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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
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DOE OSTI2014

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Popov, Berg, Sokolov: A Street with Three Plaques

The historic city of Saint Petersburg is full of memorial plaques—ballet dancers, literary giants, composers, war heroes, and even mathematicians. Here, if you go to the metro station Petrogradskaya, cross the bridge over the tiny Karpovka River, and reach ulitsa Professora Popova—Professor Popov Street—then almost surely you are going to one of two destinations. First, perhaps you are going to the Saint Petersburg Electrotechnical University, colloquially known as LETI. Second, you may be going for a stroll in the botanical garden of the V. L. Komarov Institute of the Russian Academy of Sciences.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2014

On the zero modes of the Faddeev-Popov operator in the Landau gauge

Following Henyey procedure [Phys. Rev. D 20, 1460 (1979)], we construct examples of zero modes of the Faddeev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3) groups. We obtain gauge field configurations A{sub μ}{sup a} which give rise to a field strength, F{sub μν}{sup a}=∂{sub μ}A{sub ν}{sup a}−∂{sub ν}A{sub μ}{sup a}+f{sup abc}A{sub μ}{sup b}A{sub ν}{sup c}, whose nonlinear term, f{sup abc}A{sub μ}{sup b}A{sub ν}{sup c}, turns out to be non-vanishing. To our knowledge, this is the first time where such a non-abelian configuration is explicitly obtained in the case of SU(3) in 4D.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Gribov ambiguity in asymptotically AdS three-dimensional gravity

In this paper the zero modes of the de Donder gauge Faddeev-Popov operator for three-dimensional gravity with negative cosmological constant are analyzed. It is found that the AdS{sub 3} vacuum produces (infinitely many) normalizable smooth zero modes of the Faddeev-Popov operator. On the other hand, it is found that the Banados-Teitelboim-Zanelli black hole (including the zero mass black hole) does not generate zero modes. This differs from the usual Gribov problem in QCD where, close to the maximally symmetric vacuum, the Faddeev-Popov determinant is positive definite while 'far enough' from the vacuum it can vanish. This suggests that the zero mass Banados-Teitelboim-Zanelli black hole could be a suitable ground state of three-dimensional gravity with negative cosmological constant. Because of the kinematic origin of this result, it also applies for other covariant gravity theories in three dimensions with AdS{sub 3} as maximally symmetric solution, such as new massive gravity and topologically massive gravity. The relevance of these results for supersymmetry breaking is pointed out.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The (IR-)relevance of the Gribov ambiguity in SU(2)×U(1) gauge theories with fundamental Higgs matter

It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang–Mills theories, in particular in the low momentum regime where standard perturbation theory based on the Faddeev–Popov approach fails. Recent results, derived from functional tools (Dyson–Schwinger equations or exact RG) or the effective Gribov–Zwanziger action method, pointed towards e.g. gauge boson correlation functions that are not compatible with the properties of observable degrees of freedom. Although such an observation is a welcome feature for gauge theories exhibiting confinement, it would be a discomfort for gauge theories supplemented with Higgs fields, cf. the experimental success of the electroweak model based on a SU(2)×U(1) gauge group. The purpose of this short note is to assure that the effective action resolution to the Gribov ambiguity reduces to the standard Faddeev–Popov method in the perturbative regime of sufficiently small coupling/large Higgs condensate, thereby not compromising the physical particle spectrum of massive gauge bosons and a massless photon for the SU(2)×U(1) gauge–Higgs model. The closer the theory gets to the limit of vanishing Higgs condensate, the more the Gribov problem resurfaces with all its consequences. We give some speculations w.r.t. the Fradkin–Shenker insights about the phase diagram. -- Highlights: •Gribov horizon influences gauge propagators in a strong-coupling regime. •No influence of Gribov horizon in weak-coupling. •Inclusion of U(1) factor leads to very rich behavior of propagators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The internal structure of a vortex in a two-dimensional superfluid with long healing length and its implications

We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov’s hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov’s action, which, in particular, allows for weak solutions of the Gross–Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

The inverse of the Faddeev–Popov operator plays a pivotal role within the Gribov–Zwanziger approach to the quantization of Euclidean Yang–Mills theories in Landau gauge. Following a recent proposal (Capri et al., 2014), we show that the inverse of the Faddeev–Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Comparison between microscopic methods for finite-temperature Bose gases

We analyze the equilibrium properties of a weakly interacting, trapped quasi-one-dimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a number-conserving Bogoliubov (NCB) approach and a stochastic Gross-Pitaevskii equation (SGPE) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the NCB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (NCB, canonical; SGPE, grand-canonical), they yield the correct condensate statistics in a large Bose-Einstein condensate (BEC) (strong enough particle interactions). For smaller systems, the SGPE results are prone to anomalously large number fluctuations, well known for the grand-canonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the Penrose-Onsager condensate from first- and second-order correlation functions that is both computationally convenient and of potential use to experimentalists. This also clarifies the link between condensate and quasicondensate in the Popov theory of low-dimensional systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Auxiliary-field approach to dilute Bose gases with tunable interactions

We rewrite the Lagrangian for a dilute Bose gas in terms of auxiliary fields related to the normal and anomalous condensate densities. We derive the loop expansion of the effective action in the composite-field propagators. The lowest-order auxiliary field (LOAF) theory is a conserving mean-field approximation consistent with the Goldstone theorem without some of the difficulties plaguing approximations such as the Hartree and Popov approximations. LOAF predicts a second-order phase transition. We give a set of Feynman rules for improving results to any order in the loop expansion in terms of composite-field propagators. We compare results of the LOAF approximation with those derived using the Popov approximation. LOAF allows us to explore the critical regime for all values of the coupling constant, and we determine various parameters in the unitarity limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Alternative refined Gribov-Zwanziger Lagrangian

We consider the implications of the condensation of a general local Becchi-Rouet-Stora-Tyutin invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different color tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields, other than those of the gluon and Faddeev-Popov ghost, for which there is no numerical simulation data to compare with yet.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

New photomultiplier active base for Hall C Jefferson Lab lead tungstate calorimeter

A new photomultiplier tube active base was designed and tested. The base combines active voltage division circuit and fast amplifier, powered by the current flowing through voltage divider. This base is developed to upgrade older photomultiplier bases of Jefferson Lab lead-tungsten calorimeter (about ˜1200 crystals of PbWO{sub 4} from the PrimEx experimental setup). This is needed for the extension of detectors' rate capability to meet requirements of new Hall C proposal PR12-11-102 of measurements of the L/T separated cross sections and their ratio R = πL/πT in neutral-pion p(e,e'π0)p deep exclusive and p(p(e,e'π{sup 0})p)X semi-inclusive scattering regions. New active base is direct replacement of older passive base circuit without adding of additional power or signal lines. However, it extends detectors rate capability with factor over 20. Moreover, transistorized voltage divider improves detector's amplitude resolution due to reduction of photomultiplier gain dependence from tube anode current. The PMT active base is the invention disclosed in V. Popov's U.S. Patent No. 6,791,269, which successfully works over ten years in several Jefferson Lab Cherenkov detectors. The following design is a new revised and improved electronic circuit with better gain stability and linearity in challenge to meet requirements of new Hall C experimental setup. New active base performance was tested using fast LED light source and Pr:LuAG scintillator and gamma sources. Electronics radiation hardness was tested on JLab accelerator. Results of testing R4125 Hamamatsu photomultiplier tube in new active base are presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

2D Dilute Bose Mixture at Low Temperatures

The thermodynamic and superfluid properties of the dilute two-dimensional binary Bose mixture at low temperatures are discussed. We also considered the problem of the emergence of the long-range order in these systems. All calculations are performed by means of the celebrated Popov path-integral approach to the Bose gas with a short-range interparticle potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Multi-instantons and exact results IV: Path integral formalism

Highlights: > O(N) anharmonic oscillators are considered in the path integral formalism. > Higher-order corrections to instantons are obtained using Feynman diagram calculations. > Generalized Bender-Wu formulas are confirmed. > The O(N) functional determinant describing the zero modes leads to higher-order terms. > Surprising cancellations are observed for the sextic oscillator. - Abstract: This is the fourth paper in a series devoted to the large-order properties of anharmonic oscillators. We attempt to draw a connection of anharmonic oscillators to field theory, by investigating the partition function in the path integral representation around both the Gaussian saddle point, which determines the perturbative expansion of the eigenvalues, as well as the nontrivial instanton saddle point. The value of the classical action at the saddle point is the instanton action which determines the large-order properties of perturbation theory by a dispersion relation. In order to treat the perturbations about the instanton, one has to take into account the continuous symmetries broken by the instanton solution because they lead to zero-modes of the fluctuation operator of the instanton configuration. The problem is solved by changing variables in the path integral, taking the instanton parameters as integration variables (collective coordinates). The functional determinant (Faddeev-Popov determinant) of the change of variables implies nontrivial modifications of the one-loop and higher-loop corrections about the instanton configuration. These are evaluated and compared to exact WKB calculations. A specific cancellation mechanism for the first perturbation about the instanton, which has been conjectured for the sextic oscillator based on a nonperturbative generalized Bohr-Sommerfeld quantization condition, is verified by an analytic Feynman diagram calculation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Compressible fluids with Maxwell-type equations, the minimal coupling with electromagnetic field and the Stefan–Boltzmann law

In this work we have obtained a higher-derivative Lagrangian for a charged fluid coupled with the electromagnetic fluid and the Dirac’s constraints analysis was discussed. A set of first-class constraints fixed by noncovariant gauge condition were obtained. The path integral formalism was used to obtain the partition function for the corresponding higher-derivative Hamiltonian and the Faddeev–Popov ansatz was used to construct an effective Lagrangian. Through the partition function, a Stefan–Boltzmann type law was obtained. - Highlights: • Higher-derivative Lagrangian for a charged fluid. • Electromagnetic coupling and Dirac’s constraint analysis. • Partition function through path integral formalism. • Stefan–Boltzmann-kind law through the partition function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Quantum dilute droplets of dipolar bosons at finite temperature

We systematically study the properties of dipolar Bose gases with two- and three-body contact interactions at finite temperature using the Hartree–Fock–Bogoliubov–Popov approximation. In uniform case, we obtain an exciting new extension of the seminal Lee–Huang–Yang corrected equation of state that depends explicitly on the thermal fluctuations and on the coupling constant of the three-body interaction. We investigate, on the other hand, the effects of thermal fluctuations on the occurrence and stability of a droplet state in a Bose–Einstein condensate with strong dipole–dipole interactions. We find that at finite temperature, the droplet phase appears as a narrow peak surrounded by a broader thermal halo. We show that the number of particles inside the droplet decays with increasing temperature. - Highlights: • Investigation of a dipolar Bose gas with two- and three-body interactions. • Derivation of a generalized Lee–Huang–Yang corrected equation. • Studying effects of thermal fluctuations on the nucleation of droplets in a dilute dipolar BEC. • Solving the finite-temperature GP equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗