Blade: A package for block-triangular form improved Feynman integrals decomposition
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Guan, Xin↗
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Feynman-α analysis using BGO gamma-ray detector in UTR-KINKI reactor
In conventional reactor noise measurement based on neutron detection, a neutron detector must be placed as close to a core as possible, to observe a largest possible correlation amplitude. For most of reactors other than critical assemblies, however, the placement is hardly possible. We focused on an alternative reactor noise measurement using prompt gamma-rays having a long flight range, to overcome the above constraint. A Feynman-α analysis using a NaI(Tl) scintillation detector was previously performed in UTR-KINKI, however, white noise originating from radioactivation of the scintillator significantly degraded the correlation amplitude. In this study, another Feynman-α analysis using a BGO gamma-ray detector, which never suffers from any radioactivation, is performed. A series of Feynman-α analyses for a critical state and several subcritical states of UTR-KINKI reactor has been carried out using two BGO detectors and a BF{sub 3} neutron detector to determine prompt-neutron decay constant. In the present analysis, the dead-time effect of these detectors and the delayed-neutron effect are considered. The prompt-neutron decay constant determined from Feynman-α analysis based on gamma-ray detection agrees with that from the analysis based on neutron detection. The Feynman-α analysis based on detecting gamma rays appears to be able to determine prompt-neutron decay constant at least as efficiently as the conventional analysis detecting neutrons.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Feynman path integrals for discrete-variable systems: Walks on Hamiltonian graphs
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is the Hamiltonian. By working out expressions for the partition function and transition amplitudes of discretized versions of continuous-variable quantum systems, and then taking the continuum limit, we explicitly recover Feynman's continuous-variable path integrals. We also discuss the implications of our result.
Feynman diagrams↗
Feynman rules for scalar conformal blocks
We complete the proof of “Feynman rules” for constructing M-point conformal blocks with external and internal scalars in any topology for arbitrary M in any spacetime dimension by combining the rules for the blocks (based on their Witten diagram interpretation) with the rules for the construction of conformal cross ratios (based on the OPE and “flow diagrams”). The full set of Feynman rules leads to blocks as power series of the hypergeometric type in the conformal cross ratios. We then provide a proof by recursion of the Feynman rules which relies heavily on the first Barnes lemma and the decomposition of the topology of interest in comb structures. Finally, we provide a nine-point example to illustrate the rules.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A Feynman-Kac based numerical method for the exit time probability of a class of transport problems
The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Estimating β eff from static, late-time Feynman neutron noise measurements
The effective delayed neutron fraction, β eff , is a kinematic parameter describing the contribution of delayed neutrons to the effective multiplication factor, $\kappa$ eff , and is of great interest to the nuclear criticality safety community and beyond. In fact, $\kappa$ eff presently must be inferred (as opposed to directly measured) since variables like β eff must be obtained from simulation, reference tables, or a dynamic or pulsed measurement where the assembly of fissile material is perturbed and not in steady state. Several recent works have proposed neutron noise techniques to estimate β eff from static measurements (such as benchmark experiments). This work experimentally investigates an approach based on looking at late-time (up to thousands of seconds) correlated neutrons in Feynman histograms. This work utilizes measurements of weapons grade plutonium and highly enriched uranium to construct late-time Feynman histograms and investigate a proposed methodology of estimating β eff from a fit of the distribution. Data is shown from both He-3 detectors and an organic scintillator array. This work is preliminary in nature, demonstrating some experimental feasibility and proposing improvements for future investigations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Loop-by-loop differential equations for dual (elliptic) Feynman integrals
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then, we test our formalism on a simple, but non-trivial, example: the two-loop three-mass elliptic sunrise family of integrals. We obtain an ε-form differential equation within the correct function space in a sequence of relatively simple algebraic steps. In particular, none of these steps relies on the analysis of q-series. Then, we discuss interesting properties satisfied by our dual basis as well as its simple relation to the known ε-form basis of Feynman integrands. The underlying K3-geometry of the three-loop four-mass sunrise integral is also discussed. Finally, we speculate on how to construct a “good” loop-by-loop basis at three-loop.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
An April Fools’ Day read from Lab history Famed physicist Richard Feynman’s safecracking, cipher-creating sense of play
Richard Feynman was fresh out of Princeton University’s doctoral program when recruited to assist in the creation of the atomic bomb at Los Alamos. In 1943, Lab director J. Robert Oppenheimer wrote that the 24-year-old was, “by all odds the most brilliant young physicist here, and everyone knows this.” Feynman attempted to live and examine life in a state of play and, as such, it’s only fitting to take a look back at the Nobel Prize winning scientist’s years at the wartime Lab as April Fools’ Day approaches.
99 GENERAL AND MISCELLANEOUS↗
Richard P. Feynman Center for Innovation: 2025 Annual Report
The Richard P. Feynman Center for Innovation helps businesses and organizations work with Los Alamos National Laboratory to turn research into practical products and solutions. We connect industry partners with new technologies, research expertise, and licensing opportunities. From protecting inventions to building collaborations, the Feynman Center makes it easier to bring scientific advances to the marketplace and create lasting impact.
08 HYDROGEN↗
From Feynman diagrams to the amplituhedron: a gentle review
In this article we review, for a mathematical audience, the computation of (tree-level) scattering amplitudes in Yang-Mills theory in detail. In particular we demonstrate explicitly how the same formulas for six-particle NMHV helicity amplitudes are obtained from summing Feynman diagrams and from computing the canonical form of the n=6, k=1, m=4 amplituhedron.
Feynman diagrams↗
Accurate Hellmann–Feynman forces from density functional calculations with augmented Gaussian basis sets
The Hellmann–Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upward of 10 eV/Å in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed, and HF forces can be computed as accurately as analytical forces with state-of-the-art basis sets, allowing geometry optimization and molecular dynamics to be reliably performed with HF forces. Our results pave a clear path forward for the accurate and efficient simulation of large systems using ML densities and the HF theorem.
Pathak, Shivesh (ORCID:0000000172798195)↗
Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point nonplanar QCD process with multiple mass scales. Published by the American Physical Society 2024
Physics↗
Feynman diagrams for matter wave interferometry
We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical approximation. These additional terms depend on the finite size of the initial matter wavefunction and/or have higher order dependence on ℏ. We apply the method to compute the response of matter wave interferometers to power law potentials and potentials with an arbitrary spatial dependence. The analytic expressions are validated by comparing to numerical simulations, and estimates are provided for the scale of the quantum corrections to the phase shift response to the gravitational field of the earth, anharmonic trapping potentials, and gravitational fields from local proof masses. We also find that for certain experimentally feasible parameters, these corrections are large enough to be measured and could lead to systematic errors if they are not mitigated. We find that to first order in a spatially dependent potential, quantum corrections vanish when the initial matter wavepacket has spherical symmetry and the potential satisfies Laplace's equation. We anticipate these quantum corrections will be especially important for trapped matter wave interferometers and for free-space matter wave interferometers in the presence of proof masses. These interferometers are becoming increasingly sensitive tools for mobile inertial sensing, gravity surveying, tests of gravity and its interplay with quantum mechanics, and searches for dark energy.
Glick, Jonah [Northwestern U.; Fermilab] (ORCID:00↗
UFO 2.0: the ‘Universal Feynman Output’ format
Abstract We present an update of the Universal FeynRules Output model format, commonly known as the UFO format, that is used by several automated matrix-element generators and high-energy physics software. We detail different features that have been proposed as extensions of the initial format during the last ten years, and collect them in the current second version of the model format that we coin the Universal Feynman Output format. Following the initial philosophy of the UFO, they consist of flexible and modular additions to address particle decays, custom propagators, form factors, the renormalisation group running of parameters and masses, and higher-order quantum corrections.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Status of Intersection Theory and Feynman Integrals
Here, we give a pedagogical review of the recently-introduced notion of a "scalar product" between Feynman integrals and how it helps us understand the analytic structure of the perturbative S-matrix.
97 MATHEMATICS AND COMPUTING↗
Feynman polytopes and the tropical geometry of UV and IR divergences
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
What can machine learning and the Hellmann-Feynman Theorem teach us about the limits of electron correlation?.
Abstract not provided.
Rackers, Joshua↗