algebraic obstruction that limits the universality classes accessible to this family of entanglers. Working within the wavelet MERA (wMERA) framework applied to the interacting $\phi^4$ theory in two dimensions, we show analytically that the effective potential generated by any finite-BCH polynomial entangler is necessarily of Landau form in the generic case, establishing mean-field universality for the full class; in non-generic, degenerate cases the resulting exponent departs from mean-field but still fails to reproduce the Ising value. As a numerical illustration, the critical exponent $\beta$ remains consistent with its mean-field value $\beta = 1/2$ across all ans\"{a}tze considered, with no drift toward the Ising value $\beta = 1/8$ as the nonlocality range or variational complexity increases. Reproducing non-mean-field criticality therefore might require non-polynomial or infinite-BCH constructions.

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arXiv2025

Multi-particle quantum systems within the Worldline Monte Carlo formalism

We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.

quant-ph↗

arXiv2025

Gluon amplitudes in first quantization

We compute tree-level gluon amplitudes as worldline correlators of vertex operators in a bosonic spinning particle model. In this framework, the particle's position degrees of freedom are extended by complex bosonic variables that encode its spin. In the free theory, the model exhibits a first-class constraint algebra whose gauging ensures the unitarity of the quantum theory. This algebra is a contraction of the $sl(2,\mathbb{R})$ algebra, which is by itself a subalgebra of the Virasoro algebra. In string theory, gauging the Virasoro algebra plays a similar role. Our model admits a consistent truncation to describe a pure spin-1 particle. Non-abelian interactions are introduced by using BRST techniques, which allow us to extract the vertex operators of the theory as suitable deformations of the BRST charge. BRST invariance is central to ensuring the consistency of the tree-level amplitudes analyzed in this work. We discuss connections with similar worldline constructions and comment on the potential relevance of this framework for uncovering the structures underlying the double-copy program in gauge and gravitational theories.

hep-th↗

arXiv2022

Obtaining fully polarised amplitudes in gauge invariant form

We describe progress applying the \textit{Worldline Formalism} of quantum field theory to the fermion propagator dressed by $N$-photons to study multi-linear Compton scattering processes, explaining how this approach -- whose calculational advantages are well-known at multi-loop order -- yields compact and manifestly gauge invariant scattering amplitudes.

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arXiv2022

Dimensional Regularization for the Particle Transition Amplitude in Curved Space

We compute the perturbative short-time expansion for the transition amplitude of a particle in curved space time, by employing Dimensional Regularization (DR) to treat the divergences which occur in some Feynman diagrams. The present work generalizes known results where DR was applied to the computation of one-loop effective actions, which in the worldline approach are linked to particle path integrals on the circle, i.e. with periodic boundary conditions. The main motivation of the present work comes from revived interest in particle transition amplitudes in curved space-times, due to their use in the recently proposed worldline quantum field theory (in curved space-time).

hep-th↗

arXiv2021

Spinning Particles in Quantum Mechanics and Quantum Field Theory

These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and Conformal Geometry, held at Morelia, Mexico, from November 19 through November 23, 2012. The lectures were addressed to graduate level students with a background in relativistic quantum mechanics and at least a rudimentary knowledge of field theory. They have since been updated to include a further set of lecture notes on tree level processes from a worldline perspective based on a mini-course by James P. Edwards at the Instituto de Fisica y Matematicas in Morelia, Mexico given to graduates and visiting professors during July 2017 and in various later classes, complemented by a series of three lectures titled New techniques for amplitude calculation in QED given by Naser Ahmadiniaz at the Center for Relativistic Laser Science (CoReLS), Institute for Basic Science(IBS), November 2015, Gwangju, South Korea and as an invited lecturer at the Helmholtz International Summer School (HISS) - Dubna International Advanced School of Theoretical Physics (DIAS-TH): 'Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks', July-August 2019, Dubna, Russia. These additional notes complete the picture of first quantised techniques and bring the worldline description up to date. The extended Abstract can be found in the manuscript.

hep-th↗

arXiv2021

Manifest colour-kinematics duality and double-copy in the string-based formalism

The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy colour-kinematics duality. In previous work it has been show that this arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and here we show that the tensor product for multi-particle fields arise naturally in the Bern-Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents, and to obtain both the colour-dressed Yang-Mills Berends-Giele currents in the Bern-Carrasco-Johansson gauge and the gravitational Berends-Giele currents explicitly. An attractive feature of our formalism is that it never becomes necessary to determine gauge transformation terms. Our double-copy prescription can also be applied to other cases, and to make this point we derive the double-copy perturbiners for $α'$-deformed gravity and the bi-adjoint scalar model.

hep-th↗

arXiv2021

Dressed Dirac Propagator from a Locally Supersymmetric ${\cal N}=1$ Spinning Particle

We study the Dirac propagator dressed by an arbitrary number $N$ of photons by means of a worldline approach, which makes use of a supersymmetric ${\cal N} = 1$ spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator.

hep-th↗

arXiv2021

Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes

In the first part of this series, we employed the second-order formalism and the ``symbol'' map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressed with $N$ photons, in terms of the ``$N$-photon kernel,'' where this kernel appears also in ``subleading'' terms involving only $N$-$1$ of the $N$ photons. In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications. We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for ``all $+$'' photon helicities in the massless case, and find a novel relation between the scalar and spinor spin-averaged cross sections in the massive case. Testing the formalism on the standard linear Compton scattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

hep-th↗

arXiv2021

Bosons on a rotating ring with free boundary conditions

We consider a system of interacting non-relativistic bosons confined to a one-dimensional ring in the presence of a synthetic gauge field induced by a rotating barrier. Interactions are introduced as a constraint in field space, and the barrier is modeled by general boundary conditions. Within this setup, we compute the effective action and investigate the profile of the ground state and its sensitivity from rotational velocity and the properties of the barrier.

hep-th↗

arXiv2021

One-loop quantum gravity from the N=4 spinning particle

We construct a spinning particle that reproduces the propagation of the graviton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the N=4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D=4.

hep-th↗

arXiv2021

The Quantum Darboux Theorem,

The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wavefunctions. In this picture the base manifold is an odd dimensional symplectic geometry, or quite generically a contact manifold that can be viewed as a "phase-spacetime", while the fibers are Hilbert spaces. This approach enjoys a "quantum Darboux theorem" that parallels the Darboux theorem on contact manifolds which turns local classical dynamics into straight lines. We detail how the quantum Darboux theorem works for anharmonic quantum potentials. In particular, we develop a novel diagrammatic approach for computing the asymptotics of a gauge transformation that locally makes complicated quantum dynamics trivial.

hep-th↗

arXiv2020

A Monte Carlo Approach to the Worldline Formalism in Curved Space

We present a numerical method to evaluate worldline (WL) path integrals defined on a curved Euclidean space, sampled with Monte Carlo (MC) techniques. In particular, we adopt an algorithm known as YLOOPS with a slight modification due to the introduction of a quadratic term which has the function of stabilizing and speeding up the convergence. Our method, as the perturbative counterparts, treats the non-trivial measure and deviation of the kinetic term from flat, as interaction terms. Moreover, the numerical discretization adopted in the present WLMC is realized with respect to the proper time of the associated bosonic point-particle, hence such procedure may be seen as an analogue of the time-slicing (TS) discretization already introduced to construct quantum path integrals in curved space. As a result, a TS counter-term is taken into account during the computation. The method is tested against existing analytic calculations of the heat kernel for a free bosonic point-particle in a D-dimensional maximally symmetric space.

hep-th↗

arXiv2020

Compton-like scattering of a scalar particle with N photons and one graviton

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a tree replacement rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.

hep-th↗

arXiv2020

Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes

In the first-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with $N$ photons, in terms of the "$N$-photon kernel," where off-shell this kernel appears also in "subleading" terms involving only $N-1$ of the $N$ photons. Although the parameter integrals generated by the master formula are equivalent to the usual Feynman diagrams, they are quite different since the use of the inverse symbol map avoids the appearance of long products of Dirac matrices. As a test we use the $N=2$ case for a recalculation of the one-loop fermion self energy, in $D$ dimensions and arbitrary covariant gauge, reproducing the known result. We find that significant simplification can be achieved in this calculation choosing an unusual momentum-dependent gauge parameter.

hep-th↗

arXiv2019

Worldline formalism for a confined scalar field

The worldline formalism is a useful scheme in quantum field theory which has also become a powerful tool for numerical computations. The key ingredient in this formalism is the first quantization of an auxiliary point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field which is confined within some boundaries one needs to restrict the path integration domain of the auxiliary point-particle to a specific subset of worldlines enclosed by those boundaries. We show how to implement this restriction for the case of a scalar field confined to the $D$-dimensional ball under Dirichlet and Neumann boundary conditions, and compute the first few heat-kernel coefficients as a verification of our construction. We argue that this approach could admit different generalizations.

hep-th↗

arXiv2018

$U(N)$ Yang-Mills in non-commutative space time

We present an approach to $U_\star(N)$ Yang-Mills theory in non-commutative space based upon a novel phase-space analysis of the dynamical fields with additional auxiliary variables that generate Lorentz structure and colour degrees of freedom. To illustrate this formalism we compute the quadratic terms in the effective action focusing on the planar divergences so as to extract the $β$-function for the Yang-Mills coupling constant. Nonetheless the method presented is general and can be applied to calculate the effective action at arbitrary order of expansion in the coupling constant, including both planar and non-planar contributions, and is well suited to the computation of low energy one-loop scattering amplitudes.

hep-th↗

arXiv2018

String-inspired Methods and the Worldline Formalism in Curved Space

The worldline approach to Quantum Field Theory (QFT) allows to efficiently compute several quantities, such as one-loop effective actions, scattering amplitudes and anomalies, which are linked to particle path integrals on the circle. A helpful tool in the worldline formalism on the circle, are string-inspired (SI) Feynman rules, which correspond to a specific way of factoring out a zero mode. In flat space this is known to generate no difficulties. In curved space, it was shown how to correctly achieve the zero mode factorization by applying BRST techniques to fix a shift symmetry. Using special coordinate systems, such as Riemann Normal Coordinates, implies the appearance of a non-linear map---originally introduced by Friedan---which must be taken care of in order to obtain the correct results. In particular, employing SI Feynman rules, the map introduces further interactions in the worldline path integrals. In the present paper, we compute in closed form Friedan's map for RNC coordinates in maximally symmetric spaces, and test the path integral model by computing trace anomalies. Our findings match known results.

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