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W. A. Horowitz

Publications and source records attributed to W. A. Horowitz.

At least 19 recordsLinked to original sources
arXiv2026

Variational approach to nonholonomic and inequality-constrained mechanics

Variational principles play a central role in classical mechanics, providing compact formulations of dynamics and direct access to conserved quantities. While holonomic systems admit well-known action formulations, non-holonomic systems -- subject to non-integrable velocity constraints or position inequality constraints -- have long resisted a general extremized action treatment. In this work, we construct an explicit and general action for non-holonomic motion, motivated by the classical limit of the quantum Schwinger-Keldysh action formalism, rediscovered by Galley. Our formulation recovers the correct dynamics of the Lagrange-d'Alembert equations via extremization of a scalar action. We validate the approach on canonical examples using direct numerical optimization of the novel action, bypassing equations of motion. Our framework extends the reach of variational mechanics and offers new analytical and computational tools for constrained systems.

physics.class-ph↗
arXiv2026

Jet Quenching in the Smallest Hadronic Collision Systems

We present perturbative quantum chromodynamics (pQCD) predictions for high-momentum particle yield modification in very light ion collisions - ${}^{10}\mathrm{B}+{}^{10}\mathrm{B}$, ${}^{6}\mathrm{Li}+{}^{6}\mathrm{Li}$, ${}^{4}\mathrm{He}+{}^{4}\mathrm{He}$, and ${}^{3}\mathrm{He}+{}^{3}\mathrm{He}$ - with and without medium-induced energy loss. We find non-trivial suppression in symmetric systems from ${}^{208}\mathrm{Pb}+{}^{208}\mathrm{Pb}$ to ${}^{3}\mathrm{He}+{}^{3}\mathrm{He}$ and in asymmetric $A+B$ systems, with the suppression scaling approximately as $R_{AB} \simeq (\sqrt{AB})^{1/3}$. Further, we find that ${}^{3}\mathrm{He}$ and ${}^{6}\mathrm{Li}$ offer particularly clean environments for observing final-state partonic energy loss from quark-gluon plasma (QGP) formation in extremely small systems. Finally, we show that energy loss models generically predict $v_2\{\mathrm{SP}\} \approx 0$ in small systems, indicating that the large measured $v_2 > 0$ in $p+{}^{208}\mathrm{Pb}$ is not due to energy loss.

hep-ph↗
arXiv2026

Systematic Analytic Regularization in $φ^4$ and Yukawa Theories

We introduce a novel regularization scheme: Systematic Analytic Regularization (SAR). SAR regularizes a theory at the level of the action by analytically continuing the power of the kinetic operator, ensuring that the theory is formally finite before any terms in the Dyson series are evaluated. We demonstrate that SAR fully and self-consistently regularizes $φ^4$ and Yukawa theories at NLO.

hep-th↗
arXiv2026

From Exact Space-Time Symmetry Conservation to Automatic Mesh Refinement in Discrete Initial Boundary Value Problems

In this contribution we present recent developments in the formulation and solution of Initial Boundary Value Problems (IBVPs). Building upon a modern variational action formulation of classical dynamics, we treat Initial Boundary Value Problems directly on the action level, bypassing governing equations. We show that by including coordinate maps as dynamical degrees of freedom together with propagating fields two key results emerge. Space-time symmetries remain protected even after discretization, leading to an exact conservation of Noether charges even for discrete IBVPs. The dynamical nature of the coordinate maps leads to an adjustment of space-time resolution, guided by Noether charge conservation, realizing a form of automatic adaptive mesh refinement. We stress that as long as SBP operators are used for the discretization, our results are independent of whether the dynamics are solved on the action or governing equation level and hold in particular also at high order. As proof-of-principle for our approach we present its application to scalar wave-propagation in 1+1 dimensions.

math.NA↗
arXiv2026

Energy loss predicts no $v_2$ in small systems

We present high-$p_T$ $R_{AB}$ and $v_2$ from a perturbative quantum chromodynamics-based energy loss model that includes event-by-event hydrodynamic evolution of the medium and small system size corrections to the energy loss. The model is calibrated on, and describes well, large system $R_{AA}$ and $v_2$ experimental data. The extrapolation of our model to $\mathrm{Ne}+\mathrm{Ne}$ and $\mathrm{O}+\mathrm{O}$ agrees quantitatively with recent experimental measurements of $R_{AA}$. Surprisingly, at high-$p_T$ our energy loss model predicts $v_2\approx0$ for all symmetric and asymmetric small systems when extracted using either hard-hard or hard-soft two-particle correlations. We argue that all energy loss models will in general predict $v_2\approx0$ when extracted using hard-soft correlations, which is the usual experimental method for measuring anisotropy in hadronic collisions, due to a generic geometric decorrelation between the hard and soft sector participant planes.

hep-ph↗
arXiv2026

Hamilton Revised: The Action Principle for Initial Value Problems

We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for the time dependence of the expectation value for operators in quantum mechanics. We clarify the connection between the variation of the position and the variation of the velocity of a particle when implementing Hamilton's Principle in deriving the Euler-Lagrange Equations. We show that both the plus and minus Keldysh paths (of the average and difference of the forward/backward paths) have classical paths and fluctuations -- unlike the common perception that the minus path provides the fluctuations around the single classical solution given by the plus path -- and that the fluctuations of both paths are crucial for the correct normalization of the classical limit. The classical limit yields "initial conditions" and equations of motion for the minus paths such that the unique classical solution for the minus paths is that they are identically zero, and, fascinatingly, that the minus paths' solution propagates backwards in time; thus one does not need to set the minus paths to zero by hand when taking the classical limit of the Schwinger-Keldysh formalism. We note implications for the classical and quantum mechanics of non-holonomic constraints and quantum field theories with gauges dependent on the derivatives of the fields.

physics.class-ph↗
arXiv2025

From Lead to Helium: Discovery Potential for Jet Quenching in the Smallest Collision Systems

We present perturbative quantum chromodynamics (pQCD) predictions for the modification to the yield of high-momentum particles in very light ion collisions - ${}^{10}\mathrm{B} + {}^{10}\mathrm{B}$, ${}^{6}\mathrm{Li} + {}^{6}\mathrm{Li}$, ${}^{4}\mathrm{He} + {}^{4}\mathrm{He}$, and ${}^{3}\mathrm{He} + {}^{3}\mathrm{He}$ - both with and without medium-induced energy loss. We show that there is non-trivial suppression expected from our partonic energy loss model in symmetric systems from ${}^{208}\mathrm{Pb} + {}^{208}\mathrm{Pb}$ to ${}^{3}\mathrm{He} + {}^{3}\mathrm{He}$ and in asymmetric systems $A + B$, and that the energy loss scales approximately with $(\sqrt{A B})^{1 / 3}$. Further, we find that deep inelastic scattering measurements in ${}^{3}\mathrm{He}$ and ${}^{6}\mathrm{Li}$ tightly constrain the nPDF baseline, making these isotopes a particularly clean environment for observing final-state partonic energy loss induced by the formation of a quark-gluon plasma in these very small systems.

hep-ph↗
arXiv2025

The Non-Abelian Casimir Effect for Plates, Symmetrical Tube and Box on the Lattice

We present non-perturbative results of the Casimir potential in non-abelian SU(3) gauge theory in (2+1)D and (3+1)D in the confined and deconfined phase. For the first time, geometries beyond parallel plates in (3+1)D are explored and we show that the Casimir effect for the symmetrical tube and symmetrical box is attractive. The Casimir potential for the tube differs from the massless non-interacting scalar field theory prediction, where a repulsive Casimir potential is expected. Unlike the parallel plate geometry where the plate-size is fixed, in the case of the tube and box, the sizes of the faces forming the walls of the geometries changes with separation distance. We propose various methods that can be used to account for the energy contributions from creating the boundaries. We show that increasing the temperature from a confined to a deconfined phase does not alter the Casimir potential. This observation is consistent with prior work suggesting that the region inside the walls is a boundary induced deconfined phase.

hep-lat↗
arXiv2025

Statistical analysis of pQCD energy loss across system size, flavor, $\sqrt{s_{NN}}$, and $p_T$

We present suppression predictions from our pQCD-based energy loss model, which receives small system size corrections, for high-$p_T$ $π$, $D$ and $B$ meson $R_{AB}$ as a function of centrality, flavor, $\sqrt{s_{NN}}$, and $p_T$ from large to small collision systems at RHIC and LHC. A statistical analysis is used to constrain the effective strong coupling in our model to available high-$p_T$ suppression data from central heavy-ion collisions at RHIC and LHC, yielding good agreement with all available data. We estimate two important theoretical uncertainties in our model, stemming from: the transition between vacuum and hard thermal loop propagators in the collisional energy loss, and from the angular cutoff on the radiated gluon momentum. We find, consistently, that the extracted $α_s$ remains relatively unchanged across heavy- and light-flavor final states and across central, semi-central, and peripheral collisions. We make predictions from our large-system-constrained model for small systems and find good agreement with photon-normalized $R^{π^0}_{d \text{Au}} \simeq 0.75 $ in $0-5\%$ centrality $d$ + Au collisions by PHENIX. However, we find strong disagreement with the measured $R^{h^{\pm}}_{p \text{Pb}} \gtrsim 1$ in $0-5\%$ centrality $p$ + Pb collisions by ALICE and ATLAS; we argue that this disagreement is due, in large part, to centrality bias. We make predictions for the ratio of suppression in ${}^3$He + Au and $p$ + Au collisions, which may in the future be used to disentangle final- from initial-state suppression in small systems. We then compare our results to various subsets of data, which allows us to estimate the preferred: low-$p_T$ scale at which non-perturbative processes become important, scales at which the strong coupling runs, and scale at which vacuum propagators transition to thermally modified propagators in collisional energy loss.

hep-ph↗
arXiv2025

Coherent State Path Integral Reveals Unexpected Vacuum Structure in Thermal Field Theory

We construct the path integral formulation of the partition function for a free scalar thermal field theory using coherent states, first in the ladder operator basis and then in the field operator basis. In so doing, we provide for the first time a mapping in quantum field theory between the field-basis coherent states and ladder-basis coherent states. Using either basis, one finds terms missed in the usual path integral derivation, which we identify as the vacuum energy contribution to the partition function. We then extend the field-basis coherent state method to the interacting $ϕ^4$ theory. In addition to the vacuum energy contribution, one finds a coupling of a vacuum expectation value to the mass term that is absent in the existing literature.

hep-th↗
arXiv2025

Collisional and radiative energy loss in small systems

We present an energy loss model which includes small system size corrections to both the radiative and elastic energy loss. Our model is used to compute the nuclear modification factor $R_{AB}$ of light and heavy flavor hadrons, averaged over realistic collision geometries for central and peripheral $A+A$ and central $p / d / {}^3\text{He} + A$ collisions at LHC and RHIC. We find that the predicted suppression in small systems is almost entirely due to elastic energy loss. Our results are keenly sensitive to the crossover between elastic energy loss calculated with hard thermal loop propagators and vacuum propagators, respectively, which leads to a large theoretical uncertainty. We find that the $R_{AB}$ is largely insensitive to the form of the elastic energy loss distribution - Gaussian or Poisson - surprisingly so in small systems where the central limit theorem is inapplicable. We present an expansion of the $R_{AB}$ in terms of the moments of the energy loss probability distribution, which allows for a rigorous understanding of the dependence of the $R_{AB}$ on the underlying energy loss distribution.

nucl-th↗
arXiv2025

A unified description of small, peripheral, and large system suppression data from pQCD

We present quantitative predictions for the nuclear modification factor in both small and peripheral systems from a pQCD-based energy loss model that is constrained by light- and heavy-flavor suppression data from central heavy-ion collisions. We find nearly identical suppression for central $p / d + A$ collisions as for peripheral $A + A$ collisions, quantitatively consistent with the measured 20% suppression of neutral pions produced in $d + \mathrm{Au}$ collisions by PHENIX, but dramatically inconsistent with the measured 20% enhancement of charged hadrons produced in $p + \mathrm{Pb}$ collisions by ATLAS. We demonstrate that this equivalence of central small system suppression and peripheral large system suppression is insensitive to the underlying energy loss model.

hep-ph↗
arXiv2024

Exact space-time symmetry conservation and automatic mesh refinement for classical lattice field theory

The breaking of space-time symmetries and the non-conservation of the associated Noether charges constitutes a central artifact in lattice field theory. In prior work we have shown how to overcome this limitation for classical actions describing point particle motion, using the world-line formalism of general relativity. The key is to treat coordinate maps (from an abstract parameter space into space-time) as dynamical and dependent degrees of freedom, which remain continuous after discretization of the underlying parameter space. Here we present latest results where we construct a reparameterization invariant classical action for scalar fields, which features dynamical coordinate maps. We highlight the following achievements of our approach: 1) global space-time symmetries remain intact after discretization and the associated Noether charges remain exactly preserved 2) coordinate maps adapt to the dynamics of the scalar field leading to adaptive grid resolution guided by the symmetries.

hep-lat↗
arXiv2024

Heavy Flavour Energy Loss in Small and Large Systems

We present suppression results for high-$p_T$ $D$ and $π$ mesons produced in $p / d + A$ and $A+A$ collisions at RHIC and LHC. These results are computed using a convolved elastic and radiative energy loss model, which receives small system size corrections to both the elastic and radiative energy loss. We observe that suppression in small systems is almost entirely due to elastic energy loss; furthermore, we find that our model is acutely sensitive to the transition between hard thermal loop and vacuum propagators in the elastic energy loss. Finally, we consider the central limit theorem approximation, which is commonly used to model the elastic energy loss distribution as Gaussian.

nucl-th↗
arXiv2024

Even More Generalized Hamiltonian Dynamics

We establish the procedure to derive from an action-based variational principle the classical equations of motion in Hamiltonian phase space of a particle subject to general position and velocity dependent non-holonomic equality constraints. Key to the procedure is our introduction of Flannery brackets, which generalize Poisson brackets. We conjecture on some implications, including the possibility of replacing Poisson brackets with Flannery brackets in Dirac's brackets to provide the quantization procedure for general non-holonomic equality constraint systems.

math-ph↗
arXiv2024

Exact symmetry conservation and automatic mesh refinement in discrete initial boundary value problems

We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is formulated in an abstract parameter space and an energy density scale associated with the space-time coordinates separates the dynamics of the coordinate maps and of the propagating fields. Treating coordinates as dependent, i.e. dynamical quantities, offers the opportunity to discretize the action while retaining all space-time symmetries and also provides the basis for automatic adaptive mesh refinement (AMR). The presence of unbroken space-time symmetries after discretization also ensures that the associated continuum Noether charges remain exactly conserved. The presence of coordinate maps in addition provides new freedom in the choice of boundary conditions. An explicit numerical example for wave propagation in $1+1$ dimensions is provided, using recently developed regularized summation-by-parts finite difference operators.

math.NA↗
arXiv2023

High-$p_T$ Suppression in Small Systems

We present first results for leading hadron suppression in small collision systems, from a convolved radiative and collisional pQCD energy loss model which receives a short path length correction to the radiative energy loss. We find that the short path length correction is exceptionally large for light flavor final states in both small and large collision systems, due to the disproportionate size of the correction for gluons. We examine various assumptions underlying the energy loss model through the calculation of energy loss weighted expectation values of ratios assumed small by the various assumptions. This calculation shows that the large formation time assumption, which is utilized by most contemporary energy loss models, is invalid for a large portion of the phenomenologically relevant parameter space.

hep-ph↗
arXiv2023

Inconsistencies in, and short pathlength correction to, $R_{AA}(p_T)$ in $\mathrm{A}+\mathrm{A}$ and $\mathrm{p} + \mathrm{A}$ collisions

We present the first leading hadron suppression predictions in $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{p}+\mathrm{Pb}$ collisions from a convolved radiative and collisional energy loss model in which partons propagate through a realistic background and in which the inelastic energy loss receives a short pathlength correction. We find that the short pathlength correction is small for $D$ and $B$ meson $R_{AA}(p_T)$ in both $\mathrm{Pb}+\mathrm{Pb}$ and $\mathrm{p}+\mathrm{Pb}$ collisions. However the short pathlength correction leads to a surprisingly large reduction in suppression for $π$ mesons in $\mathrm{p}+\mathrm{Pb}$ and even $\mathrm{Pb}+\mathrm{Pb}$ collisions. We systematically check the consistency of the assumptions used in the radiative energy loss derivation - such as collinearity, softness, and large formation time - with the final numerical model. While collinearity and softness are self-consistently satisfied in the final numerics, we find that the large formation time approximation breaks down at modest to high momenta $p_T \gtrsim 30$ GeV. We find that both the size of the small pathlength correction to $R_{AA}(p_T)$ and the $p_T$ at which the large formation time assumption breaks down are acutely sensitive to the chosen distribution of scattering centers in the plasma.

hep-ph↗