Lattice calculations in gauge theory

International Nuclear Information System (INIS)

Rebbi, C.

1985-01-01

The lattice formulation of quantum gauge theories is discussed as a viable technique for quantitative studies of nonperturbative effects in QCD. Evidence is presented to ascertain that whole classes of lattice actions produce a universal continuum limit. Discrepancies between numerical results from Monto Carlo simulations for the pure gauge system and for the system with gauge and quark fields are discussed. Numerical calculations for QCD require very substantial computational resources. The use of powerful vector processors of special purpose machines, in extending the scope and magnitude or the calculations is considered, and one may reasonably expect that in the near future good quantitative predictions will be obtained for QCD

Lattice gauge theories

International Nuclear Information System (INIS)

Petronzio, R.

1992-01-01

Lattice gauge theories are about fifteen years old and I will report on the present status of the field without making the elementary introduction that can be found in the proceedings of the last two conferences. The talk covers briefly the following subjects: the determination of α s , the status of spectroscopy, heavy quark physics and in particular the calculation of their hadronic weak matrix elements, high temperature QCD, non perturbative Higgs bounds, chiral theories on the lattice and induced theories

Lattice gauge theories

International Nuclear Information System (INIS)

Creutz, M.

1983-04-01

In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed

Global gauge fixing in lattice gauge theories

Energy Technology Data Exchange (ETDEWEB)

Fachin, S.; Parrinello, C. (Physics Department, New York University, 4 Washington Place, New York, New York (USA))

1991-10-15

We propose a covariant, nonperturbative gauge-fixing procedure for lattice gauge theories that avoids the problem of Gribov copies. This is closely related to a recent proposal for a gauge fixing in the continuum that we review. The lattice gauge-fixed model allows both analytical and numerical investigations: on the analytical side, explicit nonperturbative calculations of gauge-dependent quantities can be easily performed in the framework of a generalized strong-coupling expansion, while on the numerical side a stochastic gauge-fixing algorithm is very naturally associated with the scheme. In both applications one can study the gauge dependence of the results, since the model actually provides a smooth'' family of gauge-fixing conditions.

Lattice chiral gauge theories with finely-grained fermions

International Nuclear Information System (INIS)

Hernandez, P.; Sundrum, R.

1996-01-01

The importance of lattice gauge field interpolation for our recent non-perturbative formulation of chiral gauge theory is emphasized. We illustrate how the requisite properties are satisfied by our recent four-dimensional non-abelian interpolation scheme, by going through the simpler case of U(1) gauge fields in two dimensions. (orig.)

Numerical techniques for lattice gauge theories

International Nuclear Information System (INIS)

Creutz, M.

1981-01-01

The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields

Lattice gauge theory approach to quantum chromodynamics

International Nuclear Information System (INIS)

Kogut, J.B.

1983-01-01

The author reviews in a pedagogical fashion some of the recent developments in lattice quantum chromodynamics. This review emphasizes explicit examples and illustrations rather than general proofs and analyses. It begins with a discussion of the heavy-quark potential in continuum quantum chromodynamics. Asymptotic freedom and renormalization-group improved perturbation theory are discussed. A simple dielectric model of confinement is considered as an intuitive guide to the vacuum of non-Abelian gauge theories. Next, the Euclidean form of lattice gauge theory is introduced, and an assortment of calculational methods are reviewed. These include high-temperature expansions, duality, Monte Carlo computer simulations, and weak coupling expansions. A #betta#-parameter calculation for asymptotically free-spin models is presented. The Hamiltonian formulation of lattice gauge theory is presented and is illustrated in the context of flux tube dynamics. Roughening transitions, Casimir forces, and the restoration of rotational symmetry are discussed. Mechanisms of confinement in lattice theories are illustrated in the two-dimensional electrodynamics of the planar model and the U(1) gauge theory in four dimensions. Generalized actions for SU(2) gauge theories and the relevance of monopoles and strings to crossover phenomena are considered. A brief discussion of the continuity of fields and topologial charge in asymptotically free lattice models is presented. The final major topic of this review concerns lattice fermions. The species doubling problem and its relation to chiral symmetry are illustrated. Staggered Euclidean fermion methods are discussed in detail, with an emphasis on species counting, remnants of chiral symmetry, Block spin variables, and the axial anomaly. Numerical methods for including fermions in computer simulations are considered. Jacobi and Gauss-Siedel inversion methods to obtain the fermion propagator in a background gauge field are reviewed

Introduction to lattice gauge theory

International Nuclear Information System (INIS)

Gupta, R.

1987-01-01

The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off ≅ 1/α, where α is the lattice spacing. The continuum (physical) behavior is recovered in the limit α → 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs

Gauge theories and integrable lattice models

International Nuclear Information System (INIS)

Witten, E.

1989-01-01

Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question - previously considered in both the knot theory and statistical mechanics literature - are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be represented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory. (orig.)

Frustration and dual superconductivity in lattice gauge theories

International Nuclear Information System (INIS)

Orland, P.

1984-01-01

Introducing plaquette fields in SU(N) gauge theories yields a mass gap and confinement by a dual Meisnner effect. Sources for the plaquette fields are electric strings. Similiar plaquette fields exist in pure compact lattice gauge theories. In principle they make it possible to expand in h while keeping the guage field compact

Lattice gauge fixing as quenching and the violation of spectral positivity

International Nuclear Information System (INIS)

Aubin, C.; Ogilvie, Michael C.

2004-01-01

Lattice Landau gauge and other related lattice gauge-fixing schemes are known to violate spectral positivity. The most direct sign of the violation is the rise of the effective mass as a function of distance. The origin of this phenomenon lies in the quenched character of the auxiliary field g used to implement lattice gauge-fixing, and is similar to quenched QCD in this respect. This is best studied using the Parrinello Jona-Lasinio Zwanziger formalism, leading to a class of covariant gauges similar to the one-parameter class of covariant gauges commonly used in continuum gauge theories. Soluble models are used to illustrate the origin of the violation of spectral positivity. The phase diagram of the lattice theory, as a function of the gauge coupling β and the gauge-fixing parameter α, is similar to that of the unquenched theory, a Higgs model of a type first studied by Fradkin and Shenker. The gluon propagator is interpreted as yielding bound states in the confined phase, and a mixture of fundamental particles in the Higgs phase, but lattice simulation shows the two phases are connected. Gauge-field propagators from the simulation of an SU(2) lattice gauge theory on a 20 4 lattice are well described by a quenched mass-mixing model. The mass of the lightest state, which we interpret as the gluon mass, appears to be independent of α for sufficiently large α

National Computational Infrastructure for Lattice Gauge Theory

Energy Technology Data Exchange (ETDEWEB)

Brower, Richard C.

2014-04-15

SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io

Lattice gauge theories

International Nuclear Information System (INIS)

Hasenfratz, A.; Hasenfratz, P.

1985-01-01

This paper deals almost exclusively with applications in QCD. Presumably QCD will remain in the center of lattice calculations in the near future. The existing techniques and the available computer resources should be able to produce trustworthy results in pure SU(3) gauge theory and in quenched hadron spectroscopy. Going beyond the quenched approximation might require some technical breakthrough or exceptional computer resources, or both. Computational physics has entered high-energy physics. From this point of view, lattice QCD is only one (although the most important, at present) of the research fields. Increasing attention is devoted to the study of other QFTs. It is certain that the investigation of nonasymptotically free theories, the Higgs phenomenon, or field theories that are not perturbatively renormalizable will be important research areas in the future

Overview of lattice gauge theory at the CSSM

International Nuclear Information System (INIS)

Williams, A.G.

2002-01-01

Full text: I present an overview of the lattice gauge theory effort at the Special Research Centre for the Subatomic Structure of Matter (CSSM). The CSSM specializes in research into the strong interactions and into quantum chromodynamics (QCD), which is the fundamental quantum gauge field theory of the strong interactions. The primary mission of the CSSM is to attempt to solve QCD and hence test the implications of the theory against experimental evidence. The difficulty lies in the fact that the QCD is a highly nonlinear, strongly coupled theory. The only known first-principles means to solve it is to approximate space-time by a four-dimensional 'grid' or 'lattice' and to simulate this 'lattice QCD' on massively parallel supercomputers. A discussion of the Orion supercomputer of the National Computing Facility for Lattice Gauge Theory (NFCLGT) and the latest QCD predictions obtained from Orion by CSSM researchers will be presented

The cross-over points in lattice gauge theories with continuous gauge groups

International Nuclear Information System (INIS)

Cvitanovic, P.; Greensite, J.; Lautrup, B.

1981-01-01

We obtain a closed expression for the weak-to-strong coupling cross-over point in all Wilson type lattice gauge theories with continuous gauge groups. We use a weak-coupling expansion of the mean-field self-consistency equation. In all cases where our results can be compared with Monte Carlo calculations the agreement is excellent. (orig.)

Strong dynamics and lattice gauge theory

Science.gov (United States)

Schaich, David

In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses

Infrared exponents and the strong-coupling limit in lattice Landau gauge

International Nuclear Information System (INIS)

Sternbeck, Andre; Smekal, Lorenz von

2010-01-01

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit β=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta q 2 QCD 2 . In the strong-coupling limit, this same behavior is obtained for the larger values of a 2 q 2 (in units of the lattice spacing a), where it is otherwise swamped by the gauge-field dynamics. Deviations for a 2 q 2 <1 are well parameterized by a transverse gluon mass ∝1/a. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes (Phys. Rev. D 81:016005, 2010). (orig.)

Lattices for laymen: a non-specialist's introduction to lattice gauge theory

International Nuclear Information System (INIS)

Callaway, D.J.E.

1985-01-01

The review on lattice gauge theory is based upon a series of lectures given to the Materials Science and Technology Division at Argonne National Laboratory. Firstly the structure of gauge theories in the continuum is discussed. Then the lattice formulation of these theories is presented, including quantum electrodynamics and non-abelian lattice gauge theories. (U.K.)

Remarks on lattice gauge models

International Nuclear Information System (INIS)

Grosse, H.

1981-01-01

The author reports a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton and observes that it violates a positivity property. (Auth.)

Digital lattice gauge theories

Science.gov (United States)

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

2017-02-01

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

Remarks on lattice gauge models

International Nuclear Information System (INIS)

Grosse, H.

1981-01-01

The author reports on a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton (1980) and observes that it violates a positivity property. (Auth.)

Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory

International Nuclear Information System (INIS)

Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.

1996-01-01

We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined

The investigation of 1+1 dimensional lattice gauge theories with fermions, gauge bosons and scalar using Hamiltonian Monte-Carlo methods

International Nuclear Information System (INIS)

Ranft, J.

1984-01-01

Hamiltonian lattice models with fermions, gauge bosons and scalar fields are studied in 1+1 dimensions using the local Hamiltonian Monte-Carlo method. Results are presented for the massive Schwinger model with one and two flavors, for a model with interacting Higgs fields, fermions and gauge bosons, where fractionally charged solitons are found as free states of the lattice model, and for Wess-Zumino type models with restricted lattice supersymmetry, where examples for spontaneous breaking of supersymmetry are found

Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets

Science.gov (United States)

Dupoyet, B.; Fiebig, H. R.; Musgrove, D. P.

2010-01-01

We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is implemented in a numerical simulation. We arrive at a probability distribution of relative gains which matches the high frequency historical data of the NASDAQ stock exchange index.

Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

Energy Technology Data Exchange (ETDEWEB)

Solbrig, Stefan

2008-07-01

In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

International Nuclear Information System (INIS)

Solbrig, Stefan

2008-01-01

In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

Response of SU(2) lattice gauge theory to a gauge invariant external field

International Nuclear Information System (INIS)

Goepfert, M.

1980-10-01

Topologically determined Z(2) variables in pure SU(2) lattice gauge theory are discussed. They count the number of 'vortex souls'. The expectation value of the corresponding Z(2) loop and the dependence of the string tension on an external field h coupled to them is calculated to lowest order in the high temperature expansion. The result is in agreement with the conjecture that the probability distribution of vortex souls determines the string tension. A different formula for the string tension is found in the two limiting cases 0 < /h/ << β << 1 and 0 < β << h << 1. This penomenon is traced to the effect of short range interactions of the vortex souls which are mediated by the other excitations in the theory. (orig.)

Selfduality and topological-like properties of lattice gauge field theories. A proposal

Energy Technology Data Exchange (ETDEWEB)

Cotta-Ramusino, P; Dell' Antonio, G [Freie Univ. Berlin (Germany, F.R.). Inst. fuer Theoretische Physik; Rome Univ. (Italy). Istituto di Matematica)

1979-11-01

We introduce for lattice gauge theories an analogue of the Pontrjagin index and a notion of 'selfduality' and 'antiselfduality'. Selfdual and antiselfdual configurations on the lattice have much of the same properties (with some remarkable differences) as the corresponding configurations on the continuum, to which they converge when the lattice spacing goes to zero.

On the continuum limit of a Z4 lattice gauge theory

International Nuclear Information System (INIS)

Pena, A.; Socolovsky, M.

1983-01-01

The continuum limit of a Z 4 gauge plus matter lattice theory is identified with massless scalar and vector fields with quartic self-interactions phi 4 and (AμAμ) 2 , respectively. The analysis is based on the mean field approximation after gauge fixing. (orig.)

Topology in SU(2) lattice gauge theory and parallelization of functional magnetic resonance imaging

Energy Technology Data Exchange (ETDEWEB)

Solbrig, Stefan

2008-07-01

In this thesis, I discuss topological properties of quenched SU(2) lattice gauge fields. In particular, clusters of topological charge density exhibit a power-law. The exponent of that power-law can be used to validate models for lattice gauge fields. Instead of working with fixed cutoffs of the topological charge density, using the notion of a ''watermark'' is more convenient. Furthermore, I discuss how a parallel computer, originally designed for lattice gauge field simulations, can be used for functional magnetic resonance imaging. Multi parameter fits can be parallelized to achieve almost real-time evaluation of fMRI data. (orig.)

The topology of gauge fields

International Nuclear Information System (INIS)

Tellis, D.R.

2000-01-01

Full text: Instantons in pure Yang-Mills gauge theory have been studied extensively by physicists and mathematicians alike. The surprisingly rich topological structure plays an important role in hadron structure. A crucial role is played by how the boundary conditions on the gauge fields are imposed. While the topology of gauge fields in pure Yang-Mills gauge theory is understood for the compact manifold of the 4-sphere, the manifold of the 4-torus remains an active area of study. The latter is particularly important in the study of Lattice QCD

Residual gauge invariance of Hamiltonian lattice gauge theories

International Nuclear Information System (INIS)

Ryang, S.; Saito, T.; Shigemoto, K.

1984-01-01

The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)

Gauge field theories on a || lattice

International Nuclear Information System (INIS)

Burkardt, Matthias

1999-01-01

In these notes, the transverse || lattice approach is presented as a means to control the k + →0 divergences in light-front QCD. Technical difficulties of both the canonical compact formulation as well as the non-compact formulation of the || lattice motivate the color-dielectric formulation, where the link fields are linearized

Supersymmetric quiver gauge theories on the lattice

International Nuclear Information System (INIS)

Joseph, Anosh

2013-12-01

In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through the methods of topological twisting and geometric discretization of Euclidean Yang-Mills theories with eight and sixteen supercharges in two and three dimensions. We detail the lattice constructions of two-dimensional quiver gauge theories possessing four and eight supercharges and three-dimensional quiver gauge theories possessing eight supercharges.

Anomaly cancellation condition in abelian lattice gauge theories

International Nuclear Information System (INIS)

Suzuki, Hiroshi

1999-11-01

We analyze the general solution of the Wess-Zumino consistency condition in abelian lattice gauge theories, without taking the classical continuum limit. We find that, if the anomaly density is a local pseudo-scalar field on the lattice, the non-trivial anomaly is always proportional to the anomaly coefficient in the continuum theory. The possible extension of this result to non-abelian theories is briefly discussed. (author)

Internal space decimation for lattice gauge theories

International Nuclear Information System (INIS)

Flyvbjerg, H.

1984-01-01

By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed. (orig.)

Manipulating novel quantum phenomena using synthetic gauge fields

Science.gov (United States)

Zhang, Shao-Liang; Zhou, Qi

2017-11-01

The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.

Lattice Gauge Theories Have Gravitational Duals

International Nuclear Information System (INIS)

Hellerman, Simeon

2002-01-01

In this paper we examine a certain threebrane solution of type IIB string theory whose long-wavelength dynamics are those of a supersymmetric gauge theory in 2+1 continuous and 1 discrete dimension, all of infinite extent. Low-energy processes in this background are described by dimensional deconstruction, a strict limit in which gravity decouples but the lattice spacing stays finite. Relating this limit to the near-horizon limit of our solution we obtain an exact, continuum gravitational dual of a lattice gauge theory with nonzero lattice spacing. H-flux in this translationally invariant background encodes the spatial discreteness of the gauge theory, and we relate the cutoff on allowed momenta to a giant graviton effect in the bulk

Lattice Gauge Field Theory and Prismatic Sets

DEFF Research Database (Denmark)

Akyar, Bedia; Dupont, Johan Louis

as and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying......We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type...

Machines for lattice gauge theory

International Nuclear Information System (INIS)

Mackenzie, P.B.

1989-05-01

The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig

SU(N) chiral gauge theories on the lattice

International Nuclear Information System (INIS)

Golterman, Maarten; Shamir, Yigal

2004-01-01

We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-Abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the Abelian case. The new ingredient allowing us to deal with the non-Abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-Abelian group (which we will take to be SU(N)) down to its maximal Abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining Abelian gauge symmetry. This modifies the equivariant Becchi-Rouet-Stora-Tyutin (BRST) identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the Abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be added to the lattice gauge-fixing action in order to have access to the desired critical point in the phase diagram. We argue that gauge invariance is restored in the continuum limit by adjusting a finite number of counter terms. We emphasize that weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory

Monte Carlo computations for lattice gauge theories with finite gauge groups

International Nuclear Information System (INIS)

Rabbi, G.

1980-01-01

Recourse to Monte Carlo simulations for obtaining numerical information about lattice gauge field theories is suggested by the fact that, after a Wick rotation of time to imaginary time, the weighted sum over all configurations used to define quantium expectation values becomes formally identical to a statistical sum of a four-dimensional system. Results obtained in a variety of Monte Carlo investigations are described

Monte Carlo algorithms for lattice gauge theory

International Nuclear Information System (INIS)

Creutz, M.

1987-05-01

Various techniques are reviewed which have been used in numerical simulations of lattice gauge theories. After formulating the problem, the Metropolis et al. algorithm and some interesting variations are discussed. The numerous proposed schemes for including fermionic fields in the simulations are summarized. Langevin, microcanonical, and hybrid approaches to simulating field theories via differential evolution in a fictitious time coordinate are treated. Some speculations are made on new approaches to fermionic simulations

Analytical methods applied to the study of lattice gauge and spin theories

International Nuclear Information System (INIS)

Moreo, Adriana.

1985-01-01

A study of interactions between quarks and gluons is presented. Certain difficulties of the quantum chromodynamics to explain the behaviour of quarks has given origin to the technique of lattice gauge theories. First the phase diagrams of the discrete space-time theories are studied. The analysis of the phase diagrams is made by numerical and analytical methods. The following items were investigated and studied: a) A variational technique was proposed to obtain very accurated values for the ground and first excited state energy of the analyzed theory; b) A mean-field-like approximation for lattice spin models in the link formulation which is a generalization of the mean-plaquette technique was developed; c) A new method to study lattice gauge theories at finite temperature was proposed. For the first time, a non-abelian model was studied with analytical methods; d) An abelian lattice gauge theory with fermionic matter at the strong coupling limit was analyzed. Interesting results applicable to non-abelian gauge theories were obtained. (M.E.L.) [es

Genetic algorithm for lattice gauge theory on SU(2) and U(1) on 4 dimensional lattice, how to hitchhike to thermal equilibrium state

International Nuclear Information System (INIS)

Yamaguchi, A.; Sugamoto, A.

2000-01-01

Applying Genetic Algorithm for the Lattice Gauge Theory is formed to be an effective method to minimize the action of gauge field on a lattice. In 4 dimensions, the critical point and the Wilson loop behaviour of SU(2) lattice gauge theory as well as the phase transition of U(1) theory have been studied. The proper coding methodi has been developed in order to avoid the increase of necessary memory and the overload of calculation for Genetic Algorithm. How hichhikers toward equilibrium appear against kidnappers is clarified

U(1) Wilson lattice gauge theories in digital quantum simulators

Science.gov (United States)

Muschik, Christine; Heyl, Markus; Martinez, Esteban; Monz, Thomas; Schindler, Philipp; Vogell, Berit; Dalmonte, Marcello; Hauke, Philipp; Blatt, Rainer; Zoller, Peter

2017-10-01

Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication (Martinez et al 2016 Nature 534 516), we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle-antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.

Gauge theories on a small lattice

International Nuclear Information System (INIS)

Robson, D.; Webber, D.M.

1980-01-01

We present exact solutions to U(1), SU(2), and SU(3) lattice gauge theories on a Kogut-Susskind lattice consisting of a single plaquette. We demonstrate precise equivalence between the U(1) theory and the harmonic oscillator on an infinite one-dimensional lattice, and between the SU(N) theory and an N-fermion Schroedinger equation. (orig.)

Effective monopole potential for SU(2) lattice gluodynamics in spatial maximal Abelian gauge

International Nuclear Information System (INIS)

Chernodub, M.N.; Polikarpov, M.I.; Veselov, A.I.

1999-01-01

We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more physical than the ordinary Maximal Abelian gauge due to absence of non-localities in temporal direction. We shown numerically that in the Spatial Maximal Abelian gauge the probability distribution of the abelian monopole field is consistent with the dual superconductor mechanism of confinement [ru

Tadpole-improved SU(2) lattice gauge theory

Science.gov (United States)

Shakespeare, Norman H.; Trottier, Howard D.

1999-01-01

A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is made. Simulations are done on isotropic and anisotropic lattices, with and without improvement. Two tadpole renormalization schemes are employed, one using average plaquettes, the other using mean links in the Landau gauge. Simulations are done with spatial lattice spacings as in the range of about 0.1-0.4 fm. Results are presented for the static quark potential, the renormalized lattice anisotropy at/as (where at is the ``temporal'' lattice spacing), and for the scalar and tensor glueball masses. Tadpole improvement significantly reduces discretization errors in the static quark potential and in the scalar glueball mass, and results in very little renormalization of the bare anisotropy that is input to the action. We also find that tadpole improvement using mean links in the Landau gauge results in smaller discretization errors in the scalar glueball mass (as well as in the static quark potential), compared to when average plaquettes are used. The possibility is also raised that further improvement in the scalar glueball mass may result when the coefficients of the operators which correct for discretization errors in the action are computed beyond the tree level.

Classical solutions in lattice gauge theories

International Nuclear Information System (INIS)

Mitrjushkin, V.K.

1996-08-01

The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed. (orig.)

Chirality conservation in the lattice gauge theory

International Nuclear Information System (INIS)

Peskin, M.E.

1978-01-01

The derivation of conservation laws corresponding to chiral invariance in quantum field theories of interacting quarks and gluons are studied. In particular there is interest in observing how these conservation laws are constrained by the requirement that the field theory be locally gauge invariant. To examine this question, a manifestly gauge-invariant definition of local operators in a quantum field theory is introduced, a definition which relies in an essential way on the use of the formulation of gauge fields on a lattice due to Wilson and Polyakov to regulate ultraviolet divergences. The conceptual basis of the formalism is set out and applied to a long-standing puzzle in the phenomenology of quark-gluon theories: the fact that elementary particle interactions reflect the conservation of isospin-carrying chiral currents but not of the isospin-singlet chiral current. It is well known that the equation for the isospin-singlet current contains an extra term, the operator F/sub mu neu/F/sup mu neu/, not present in the other chirality conservation laws; however, this term conventionally has the form of a total divergence and so still allows the definition of a conserved chiral current. It is found that, when the effects of maintaining gauge invariance are properly taken into account, the structure of this operator is altered by renormalization effects, so that it provides an explicit breaking of the unwanted chiral invariance. The relation between this argument, based on renormaliztion, is traced to a set of more heuristic arguments based on gauge field topology given by 't Hooft; it is shown that the discussion provides a validation, through short-distance analysis, of the picture 'Hooft has proposed. The formal derivation of conservation laws for chiral currents are set out in detail

Blockspin transformations for finite temperature field theories with gauge fields

International Nuclear Information System (INIS)

Kerres, U.

1996-08-01

A procedure is proposed to study quantum field theories at zero or at finite temperature by a sequence of real space renormalization group (RG) or blockspin transformations. They transform to effective theories on coarser and coarser lattices. The ultimate aim is to compute constraint effective potentials, i.e. the free energy as a function of suitable order parameters. From the free energy one can read off the thermodynamic behaviour of the theory, in particular the existence and nature of phase transitions. In a finite temperature field theory one begins with either one or a sequence of transformations which transform the original theory into an effective theory on a three-dimensional lattice. Its effective action has temperature dependent coefficients. Thereafter one may proceed with further blockspin transformations of the three-dimensional theory. Assuming a finite volume, this can in principle be continued until one ends with a lattice with a single site. Its effective action is the constraint effective potential. In each RG-step, an integral over the high frequency part of the field, also called the fluctuation field, has to be performed. This is done by perturbation theory. It requires the knowledge of bare fluctuation field propagators and of interpolation operators which enter into the vertices. A detailed examination of these quantities is presented for scalar fields, abelian gauge fields and for Higgs fields, finite temperature is admitted. The lattice perturbation theory is complicated because the bare lattice propagators are complicated. This is due to a partial loss of translation invariance in each step. Therefore the use of translation invariant cutoffs in place of a lattice is also discussed. In case of gauge fields this is only possible as a continuum version of the blockspin method. (orig.)

Scaled lattice fermion fields, stability bounds, and regularity

Science.gov (United States)

O'Carroll, Michael; Faria da Veiga, Paulo A.

2018-02-01

We consider locally gauge-invariant lattice quantum field theory models with locally scaled Wilson-Fermi fields in d = 1, 2, 3, 4 spacetime dimensions. The use of scaled fermions preserves Osterwalder-Seiler positivity and the spectral content of the models (the decay rates of correlations are unchanged in the infinite lattice). In addition, it also results in less singular, more regular behavior in the continuum limit. Precisely, we treat general fermionic gauge and purely fermionic lattice models in an imaginary-time functional integral formulation. Starting with a hypercubic finite lattice Λ ⊂(aZ ) d, a ∈ (0, 1], and considering the partition function of non-Abelian and Abelian gauge models (the free fermion case is included) neglecting the pure gauge interactions, we obtain stability bounds uniformly in the lattice spacing a ∈ (0, 1]. These bounds imply, at least in the subsequential sense, the existence of the thermodynamic (Λ ↗ (aZ ) d) and the continuum (a ↘ 0) limits. Specializing to the U(1) gauge group, the known non-intersecting loop expansion for the d = 2 partition function is extended to d = 3 and the thermodynamic limit of the free energy is shown to exist with a bound independent of a ∈ (0, 1]. In the case of scaled free Fermi fields (corresponding to a trivial gauge group with only the identity element), spectral representations are obtained for the partition function, free energy, and correlations. The thermodynamic and continuum limits of the free fermion free energy are shown to exist. The thermodynamic limit of n-point correlations also exist with bounds independent of the point locations and a ∈ (0, 1], and with no n! dependence. Also, a time-zero Hilbert-Fock space is constructed, as well as time-zero, spatially pointwise scaled fermion creation operators which are shown to be norm bounded uniformly in a ∈ (0, 1]. The use of our scaled fields since the beginning allows us to extract and isolate the singularities of the free

Confinement in dually transformed U(1) lattice gauge theory

International Nuclear Information System (INIS)

Zach, M.

1997-10-01

The aim of this work is a detailed investigation of the confinement mechanism in U(1) lattice gauge theory. In the first chapters we give a review on the definition of compact Abelian gauge theory on space-time lattices, the numerical calculation of physical observables for exploring confinement, and the interpretation of the results in terms of the dual superconductor picture, which is introduced at two levels of description. We work out that the electric field strength and the magnetic currents around a charge pair can be described very well by a classical effective model of Maxwell and London equations, if fluctuations of the occurring fluxoid string are considered. In order to obtain a deeper understanding of confinement in U(1), we extend the duality transformation of the path integral to the correlation functions which are used to calculate expectation values of fields and currents. This not only helps to interpret U(1) lattice gauge theory as a limit of the dual Higgs model, but also opens the possibility for efficient calculations of expectation values in the presence of static charges by simulating the dual model. Using this technique we are able to consider large flux tube lengths, low temperatures, and multiply charged systems without loss of numerical precision. The dual simulation is applied to flux tubes between static charges, to periodically closed flux tubes (torelons), and to doubly charged systems. We find that the behavior of flux tubes for large charge distances cannot be explained by the picture of a classical dual type-II superconductor; the observed roughening of the flux tube agrees very well with the prediction from the effective string description. We also analyze the different contributions to the total energy of the electromagnetic field. For torelons we calculate both the free energy and the total field energy, split the free energy into a string tension and a string fluctuation part, and apply lattice sum rules modified for finite

Non-Abelian gauge fields

Science.gov (United States)

Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus

2013-07-01

Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another

Soft covariant gauges on the lattice

Energy Technology Data Exchange (ETDEWEB)

Henty, D.S.; Oliveira, O.; Parrinello, C.; Ryan, S. [Department of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (UKQCD Collaboration)

1996-12-01

We present an exploratory study of a one-parameter family of covariant, nonperturbative lattice gauge-fixing conditions that can be implemented through a simple Monte Carlo algorithm. We demonstrate that at the numerical level the procedure is feasible, and as a first application we examine the gauge dependence of the gluon propagator. {copyright} {ital 1996 The American Physical Society.}

A map between corner and link operators in lattice gauge theories

International Nuclear Information System (INIS)

Bars, I.

1979-01-01

A completely local gauge-invariant lattice gauge theory is formulated in terms of a new set of variables introduced earlier in the continuum. This theory uses local 'corner' variables defined on lattice sites only, as opposed to the conventional 'link' variables. It is shown via a map that the formulation gives identical results to the usual lattice gauge theory. The properties of the quantum commutators in the continuum limit is also discussed and contrasted for the two lattice approaches. In terms of the corner operators the quantized lattice theory is seen to be closely related to continuum QCD. (Auth.)

Instantons and topological charge in lattice gauge theory

International Nuclear Information System (INIS)

Iwasaki, Y.; Yoshie, T.

1983-01-01

The existence of instantons on the lattice in SU(2) lattice gauge theory is investigated for various lattice actions with loops of up to six lattice spacings. Instantons exist only for the actions where short range fluctuations are suppressed. A formula for topological properties of the solutions are examined. (orig.)

Unexpected behavior of an order parameter for lattice gauge theories with matter fields

International Nuclear Information System (INIS)

Meyer, H.

1983-07-01

I consider a slightly modified definition of an order parameter that was recently suggested by DeTar and McLerran. It is supposed to test for confinement in lattice gauge theories when arbitrary matter fields are present, at finite physical temperature β -1 > 0. Its definition is quite directly related to confinement in the sense that no physical states with fractional baryon number can be observed. We test the parameter for different ranges of the coupling constants in the Z(2) Higgs model, whose phase structure is well known at zero temperature. It is found that the order parameter always shows the behavior characteristic of confinement, for all values of the coupling constants and arbitrary nonzero temperature. (orig.)

Gauge-invariant variational methods for Hamiltonian lattice gauge theories

International Nuclear Information System (INIS)

Horn, D.; Weinstein, M.

1982-01-01

This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum

Atomic quantum simulation of the lattice gauge-Higgs model: Higgs couplings and emergence of exact local gauge symmetry.

Science.gov (United States)

Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo

2013-09-13

Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.

Semiclassical analysis of the weak-coupling limit of SU(2) lattice gauge theory: The subspace of constant fields

International Nuclear Information System (INIS)

Bartels, J.; Wu, T.T.

1988-01-01

This paper contains the first part of a systematic semiclassical analysis of the weak-coupling limit of lattice gauge theories, using the Hamiltonian formulation. The model consists of an N 3 cubic lattice of pure SU(2) Yang-Mills theory, and in this first part we limit ourselves to the subspace of constant field configurations. We investigate the flow of classical trajectories, with a particular emphasis on the existence and location of caustics. There the ground-state wave function is expected to peak. It is found that regions densely filled with caustics are very close to the origin, i.e., in the domain of weak field configurations. This strongly supports the expectation that caustics are essential for quantities of physical interest

Topics in two dimensional conformal field theory and three dimensional topological lattice field theory

International Nuclear Information System (INIS)

Chung, Stephen-wei.

1993-01-01

The authors first construct new parafermions in two-dimensional conformal field theory, generalizing the Z L parafermion theories from integer L to rational L. These non-unitary parafermions have some novel features: an infinite number of currents with negative conformal dimensions for most (if not all) of them. String functions of these new parafermion theories are calculated. They also construct new representations of N = 2 superconformal field theories, whose characters are obtained in terms of these new string functions. They then generalize Felder's BRST cohomology method to construct the characters and branching functions of the SU(2) L x SU(2) K /SU(2) K+L coset theories, where one of the (K,L) is an integer. This method of obtaining the branching functions also serves as a check of their new Z L parafermion theories. The next topic is the Lagrangian formulation of conformal field theory. They construct a chiral gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R , which can be different groups. This new construction is beyond the ordinary vector gauged WZW theory, whose gauge group H is a subgroup of both G L and G R . In the special case where H L = H R , the quantum theory of chiral gauged WZW theory is equivalent to that of the vector gauged WZW theory. It can be further shown that the chiral gauged WZW theory is equivalent to [G L /H L ](z) direct-product [G R /H R ](bar z) coset models in conformal field theory. In the second half of this thesis, they construct topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, they impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint

Five-dimensional Lattice Gauge Theory as Multi-Layer World

OpenAIRE

Murata, Michika; So, Hiroto

2003-01-01

A five-dimensional lattice space can be decomposed into a number of four-dimens ional lattices called as layers. The five-dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. In the theory, there exist two independent coupling constants; $\\beta_4$ controls the dynamics inside a layer and $\\beta_5$ does the strength of the inter-layer interaction.We propose the new possibility to realize t...

Lattice gauge theories, confinement, strings and all that

International Nuclear Information System (INIS)

Muenster, G.

1980-11-01

In this talk I would like to give an overview over some developments in lattice gauge theory, which might be of some interest for experimental physicists. In particular, I shall try to convince you that lattice gauge theory is not only a play-ground for theorists, but is able to produce numerical results for some non-perturbative quantities. And, of course, I would like to tell you about some work, which has been done here in Hamburg. (orig.)

Geometry of lattice field theory

International Nuclear Information System (INIS)

Honan, T.J.

1986-01-01

Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus

Recent developments in chiral gauge theories: approach of infinitely many fermi fields

International Nuclear Information System (INIS)

Narayanan, R.

1994-01-01

I present the recent developments in a specific sub-field of chiral gauge theories on the lattice. This subfield pertains to the use of infinitely many fermi fields to describe a single chiral field. In this approach, both anomalous and anomaly free theories can be discussed in equal footing. It produces the correct anomaly in the continuum limit. It has the potential to describe fermion number violating processes in the presence of a gauge field background with non-trivial topological charge on a finite lattice. (orig.)

Discretisation errors in Landau gauge on the lattice

International Nuclear Information System (INIS)

Bonnet DR, Frederic; Bowman O, Patrick; Leinweber B, Derek; Williams G, Anthony; Richards G, David G.

1999-01-01

Lattice discretization errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which O(a 2 ) errors are removed is presented. O(a 2 ) improvement of the gauge fixing condition improves comparison with continuum Landau gauge in two ways: (1) through the elimination of O(a 2 ) errors and (2) through a secondary effect of reducing the size of higher-order errors. These results emphasize the importance of implementing an improved gauge fixing condition

A technique for analytical calculation of observables in lattice gauge theories

International Nuclear Information System (INIS)

Narayanan, R.; Vranas, P.

1990-01-01

It is shown that the partition function for a finite lattice factorizes into terms that can be associated with each vertex in the finite lattice. This factorization property forms the basis of well defined and efficient technique developed to calculate partition functions to high accuracy, on finite lattices for gauge theories. This technique along with the expansion in finite lattices, provides a powerful means for calculating observables in lattice gauge theories. This is applied to SU(2) lattice gauge theory in four dimensions. The free energy, expectation value of a plaquette and specific heat are calculated. The results are very good in the strong coupling region, succeed in entering the weak coupling region and describe the crossover region quite well, agreeing all the way with the Monte Carlo data. (orig.)

Lattices gauge theories in terms of knots

International Nuclear Information System (INIS)

Vecernyes, P.

1989-01-01

Cluster expansion is developed in lattice gauge theories with finite gauge groups in d≥3 dimensions where the clusters are connected (d - 2)-dimensional surfaces which can branch along (d - 3)-cells. The interaction between them has a knot theoretical interpretation. It can be many body linking or knotting self-interaction. For small enough gauge coupling g the authors prove analyticity of the correlation functions in the variable exp(-1/g 2

SU(3) lattice gauge fixing with overrelaxation and Gribov copies

Energy Technology Data Exchange (ETDEWEB)

Paciello, M.L.; Taglienti, B. (INFN La Sapienza, Rome (Italy)); Parrinello, C. (Physics Dept., New York Univ., NY (United States)); Petrarca, S. (Theory Div., CERN, Geneva (Switzerland)); Vladikas, A. (Dipt. di Fisica, Univ. Tor Vergata, Rome (Italy) INFN Tor Vergata, Rome (Italy))

1992-02-06

We report on the phenomenology of SU(3) lattice Landau gauge fixing as obtained by using an overrelaxation algorithm. An interesting result obtained using this very efficient algorithm is that distinct Gribov copies are generated by simply modifying the value {omega} of the overrelaxation parameter for a fixed starting configuration. By generating random gauge equivalent configurations, we study the variation of the number of copies with the lattice volume and gauge coupling. (orig.).

Discretisation errors in Landau gauge on the lattice

International Nuclear Information System (INIS)

Bonnet, F.D.R.; Bowmen, P.O.; Leinweber, D.B.

1999-01-01

Lattice discretisation errors in the Landau gauge condition are examined. An improved gauge fixing algorithm in which O(a 2 ) errors are removed is presented. O(a 2 ) improvement of the gauge fixing condition improves comparison with the continuum Landau gauge in two ways: (1) through the elimination of O(a 2 ) errors and (2) through a secondary effect of reducing the size of higher-order errors. These results emphasise the importance of implementing an improved gauge fixing condition. Copyright (1999) CSIRO Australia

Status and future of lattice gauge theory

International Nuclear Information System (INIS)

Hoek, J.

1989-07-01

The current status of lattice Quantum Chromo Dynamics (QCD) calculations, the computer requirements to obtain physical results and the direction computing is taking are described. First of all, there is a lot of evidence that QCD is the correct theory of strong interactions. Since it is an asymptotically free theory we can use perturbation theory to solve it in the regime of very hard collisions. However even in the case of very hard parton collisions the end-results of the collisions are bound states of quarks and perturbation theory is not sufficient to calculate these final stages. The way to solve the theory in this regime was opened by Wilson. He contemplated replacing the space-time continuum by a discrete lattice, with a lattice spacing a. Continuum physics is then recovered in the limit where the correlation length of the theory, say ξ. is large with respect to the lattice spacing. This will be true if the lattice spacing becomes very small, which for asymptotically free theories also implies that the coupling g becomes small. The lattice approach to QCD is in many respects analogous to the use of finite element methods to solve classical field theories. These finite element methods are easy to apply in 2-dimensional simulations but are computationally demanding in the 3-dimensional case. Therefore it is not unexpected that the 4-dimensional simulations needed for lattice gauge theories have led to an explosion in demand for computing power by theorists. (author)

Lattice gauge theories and Monte Carlo simulations

International Nuclear Information System (INIS)

Rebbi, C.

1981-11-01

After some preliminary considerations, the discussion of quantum gauge theories on a Euclidean lattice takes up the definition of Euclidean quantum theory and treatment of the continuum limit; analogy is made with statistical mechanics. Perturbative methods can produce useful results for strong or weak coupling. In the attempts to investigate the properties of the systems for intermediate coupling, numerical methods known as Monte Carlo simulations have proved valuable. The bulk of this paper illustrates the basic ideas underlying the Monte Carlo numerical techniques and the major results achieved with them according to the following program: Monte Carlo simulations (general theory, practical considerations), phase structure of Abelian and non-Abelian models, the observables (coefficient of the linear term in the potential between two static sources at large separation, mass of the lowest excited state with the quantum numbers of the vacuum (the so-called glueball), the potential between two static sources at very small distance, the critical temperature at which sources become deconfined), gauge fields coupled to basonic matter (Higgs) fields, and systems with fermions

Topological charge in non-abelian lattice gauge theory

International Nuclear Information System (INIS)

Lisboa, P.

1983-01-01

We report on a numerical calculation of topological charge densities in non-abelian gauge theory with gauge groups SU(2) and SU(3). The group manifold is represented by a discrete subset thereof which lies outside its finite subgroups. The results shed light on the usefulness of these representations in Monte Carlo evaluations of non-abelian lattice gauge theory. (orig.)

Role of gauge invariance in a variational and mean-field calculation

International Nuclear Information System (INIS)

Masperi, L.; Omero, C.

1981-08-01

We show that the implementation of gauge invariance is essential for a variational treatment to correctly reproduce all the features of the phase diagram for the Z(2) lattice gauge theory with matter field. (author)

Quiver gauge theories and integrable lattice models

International Nuclear Information System (INIS)

Yagi, Junya

2015-01-01

We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.

Magnetic polarizabilities of light mesons in SU(3 lattice gauge theory

Directory of Open Access Journals (Sweden)

E.V. Luschevskaya

2015-09-01

Full Text Available We investigate the ground state energies of neutral pseudoscalar and vector meson in SU(3 lattice gauge theory in the strong abelian magnetic field. The energy of ρ0 meson with zero spin projection sz=0 on the axis of the external magnetic field decreases, while the energies with non-zero spins sz=−1 and +1 increase with the field. The energy of π0 meson decreases as a function of the magnetic field. We calculate the magnetic polarizabilities of pseudoscalar and vector mesons for lattice volume 184. For ρ0 with spin |sz|=1 and π0 meson the polarizabilities in the continuum limit have been evaluated. We do not observe any evidence in favour of tachyonic mode existence.

Hadron mass spectrum in a lattice gauge theory

International Nuclear Information System (INIS)

Seo, Koichi

1978-01-01

We perform the strong coupling expansion in a lattice gauge theory and obtain the hadron mass spectrum. We develop a theory in the Hamiltonian formalism following Kogut and Susskind, but our treatment of quark fields is quite different from theirs. Thus our results largely differ from theirs. In our model and approximation, the pseudoscalar mesons have the same mass as the vectors. The baryon decuplet and the octet are also degenerate. The excited meson states are studied in detail. (auth.)

Monopoles and confinement in lattice gauge theory

International Nuclear Information System (INIS)

Singh, V.

1992-01-01

The mechanism by which quarks, believed to be the fundamental constituents of matter, are prevented from existing in the free state is fundamental problems in physics. One of the most viable candidates for a hypothesis of confinement is the dual superconductor mechanism that likens quark confinement to the Meissner effect in superconductors. The peculiarities of quark interactions make a numerical approach to the subject a necessity, and therefore, much of the work in this area has been done through the methods of lattice gauge theory, with the simplicities afforded by putting spacetime on a four-dimensional grid. Over the years a large amount of indirect evidence has accumulated that the dual superconductor hypothesis does indeed lead to quark confinement but unambiguous evidence has eluded research efforts until recently. This work presents the first direct proof of a Meissner-like effect that leads to confinement, using the numerical techniques of lattice gauge theory. It is shown that for a U(1) lattice gauge theory, that serves as a toy model of the real world of quarks, a dual London relation and an electric fluxoid qauntization condition is satisfied, allowing the author to conclude that the vacuum in this case acts like an extreme type-II superconductor, and that quarks are confined. The author also shows that SU(2) lattice gauge theory, which is qualitatively different and another step closer to reality, shows a Meissner-like effect. In contrast to the U(1) case, the author's results are found consistent with a dual version of the Ginsburg-Landau theory of superconductor on the borderline between type-I and type-II. This approach paves the wave for a study of the more complicated theory, quantum chromodynamics, that is believed to describe quarks

An approach to higher dimensional theories based on lattice gauge theory

International Nuclear Information System (INIS)

Murata, M.; So, H.

2004-01-01

A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram

Fundamental problems of gauge field theory

International Nuclear Information System (INIS)

Velo, G.; Wightman, A.S.

1986-01-01

As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now provides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lecture notes collected in this volume concentrate on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the exploration of the extraordinary enigmatic connections between Kac-Moody-Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories are mentioned

Efficient implementation of the Monte Carlo method for lattice gauge theory calculations on the floating point systems FPS-164

International Nuclear Information System (INIS)

Moriarty, K.J.M.; Blackshaw, J.E.

1983-01-01

The computer program calculates the average action per plaquette for SU(6)/Z 6 lattice gauge theory. By considering quantum field theory on a space-time lattice, the ultraviolet divergences of the theory are regulated through the finite lattice spacing. The continuum theory results can be obtained by a renormalization group procedure. Making use of the FPS Mathematics Library (MATHLIB), we are able to generate an efficient code for the Monte Carlo algorithm for lattice gauge theory calculations which compares favourably with the performance of the CDC 7600. (orig.)

Lattice gauge theory on the hypercube

International Nuclear Information System (INIS)

Apostolakis, J.; Baillie, C.; Ding, Hong-Qiang; Flower, J.

1988-01-01

Lattice gauge theory, an extremely computationally intensive problem, has been run successfully on hypercubes for a number of years. Herein we give a flavor of this work, discussing both the physics and the computing behind it. 19 refs., 5 figs., 27 tabs

Correlation of the ghost and the quark in the lattice Landau gauge QCD

International Nuclear Information System (INIS)

Furui, Sadataka; Nakajima, Hideo

2007-01-01

Effects of the quark field on the ghost propagator of the lattice Landau gauge are investigated by using the unquenched SU(3) configurations produced by the MILC collaboration and compared with quenched gauge configurations of SU(2) first copy of the over relaxation gauge fixing, the parallel tempering (PT) gauge fixing and quenched SU(3) 56 4 configurations. We measure the color symmetric and the color antisymmetric ghost propagator and the Binder cumulant of the l 1 norm and the l 2 norm of color antisymmetric ghost propagators and investigate deviation from those of Gaussian distributions. In the first copy samples of quenched SU(2) we observe a large fluctuation in the Binder cumulant at the lowest momentum point. This fluctuation is reduced in the P T gauge fixed samples. The color anti-symmetric ghost propagator of quenched SU(3) configurations depends on the lattice size and is small as compared to the symmetric one in the large lattice of 56 4 . The Binder cumulant of the quenched SU(2) and the N f = 2 + 1 unquenched SU(3) are almost consistent with 3-d and 8-d Gaussian distribution, respectively. A comparison of the SU(3) unquenched configurations and quenched configurations indicates that the dynamical quarks have the effect of making color antisymmetric ghost propagator closer to the Gaussian distribution and the Kugo-Ojima color confinement parameter c closer to 1. (author)

Lattice worldline representation of correlators in a background field

International Nuclear Information System (INIS)

Epelbaum, Thomas; Gelis, François; Wu, Bin

2015-01-01

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.

Self-consistent normal ordering of gauge field theories

International Nuclear Information System (INIS)

Ruehl, W.

1987-01-01

Mean-field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. First an appropriate real action mean-field theory is constructed. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived. (author). 4 refs

Majorana and Majorana-Weyl fermions in lattice gauge theory

International Nuclear Information System (INIS)

Inagaki, Teruaki; Suzuki, Hiroshi

2004-01-01

In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factorized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find. (author)

Gauge-invariant charged, monopole and dyon fields in gauge theories

International Nuclear Information System (INIS)

Froehlich, J.; Marchetti, P.A.

1999-01-01

We propose explicit recipes to construct the Euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an Euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed

Recent advances in lattice gauge theories

Indian Academy of Sciences (India)

Abstract. Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.

Global anomalies in chiral lattice gauge theories

International Nuclear Information System (INIS)

Baer, O.

2000-07-01

We study global anomalies in a new approach to chiral gauge theories on the lattice, which is based on the Ginsparg-Wilson relation. In this approach, global anomalies make it impossible to define consistently a fermionic measure for the functional integral. We show that a global anomaly occurs in an SU(2) theory if the fundamental representation is used for the fermion fields. The generalization to higher representations is also discussed. In addition we establish a close relation between global anomalies and the spectral flow of the Dirac operator and employ it in a numerical computation to prove the existence of the global SU(2) anomaly in a different way. This method is inspired by an earlier work of Witten who first discovered this type of anomalies in continuum field theory. (orig.)

Analytic approximations to hamiltonian lattice field theories. Pt. 2

International Nuclear Information System (INIS)

Surany, P.

1983-01-01

It is shown that at weak coupling physical quantities in hamiltonian U(1) lattice gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d - 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions. Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2 + 1 U(1) gauge theory confines electric charges at all non-vanishing coupling. (orig.)

Mass corrections in string theory and lattice field theory

International Nuclear Information System (INIS)

Del Debbio, Luigi; Kerrane, Eoin; Russo, Rodolfo

2009-01-01

Kaluza-Klein (KK) compactifications of higher-dimensional Yang-Mills theories contain a number of 4-dimensional scalars corresponding to the internal components of the gauge field. While at tree level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1 loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius R is much bigger than the scale of the UV completion (R>>√(α ' ), a), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in N=2, 4 super Yang-Mills is highly suppressed, even if the lattice regularization breaks all supersymmetries explicitly. This is due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.

Working Group Report: Lattice Field Theory

Energy Technology Data Exchange (ETDEWEB)

Blum, T.; et al.,

2013-10-22

This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.

Fusion basis for lattice gauge theory and loop quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Delcamp, Clement [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo,Waterloo, Ontario N2L 3G1 (Canada); Dittrich, Bianca; Riello, Aldo [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)

2017-02-10

We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2+1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel’d double of the gauge group, and can be readily “fused” together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2+1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.

Fusion basis for lattice gauge theory and loop quantum gravity

International Nuclear Information System (INIS)

Delcamp, Clement; Dittrich, Bianca; Riello, Aldo

2017-01-01

We introduce a new basis for the gauge-invariant Hilbert space of lattice gauge theory and loop quantum gravity in (2+1) dimensions, the fusion basis. In doing so, we shift the focus from the original lattice (or spin-network) structure directly to that of the magnetic (curvature) and electric (torsion) excitations themselves. These excitations are classified by the irreducible representations of the Drinfel’d double of the gauge group, and can be readily “fused” together by studying the tensor product of such representations. We will also describe in detail the ribbon operators that create and measure these excitations and make the quasi-local structure of the observable algebra explicit. Since the fusion basis allows for both magnetic and electric excitations from the onset, it turns out to be a precious tool for studying the large scale structure and coarse-graining flow of lattice gauge theories and loop quantum gravity. This is in neat contrast with the widely used spin-network basis, in which it is much more complicated to account for electric excitations, i.e. for Gauß constraint violations, emerging at larger scales. Moreover, since the fusion basis comes equipped with a hierarchical structure, it readily provides the language to design states with sophisticated multi-scale structures. Another way to employ this hierarchical structure is to encode a notion of subsystems for lattice gauge theories and (2+1) gravity coupled to point particles. In a follow-up work, we have exploited this notion to provide a new definition of entanglement entropy for these theories.

BROOKHAVEN: Lattice gauge theory symposium

Energy Technology Data Exchange (ETDEWEB)

Anon.

1986-12-15

Originally introduced by Kenneth Wilson in the early 70s, the lattice formulation of a quantum gauge theory became a hot topic of investigation after Mike Creutz, Laurence Jacobs and Claudio Rebbi demonstrated in 1979 the feasibility of meaningful computer simulations. The initial enthusiasm led gradually to a mature research effort, with continual attempts to improve upon previous results, to develop better computational techniques and to find new domains of application.

Evidence for the existence of Gribov copies in Landau gauge lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Marinari, E.; Ricci, R. (Rome-2 Univ. (Italy). Dipt. di Fisica INFN, Rome (Italy)); Parrinello, C. (New York Univ., NY (USA). Physics Dept.)

1991-09-16

We unambiguously show the existence of Gribov copies in a pure SU(3) gauge lattice model, with Wilson action. We show that the usual steepest-descent algorithms used for implementing the lattice Landau gauge lead to ambiguities, which are related to the existence of Gribov copies in the model. (orig.).

Variational estimates for the mass gap of SU(2) Euclidean lattice gauge theory

International Nuclear Information System (INIS)

Hari Dass, N.D.

1984-10-01

The purpose of this letter is to report on the progress made in our understanding of series expansions for the masses in lattice gauge theories by the application of variational techniques to the Euclidean SU(2) lattice gauge theory. (Auth.)

One-loop fermion contribution in an asymmetric lattice regularization of SU(N) gauge theories

International Nuclear Information System (INIS)

Trinchero, R.C.

1983-01-01

Using the background field method we calculate the one-loop fermion corrections in an asymmetric lattice version of SU(N) gauge theories with massless fermions. The introduction of different lattice spacings for spatial (a) and temporal (a 4 ) links requires the introduction of two different bare coupling constants, gsub(sigma) and gsub(tau). Our calculation provides the value of the derivatives of the couplings with respect to xi=a/a 4 at xi=1; these derivatives are of particular relevance for finite-temperature lattice calculations. With xi->infinite, the lattice hamiltonian version is obtained, and the ratio of scale parameters Λsub(H)/Λsub(E) is calculated. (orig.)

Observing long colour flux tubes in SU(2) lattice gauge theory

CERN Document Server

Bali, G S; Schlichter, C; Bali, G S; Schilling, K; Schlichter, C

1995-01-01

We present results of a high statistics study of the chromo field distribution between static quarks in SU(2) gauge theory on lattices of volumes 16^4, 32^4, and 48^3*64, with physical extent ranging from 1.3 fm up to 2.7 fm at beta=2.5, beta=2.635, and beta=2.74. We establish string formation over physical distances as large as 2 fm. The results are tested against Michael's sum rules. A detailed investigation of the transverse action and energy flux tube profiles is provided. As a by-product, we obtain the static lattice potential in unpreceded accuracy.

Finite size scaling and lattice gauge theory

International Nuclear Information System (INIS)

Berg, B.A.

1986-01-01

Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs

Calculations in the weak and crossover regions of SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Greensite, J.; Hansson, T.H.; Hari Dass, N.D.; Lauwers, P.G.

1981-07-01

A calculational scheme for lattice gauge theory is proposed which interpolates between lowest order mean-field and full Monte-Carlo calculations. The method is to integrate over a restricted set of link variables in the functional integral, with the remainder fixed at their mean-field value. As an application the authors compute small SU(2) Wilson loops near and above the weak-to-strong coupling transition point. (Auth.)

Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories

International Nuclear Information System (INIS)

Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke

2000-01-01

The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the 'Chern character' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Luescher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions

The fixed point structure of lattice field theories

International Nuclear Information System (INIS)

Baier, R.; Reusch, H.J.; Lang, C.B.

1989-01-01

Monte-Carlo renormalization group methods allow to analyze lattice regularized quantum field theories. The properties of the quantized field theory in the continuum may be recovered at a critical point of the lattice model. This requires a study of the phase diagram and the renormalization flow structure of the coupling constants. As an example the authors discuss the results of a recent MCRG investigation of the SU(2) adjoint Higgs model, where they find evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β

arXiv Stochastic locality and master-field simulations of very large lattices

CERN Document Server

Lüscher, Martin

2018-01-01

In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.

Two-dimensional N=(2,2) lattice gauge theories with matter in higher representations

International Nuclear Information System (INIS)

Joseph, Anosh

2014-06-01

We construct two-dimensional N=(2,2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gauge-invariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.

The Lanczos method in lattice gauge theories

International Nuclear Information System (INIS)

Barbour, I.M.; Behilil, N.E.; Gibbs, P.E.; Teper, M.; Schierholz, G.

1984-09-01

We present a modified version of the Lanczos algorithm as a computational method for tridiagonalising large sparse matrices, which avoids the requirement for large amounts of storage space. It can be applied as a first step in calculating eigenvalues and eigenvectors or for obtaining the inverse of a matrix row by row. Here we describe the method and apply it to various problems in lattice gauge theories. We have found it to have excellent convergence properties. In particular it enables us to do lattice calculations at small and even zero quark mass. (orig.)

Monte Carlo simulations of lattice gauge theories

International Nuclear Information System (INIS)

Forcrand, P. de; Minnesota Univ., Minneapolis, MN

1989-01-01

Lattice gauge simulations are presented in layman's terms. The need for large computer resources is justified. The main aspects of implementations on vector and parallel machines are explained. An overview of state of the art simulations and dedicated hardware projects is presented. 8 refs.; 1 figure; 1 table

Real-Time Dynamics in U(1 Lattice Gauge Theories with Tensor Networks

Directory of Open Access Journals (Sweden)

T. Pichler

2016-03-01

Full Text Available Tensor network algorithms provide a suitable route for tackling real-time-dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1 lattice gauge theory in (1+1 dimensions in the presence of dynamical matter for different mass and electric-field couplings, a theory akin to quantum electrodynamics in one dimension, which displays string breaking: The confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric-field and particle fluctuations. We determine a dynamical state diagram for string breaking and quantitatively evaluate the time scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present a variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.

Decorated tensor network renormalization for lattice gauge theories and spin foam models

International Nuclear Information System (INIS)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-01-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions. (paper)

Decorated tensor network renormalization for lattice gauge theories and spin foam models

Science.gov (United States)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-05-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.

Numerical studies of gauge field theories

International Nuclear Information System (INIS)

Creutz, M.

1981-06-01

Monte Carlo simulation of statistical systems is a well established technique of the condensed matter physicist. In the last few years, particle theorists have rediscovered this method and are having a marvelous time applying it to quantized gauge field theories. The main result has been strong numerical evidence that the standard SU(3) non-Abelian gauge theory of the strong interaction is capable of simultaneously confining quarks into the physical hadrons and exhibiting asymptotic freedom, the phenomenon of quark interactions being small at short distances. In four dimensions, confinement is a non-perturbative phenomenon. Essentially all models of confinement tie widely separated quarks together with strings of gauge field flux. This gives rise to a linear potential at long distances. A Monte Carlo program generates a sequence of field configuration by a series of random changes of the fields. The algorithm is so constructed that ultimately the probability density for finding any given configuration is proportional to the Boltzmann weighting. We bring our lattices into thermal equilibrium with a heat bath at a temperature specified by the coupling constant. Thus we do computer experiments with four-dimensional crystals stored in a computer memory. As the entire field configuration is stored, we have access to any correlation function desired. These lectures describe the kinds of experiments being done and the implications of these results for strong interaction physics

Lattice gauge theory on a parallel computer

International Nuclear Information System (INIS)

Flower, J.W.

1987-01-01

The results of several numerical simulations of QCD by Monte Carlo lattice gauge theory are presented. Studying the mesonic potential on a 20 4 lattice, we conclude that asymptotic scaling does not hold over the range 6.1 ≤ β ≤ 6.7, although we are not able to quantify the discrepancies. The effect of discrete rotational symmetry on physical parameters is examined and seems to modify the string tension by 15% at β = 6.1, while at β = 6.3 the change was less than 1%. The potential between three charges is studied and yields a string tension of .18 GeV 2 , consistent with mesonic calculations and relativized potential models. Contributions to the potential from low-energy string vibrations appear small in the range x ≤ .5 fm. We perform energy density measurements in the color fields surrounding both mesons and baryons, which provide strong evidence in favor of the dual superconductor picture of confinement. It is also suggested that the confining strings in the baryon meet at a central point rather than joining the quarks pairwise. Several algorithms are explored in an attempt to develop simulation methods which are able to directly account for the currents generated by color sources. The extension of the Langevin equation to complex degrees of freedom is derived leading to a Fokker-Planck equation for a complex 'Probability distribution'. Using this technique we are then able to calculate energy densities in U(1) gauge theory at large charge separations. The extension of the method to non-Abelian theories comes up against an unresolved problem in segregation for certain types of observable. 145 refs., 36 figs

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

Science.gov (United States)

Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer

2016-06-01

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Yang-Mills theory on a momentum lattice: Gauge invariance, chiral invariance, and no fermion doubling

International Nuclear Information System (INIS)

Berube, D.; Kroeger, H.; Lafrance, R.; Marleau, L.

1991-01-01

We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum (k) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like logV with the lattice volume V. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being c-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the φ 4 model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator left-angle φ(k)φ(k')right-angle in the φ 4 model, investigate Euclidean invariance, and extract m R as well as Z R . Moreover we compute left-angle F μν (k)F μν (k')right-angle in the SU(2) model

Some approximate calculations in SU2 lattice mean field theory

International Nuclear Information System (INIS)

Hari Dass, N.D.; Lauwers, P.G.

1981-12-01

Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)

Status of glueball mass calculations in lattice gauge theory

International Nuclear Information System (INIS)

Kronfeld, A.S.

1989-11-01

The status of glueball spectrum calculations in lattice gauge theory is briefly reviewed, with focus on the comparison between Monte Carlo simulations and small-volume analytical calculations in SU(3). The agreement gives confidence that the large-volume Monte Carlo results are accurate, at least in the context of the pure gauge theory. An overview of some of the technical questions, which is aimed at non-experts, serves as an introduction. 19 refs., 1 fig

Phase diagrams of exceptional and supersymmetric lattice gauge theories

Energy Technology Data Exchange (ETDEWEB)

Wellegehausen, Bjoern-Hendrik

2012-07-10

In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G{sub 2}, that has a trivial centre. To investigate G{sub 2} gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.

Phase diagrams of exceptional and supersymmetric lattice gauge theories

International Nuclear Information System (INIS)

Wellegehausen, Bjoern-Hendrik

2012-01-01

In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G 2 , that has a trivial centre. To investigate G 2 gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.

Wormholes, emergent gauge fields, and the weak gravity conjecture

Energy Technology Data Exchange (ETDEWEB)

Harlow, Daniel [Center for the Fundamental Laws of Nature, Physics Department, Harvard University,Cambridge MA, 02138 (United States)

2016-01-20

This paper revisits the question of reconstructing bulk gauge fields as boundary operators in AdS/CFT. In the presence of the wormhole dual to the thermofield double state of two CFTs, the existence of bulk gauge fields is in some tension with the microscopic tensor factorization of the Hilbert space. I explain how this tension can be resolved by splitting the gauge field into charged constituents, and I argue that this leads to a new argument for the “principle of completeness”, which states that the charge lattice of a gauge theory coupled to gravity must be fully populated. I also claim that it leads to a new motivation for (and a clarification of) the “weak gravity conjecture”, which I interpret as a strengthening of this principle. This setup gives a simple example of a situation where describing low-energy bulk physics in CFT language requires knowledge of high-energy bulk physics. This contradicts to some extent the notion of “effective conformal field theory”, but in fact is an expected feature of the resolution of the black hole information problem. An analogous factorization issue exists also for the gravitational field, and I comment on several of its implications for reconstructing black hole interiors and the emergence of spacetime more generally.

Standard model and chiral gauge theories on the lattice

International Nuclear Information System (INIS)

Smit, J.

1990-01-01

A review is given of developments in lattice formulations of chiral gauge theories. There is now evidence that the unwanted fermion doublers can be decoupled satisfactorily by giving them masses of the order of the cutoff. (orig.)

National Computational Infrastructure for Lattice Gauge Theory: Final Report

International Nuclear Information System (INIS)

Richard Brower; Norman Christ; Michael Creutz; Paul Mackenzie; John Negele; Claudio Rebbi; David Richards; Stephen Sharpe; Robert Sugar

2006-01-01

This is the final report of Department of Energy SciDAC Grant ''National Computational Infrastructure for Lattice Gauge Theory''. It describes the software developed under this grant, which enables the effective use of a wide variety of supercomputers for the study of lattice quantum chromodynamics (lattice QCD). It also describes the research on and development of commodity clusters optimized for the study of QCD. Finally, it provides some high lights of research enabled by the infrastructure created under this grant, as well as a full list of the papers resulting from research that made use of this infrastructure

About relation between mass absence and gap in the lattice gauge theories

International Nuclear Information System (INIS)

Barata, J.C.A.

1985-01-01

The absence of electric charge in a dipole state, with limited energy, in a U(1) lattice gauge theory with scalar matter field, in the 'screening-confinement' region of the phase diagram of the theory, in the limit in which we take one of the constituent particles to infinity, is studied. It contains an introductory part, an apendix on polymer expansions and a review of results on changed states in the Z 2 model (Author) [pt

Bookshelf (Quantum Fields on a Lattice, by Istvan Montvay and Gernot Muenster)

Energy Technology Data Exchange (ETDEWEB)

Wolff, U.

1994-09-15

In four space-time dimensions, lattice regularization often represents the only non-perturbative definition of a quantum field theory. On this basis, and in connection with numerical simulation techniques and the spreading of powerful parallel computers, more and more realistic calculations are carried out. There has been a great need for a textbook for advanced students to enter this field. While the recent book by H. J. Rothe (Lattice Gauge Theories, Word Scientific) covers the more formal and analytic aspects, this new book provides excellent coverage of a large section of the field, including details of Monte Carlo simulations and algorithms. It is well suitable to prepare a student for reading reviews as they appear in annual proceedings of lattice conferences. The book starts with an introduction to euclidean fields and path-integrals including nontrivial details like reflection positivity. Here the authors succeed very well in avoiding the use of both over-formal machinery as well as an unduly schematic and superficial presentation. Then several sections introduce lattice scalar, fermion, and gauge fields in the traditional division of field theory texts. Lattice specialties, like the semi-analytic Luescher-Weisz solution and the problem of fermion doubling, are enlarged on. Bridges toward current research are included in chapters on QCD and Higgs and Yukawa models. The book ends with practical considerations about algorithms, including hybrid Monte Carlo, and error analysis. This textbook is an excellent introduction to present day lattice methods for particle physics. In its scope it is almost unrivalled and is a must for every student taking up the subject. The researcher in the field will value it as a standard reference and entry point to the literature.

Bookshelf (Quantum Fields on a Lattice, by Istvan Montvay and Gernot Muenster)

International Nuclear Information System (INIS)

Wolff, U.

1994-01-01

In four space-time dimensions, lattice regularization often represents the only non-perturbative definition of a quantum field theory. On this basis, and in connection with numerical simulation techniques and the spreading of powerful parallel computers, more and more realistic calculations are carried out. There has been a great need for a textbook for advanced students to enter this field. While the recent book by H. J. Rothe (Lattice Gauge Theories, Word Scientific) covers the more formal and analytic aspects, this new book provides excellent coverage of a large section of the field, including details of Monte Carlo simulations and algorithms. It is well suitable to prepare a student for reading reviews as they appear in annual proceedings of lattice conferences. The book starts with an introduction to euclidean fields and path-integrals including nontrivial details like reflection positivity. Here the authors succeed very well in avoiding the use of both over-formal machinery as well as an unduly schematic and superficial presentation. Then several sections introduce lattice scalar, fermion, and gauge fields in the traditional division of field theory texts. Lattice specialties, like the semi-analytic Luescher-Weisz solution and the problem of fermion doubling, are enlarged on. Bridges toward current research are included in chapters on QCD and Higgs and Yukawa models. The book ends with practical considerations about algorithms, including hybrid Monte Carlo, and error analysis. This textbook is an excellent introduction to present day lattice methods for particle physics. In its scope it is almost unrivalled and is a must for every student taking up the subject. The researcher in the field will value it as a standard reference and entry point to the literature.

Applications of Jarzynski's relation in lattice gauge theories

DEFF Research Database (Denmark)

Nada, Alessandro; Caselle, Michele; Costagliola, Gianluca

2016-01-01

Jarzynski's equality is a well-known result in statistical mechanics, relating free-energy differences between equilibrium ensembles with fluctuations in the work performed during non-equilibrium transformations from one ensemble to the other. In this work, an extension of this relation to lattice...... gauge theory will be presented, along with numerical results for the ℤ2 gauge model in three dimensions and for the equation of state in SU(2) Yang-Mills theory in four dimensions. Then, further applications will be discussed, in particular for the Schrödinger functional and for the study of QCD...

Phases of renormalized lattice gauge theories with fermions

International Nuclear Information System (INIS)

Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)

1979-01-01

Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory

A preliminary study of the Gribov ambiguity in lattice SU(3) Coulomb gauge

Energy Technology Data Exchange (ETDEWEB)

Parrinello, C. (Physics Dept., New York Univ., NY (United States)); Petrarca, S. (Dipt. di Fisica, Rome-1 Univ. (Italy) INFN, Rome (Italy)); Vladikas, A. (Dipt. di Fisica, Rome-2 Univ. (Italy) INFN, Rome (Italy))

1991-10-10

We report on simulations of pure SU(3) gauge theory on a 10{sup 3}x20 lattice at {beta}=6.0 in the Coulomb gauge, from which the Gribov ambiguity appears to be maximal, in the sense that the gauge-fixing process is highly unstable with respect to variations of the starting configuration via random gauge transformations. We give a heuristic explanation of the larger number of Gribov copies in such a gauge with respect to the Landau gauge. (orig.).

Global anomalies in chiral gauge theories on the lattice

International Nuclear Information System (INIS)

Baer, O.; Campos, I.

2000-01-01

We discuss the issue of global anomalies in chiral gauge theories on the lattice. In Luescher's approach, these obstructions make it impossible to define consistently a fermionic measure for the path integral. We show that an SU(2) theory has such a global anomaly if the Weyl fermion is in the fundamental representation. The anomaly in higher representations is also discussed. We finally show that this obstruction is the lattice analogue of the SU(2) anomaly first discovered by Witten. (orig.)

Abelian gauge theories with tensor gauge fields

International Nuclear Information System (INIS)

Kapuscik, E.

1984-01-01

Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)

Lattice gauge theory in the microcanonical ensemble

International Nuclear Information System (INIS)

Callaway, D.J.E.; Rahman, A.

1983-01-01

The microcanonical-ensemble formulation of lattice gauge theory proposed recently is examined in detail. Expectation values in this new ensemble are determined by solving a large set of coupled ordinary differential equations, after the fashion of a molecular dynamics simulation. Following a brief review of the microcanonical ensemble, calculations are performed for the gauge groups U(1), SU(2), and SU(3). The results are compared and contrasted with standard methods of computation. Several advantages of the new formalism are noted. For example, no random numbers are required to update the system. Also, this update is performed in a simultaneous fashion. Thus the microcanonical method presumably adapts well to parallel processing techniques, especially when the p action is highly nonlocal (such as when fermions are included)

Field strength correlators in QCD: new fits to the lattice data

International Nuclear Information System (INIS)

Meggiolaro, E.

1999-01-01

We discuss the results obtained by fitting the lattice data of the gauge-invariant field strength correlators in QCD with some particular functions which are commonly used in the literature in some phenomenological approaches to high-energy hadron-hadron scattering. A comparison is done with the results obtained in the original fits to the lattice data. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Microcanonical ensemble formulation of lattice gauge theory

International Nuclear Information System (INIS)

Callaway, D.J.E.; Rahman, A.

1982-01-01

A new formulation of lattice gauge theory without explicit path integrals or sums is obtained by using the microcanonical ensemble of statistical mechanics. Expectation values in the new formalism are calculated by solving a large set of coupled, nonlinear, ordinary differential equations. The average plaquette for compact electrodynamics calculated in this fashion agrees with standard Monte Carlo results. Possible advantages of the microcanonical method in applications to fermionic systems are discussed

Multigrid Methods for the Computation of Propagators in Gauge Fields

Science.gov (United States)

Kalkreuter, Thomas

Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.

Gauge fields

International Nuclear Information System (INIS)

Mills, R.

1989-01-01

This article is a survey of the history and ideas of gauge theory. Described here are the gradual emergence of symmetry as a driving force in the shaping of physical theory; the elevation of Noether's theorem, relating symmetries to conservation laws, to a fundamental principle of nature; and the force of the idea (''the gauge principle'') that the symmetries of nature, like the interactions themselves, should be local in character. The fundamental role of gauge fields in mediating the interactions of physics springs from Noether's theorem and the gauge principle in a remarkably clean and elegant way, leaving, however, some tantalizing loose ends that might prove to be the clue to a future deeper level of understanding. The example of the electromagnetic field as the prototype gauge theory is discussed in some detail and serves as the basis for examining the similarities and differences that emerge in generalizing to non-Abelian gauge theories. The article concludes with a brief examination of the dream of total unification: all the forces of nature in a single unified gauge theory, with the differences among the forces due to the specific way in which the fundamental symmetries are broken in the local environment

Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations

Science.gov (United States)

Roy, Sthitadhi; Kolodrubetz, Michael; Goldman, Nathan; Grushin, Adolfo G.

2018-04-01

In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field \

Anyonic order parameters for discrete gauge theories on the lattice

International Nuclear Information System (INIS)

Bais, F.A.; Romers, J.C.

2009-01-01

We present a new family of gauge invariant non-local order parameters Δ α A for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular, cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the 't Hooft operators, respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.

Ground-state projection multigrid for propagators in 4-dimensional SU(2) gauge fields

International Nuclear Information System (INIS)

Kalkreuter, T.

1991-09-01

The ground-state projection multigrid method is studied for computations of slowly decaying bosonic propagators in 4-dimensional SU(2) lattice gauge theory. The defining eigenvalue equation for the restriction operator is solved exactly. Although the critical exponent z is not reduced in nontrivial gauge fields, multigrid still yields considerable speedup compared with conventional relaxation. Multigrid is also able to outperform the conjugate gradient algorithm. (orig.)

Departures from scaling in SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Gutbrod, F.

1987-01-01

High statistics Monte Carlo Data in SU(2) lattice gauge theory are presented. At β = 2.6 and β = 2.7 large deviations form scaling are observed for Creutz ratios, when 12 4 and 24 4 lattice data are compared. There is a trend towards a restauration of asymptotic scaling with increasing β, which vanishes if at the higher value of β larger loops are considered than at lower β. The static qanti q-potential and an upper limit for the string tension are given. (orig.)

The Origins of Lattice Gauge Theory

International Nuclear Information System (INIS)

Wilson, Kenneth

2004-01-01

The main focus of this talk is an anecdotal account of the history underlying my 1974 article entitled 'Confinement of Quarks.' In preparing this talk, I will draw on a historical interview conducted by the project for History of Recent Science and Technology at the Dibner Institute for the History of Science and Technology at MIT, and on a theory of invention proposed by Peter Drucker in his book 'Innovation and Entrepreneurship.' I will explain this theory; no background is needed. The account will start with related work in the 1960's. I will end the talk with a plea for lattice gauge researchers to be alert for unexpected scalar or vector colored particles that are invisible to experimentalists yet could start to spoil the agreement of computations with experiment. Note: In association with the Symposium ' 'Lattice 2004,' June 21 to June 26, 2004.

Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8

International Nuclear Information System (INIS)

1998-01-01

The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U A (1) symmetry and the η' for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk

Higgs compositeness in Sp(2N) gauge theories - Determining the low-energy constants with lattice calculations

Science.gov (United States)

Bennett, Ed; Ki Hong, Deog; Lee, Jong-Wan; David Lin, C.-J.; Lucini, Biagio; Piai, Maurizio; Vadacchino, Davide

2018-03-01

As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) → Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the effective field theory and we test the method on the quenched theory. We also report early results from dynamical simulations, focussing on the phase structure of the lattice theory and a calculation of the lowest-lying meson spectrum at coarse lattice spacing. Combined contributions of B. Lucini (e-mail: b.lucini@swansea.ac.uk) and J.-W. Lee (e-mail: wlee823@pusan.ac.kr).

Supersymmetric lattices

International Nuclear Information System (INIS)

Catterall, Simon

2013-01-01

Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on N = 4 super Yang-Mills theory.

Study of unique trajectories in SU(2) and SU(3) lattice Gauge theories

International Nuclear Information System (INIS)

Nerses, Hudaverdian

1985-01-01

As is well known, in the context of quantum field theories describing different types of interactions in the domain of particle physics, there are rampant ultraviolet infinite which are subtly taken care of by adequate renormalization procedures. The most conventional perturbative regularization schemes are based on the Feynman expansion, so successfully used in quantum electrodynamics. But the unique feature of confinement in strong interactions has forced physicists to search for a non-perturbative cut-off, and this has been provided by the introduction of discrete spacetime lattices over which the field theories have been formulated. the lattice represents a mathematical trick, a more scaffolding, an intermediate step, used to analyze a difficult non-linear system, of an infinite number of degree of freedom. Herein lies the main virtue of the lattice, which directly eliminates all wavelengths less than twice the lattice spacing.Consequently, regarding the lattice merely as an ultraviolet cut-off, physicists should remove this regulator and expect observable quantities to approach their physical values. However as the removal of the regulator is discussed, the question of renormalization emerges, and it is here that the Migdal-Kadanoff recursion relations, representing a simple approximate method for comparing theories with different lattice spacings bring in their virtue by providing a simple method for obtaining an approximate renormalization group function. It is hoped, and currently extensively investigated whether the Migdal renormalization group approach, combined with some other methods, can really provide useful information on the phase structures of lattice gauge theories

Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

International Nuclear Information System (INIS)

Maas, Axel; Pawlowski, Jan M.; Spielmann, Daniel; Sternbeck, Andre; Smekal, Lorenz von

2010-01-01

We study the strong-coupling limit β=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite β. In turn, the gluon propagator only mildly depends on the Gribov ambiguity. (orig.)

On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity

Energy Technology Data Exchange (ETDEWEB)

Delcamp, Clement [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Department of Physics & Astronomy and Guelph-Waterloo Physics Institute, University of Waterloo,200 University Avenue West, Waterloo, Ontario N2L 3G1 (Canada); Dittrich, Bianca; Riello, Aldo [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)

2016-11-18

Entanglement entropy is a valuable tool for characterizing the correlation structure of quantum field theories. When applied to gauge theories, subtleties arise which prevent the factorization of the Hilbert space underlying the notion of entanglement entropy. Borrowing techniques from extended topological field theories, we introduce a new definition of entanglement entropy for both Abelian and non-Abelian gauge theories. Being based on the notion of excitations, it provides a completely relational way of defining regions. Therefore, it naturally applies to background independent theories, e.g. gravity, by circumventing the difficulty of specifying the position of the entangling surface. We relate our construction to earlier proposals and argue that it brings these closer to each other. In particular, it yields the non-Abelian analogue of the ‘magnetic centre choice’, as obtained through an extended-Hilbert-space method, but applied to the recently introduced fusion basis for 3D lattice gauge theories. We point out that the different definitions of entanglement entropy can be related to a choice of (squeezed) vacuum state.

Gauge theories on the lattice at N/sub c/ = infinity

International Nuclear Information System (INIS)

Cristofano, G.A.

1982-01-01

The thesis is devoted to the study of the physical properties of the SU(N/sub c/) Yang Mills theory on the lattice at N/sub c/ = infinity. Since the lattice approach provides a natural framework toward a better understanding of nonperturbative phenomena, like quark confinement, nonperturbative physical quantities, like the string tension and the glueball mass are studied. The first two chapters are introductory in nature. In chapters (3,4) the strong coupling expansion for the Euclidean SU(N/sub c/) lattice gauge theory at N/sub c/ = infinity to 16th and 12th order in β = 1/g 0 2 N/sub c/ for the free energy F and the string tension k respectively is performed. Estimates of the ratio √k/Λ/sub L/ and of the crossover point from strong to weak coupling for the string tension are made by matching the strong coupling series to the asymptotically free continuum theory. In chapter (5) the strong coupling expansion for the glueball mass m/sub g/ to the 8th order in β for the Euclidean SU(infinity) lattice gauge theory is performed. The ratio of the glueball mass m/sub g/ to the squareroot of the string tension √k for the SU(infinity) theory is estimated to be m/sub g//√k = 2.6 +/- 0.2. It is found that the ratio m/sub g//√k has a rather small dependence on N/sub c/ and appears to increase with the number of colors N/sub c/. In chapter (6) two-point Pade approximants for the one plaquette expectation value E/sub p/ for the SU(2) lattice gauge theory by using the known strong and weak coupling series for D/sub p/ is performed. Comparison with the correspondent Monte Carlo results is made, especially in the delicate transition region, at intermediate β = 4/g 0 2

Efficient multitasking of the SU(3) lattice gauge theory algorithm on the CRAY X-MP

International Nuclear Information System (INIS)

Kuba, D.W.; Moriarty, K.J.M.

1985-01-01

The Monte Carlo lattice gauge theory algorithm with the Metropolis et.al. updating procedure is vectorized and multitasked on the four processor CRAY X-MP and results in a code with a link-update-time, in 64-bit arithmetic and 10 hits-per-link, of 11.0 μs on a 16 4 lattice, the fastest link-update-time so far achieved. The program calculates the Wilson loops of size up to L/2.L/2 for an L 4 lattice for SU(3) gauge theory. (orig./HSI)

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

Directory of Open Access Journals (Sweden)

Gattringer Christof

2018-01-01

Full Text Available We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes, or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles. Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2 principal chiral model with chemical potential coupled to two of the Noether charges, SU(2 lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

Science.gov (United States)

Gattringer, Christof; Göschl, Daniel; Marchis, Carlotta

2018-03-01

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

Inequalities for magnetic-flux free energies and confinement in lattice gauge theories

International Nuclear Information System (INIS)

Yoneya, T.

1982-01-01

Rigorous inequalities among magnetic-flux free energies of tori with varying diameters are derived in lattice gauge theories. From the inequalities, it follows that if the magnetic-flux free energy vanishes in the limit of large uniform dilatation of a torus, the free energy must always decrease exponentially with the area of the cross section of the torus. The latter property is known to be sufficient for permanent confinement of static quarks. As a consequence of this property, a lower bound V(R) >= const x R for the static quark-antiquark potential is obtained in three-dimensional U(n) lattice gauge theory for sufficiently large R. (orig.)

Invariant gauge families inherent in Abelian-gauge field theory. [Scalar dipole ghost field, free-field equations

Energy Technology Data Exchange (ETDEWEB)

Yokoyama, Kan-ichi; Kubo, Reijiro

1974-12-01

The framework of the Nakanishi-Lautrup formalism should be enlarged by introducing a scalar dipole ghost field B(x), which is called gauge on field, together with its pair field. By taking free Lagrangian density, Free-field equations can be described. The vacuum is defined by using a neutral vector field U..mu..(x). The state-vector space is generated by the adjoining conjugates of U..mu..sup((+))(x), and auxiliary fields B(x), B/sub 1/(x) and B/sub 2/(x), which were introduced in the form of the Lagrangian density. The physical states can be defined by the supplementary conditions of the form B/sub 1/sup((+))(x) 1 phys>=B/sub 2/sup((+))(x) 1 phys>=0. It is seen that all the field equations and all the commutators are kept form-invariant, and that the gauge parameter ..cap alpha.. is transformed into ..cap alpha..' given by ..cap alpha..'=..cap alpha..+lambda, with epsilon unchanged. The Lagrangian density is specified only by the gauge invariant parameter epsilon. The gauge structure of theory has universal meaning over whole Abelian-gauge field. C-number gauge transformation and the gauge structure in the presence of interaction are also discussed.

Monte Carlo sampling strategies for lattice gauge calculations

International Nuclear Information System (INIS)

Guralnik, G.; Zemach, C.; Warnock, T.

1985-01-01

We have sought to optimize the elements of the Monte Carlo processes for thermalizing and decorrelating sequences of lattice gauge configurations and for this purpose, to develop computational and theoretical diagnostics to compare alternative techniques. These have been applied to speed up generations of random matrices, compare heat bath and Metropolis stepping methods, and to study autocorrelations of sequences in terms of the classical moment problem. The efficient use of statistically correlated lattice data is an optimization problem depending on the relation between computer times to generate lattice sequences of sufficiently small correlation and times to analyze them. We can solve this problem with the aid of a representation of auto-correlation data for various step lags as moments of positive definite distributions, using methods known for the moment problem to put bounds on statistical variances, in place of estimating the variances by too-lengthy computer runs

Gauge-invariant scalar and field strength correlators in 3d

CERN Document Server

Laine, Mikko

1998-01-01

Gauge-invariant non-local scalar and field strength operators have been argued to have significance, e.g., as a way to determine the behaviour of the screened static potential at large distances, as order parameters for confinement, as input parameters in models of confinement, and as gauge-invariant definitions of light constituent masses in bound state systems. We measure such "correlators" in the 3d pure SU(2) and SU(2)+Higgs models on the lattice. We extract the corresponding mass parameters and discuss their scaling and physical interpretation. We find that the finite part of the MS-bar scheme mass measured from the field strength correlator is large, more than half the glueball mass. We also determine the non-perturbative contribution to the Debye mass in the 4d finite T SU(2) gauge theory with a method due to Arnold and Yaffe, finding $\\delta m_D\\approx 1.06(4)g^2T$.

MEETING: Lattice 88

Energy Technology Data Exchange (ETDEWEB)

Mackenzie, Paul

1989-03-15

The forty-year dream of understanding the properties of the strongly interacting particles from first principles is now approaching reality. Quantum chromodynamics (QCD - the field theory of the quark and gluon constituents of strongly interacting particles) was initially handicapped by the severe limitations of the conventional (perturbation) approach in this picture, but Ken Wilson's inventions of lattice gauge theory and renormalization group methods opened new doors, making calculations of masses and other particle properties possible. Lattice gauge theory became a major industry around 1980, when Monte Carlo methods were introduced, and the first prototype calculations yielded qualitatively reasonable results. The promising developments over the past year were highlighted at the 1988 Symposium on Lattice Field Theory - Lattice 88 - held at Fermilab.

MEETING: Lattice 88

International Nuclear Information System (INIS)

Mackenzie, Paul

1989-01-01

The forty-year dream of understanding the properties of the strongly interacting particles from first principles is now approaching reality. Quantum chromodynamics (QCD - the field theory of the quark and gluon constituents of strongly interacting particles) was initially handicapped by the severe limitations of the conventional (perturbation) approach in this picture, but Ken Wilson's inventions of lattice gauge theory and renormalization group methods opened new doors, making calculations of masses and other particle properties possible. Lattice gauge theory became a major industry around 1980, when Monte Carlo methods were introduced, and the first prototype calculations yielded qualitatively reasonable results. The promising developments over the past year were highlighted at the 1988 Symposium on Lattice Field Theory - Lattice 88 - held at Fermilab

Interpolating Lagrangians and SU(2) gauge theory on the lattice

International Nuclear Information System (INIS)

Buckley, I.R.C.; Jones, H.F.

1992-01-01

We apply the linear δ expansion to non-Abelian gauge theory on the lattice, with SU(2) as the gauge group. We establish an appropriate parametrization and evaluate the average plaquette energy E P to O(δ). As a check on our results, we recover the large-β expansion up to O(1/β 2 ), which involves some O(δ 2 ) contributions. Using these contributions we construct a variant of the 1/β expansion which gives a good fit to the data down to the transition region

National Computational Infrastructure for Lattice Gauge Theory: Final report

International Nuclear Information System (INIS)

Reed, Daniel A.

2008-01-01

In this document we describe work done under the SciDAC-1 Project National Computerational Infrastructure for Lattice Gauge Theory. The objective of this project was to construct the computational infrastructure needed to study quantum chromodynamics (QCD). Nearly all high energy and nuclear physicists in the United States working on the numerical study of QCD are involved in the project, as are Brookhaven National Laboratory (BNL), Fermi National Accelerator Laboratory (FNAL), and Thomas Jefferson National Accelerator Facility (JLab). A list of the senior participants is given in Appendix A.2. The project includes the development of community software for the effective use of the terascale computers, and the research and development of commodity clusters optimized for the study of QCD. The software developed as part of this effort is publicly available, and is being widely used by physicists in the United States and abroad. The prototype clusters built with SciDAC-1 fund have been used to test the software, and are available to lattice gauge theorists in the United States on a peer reviewed basis

Statistical mechanics and stability of random lattice field theory

International Nuclear Information System (INIS)

Baskaran, G.

1984-01-01

The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities. (orig.)

Lattice field theories: non-perturbative methods of analysis

International Nuclear Information System (INIS)

Weinstein, M.

1978-01-01

A lecture is given on the possible extraction of interesting physical information from quantum field theories by studying their semiclassical versions. From the beginning the problem of solving for the spectrum states of any given continuum quantum field theory is considered as a giant Schroedinger problem, and then some nonperturbative methods for diagonalizing the Hamiltonian of the theory are explained without recourse to semiclassical approximations. The notion of a lattice appears as an artifice to handle the problems associated with the familiar infrared and ultraviolet divergences of continuum quantum field theory and in fact for all but gauge theories. 18 references

Topological charge and cooling scales in pure SU(2) lattice gauge theory

OpenAIRE

Berg, Bernd A.; Clarke, David A.

2018-01-01

Using Monte Carlo simulations with overrelaxation, we have equilibrated lattices up to β=2.928, size 604, for pure SU(2) lattice gauge theory with the Wilson action. We calculate topological charges with the standard cooling method and find that they become more reliable with increasing β values and lattice sizes. Continuum limit estimates of the topological susceptibility χ are obtained of which we favor χ1/4/Tc=0.643(12), where Tc is the SU(2) deconfinement temperature. Differences between ...

Plaquette-plaquette correlations in the SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Berg, B.

1980-09-01

Monte Carlo measurements of plaquette-plaquette correlations in the 4-dimensional SU(2) lattice gauge theory are reported. For low temperatures the glue ball mass (= inverse correlation length) is estimated to be msub(g) = (3.7 +- 1.2) √K, where K is the string tension. (orig.)

Uses of Effective Field Theory in Lattice QCD

OpenAIRE

Kronfeld, Andreas S.

2002-01-01

Several physical problems in particle physics, nuclear physics, and astrophysics require information from non-perturbative QCD to gain a full understanding. In some cases the most reliable technique for quantitative results is to carry out large-scale numerical calculations in lattice gauge theory. As in any numerical technique, there are several sources of uncertainty. This chapter explains how effective field theories are used to keep them under control and, then, obtain a sensible error ba...

Thick vortices in SU(2) lattice gauge theory

OpenAIRE

Cheluvaraja, Srinath

2004-01-01

Three dimensional SU(2) lattice gauge theory is studied after eliminating thin monopoles and the smallest thick monopoles. Kinematically this constraint allows the formation of thick vortex loops which produce Z(2) fluctuations at longer length scales. The thick vortex loops are identified in a three dimensional simulation. A condensate of thick vortices persists even after the thin vortices have all disappeared. The thick vortices decouple at a slightly lower temperature (higher beta) than t...

Can Lorentz-breaking fermionic condensates form in large N strongly-coupled Lattice Gauge Theories?

OpenAIRE

Tomboulis, E. T.

2010-01-01

The possibility of Lorentz symmetry breaking (LSB) has attracted considerable attention in recent years for a variety of reasons, including the attractive prospect of the graviton as a Goldstone boson. Though a number of effective field theory analyses of such phenomena have recently been given it remains an open question whether they can take place in an underlying UV complete theory. Here we consider the question of LSB in large N lattice gauge theories in the strong coupling limit. We appl...

Many-Body Localization Dynamics from Gauge Invariance

Science.gov (United States)

Brenes, Marlon; Dalmonte, Marcello; Heyl, Markus; Scardicchio, Antonello

2018-01-01

We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, the Gauss law effectively induces a dynamics which can be described as a disorder average over gauge superselection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow, double-logarithmic entanglement growth are present in a broad regime of parameters—in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ion experiments realizing dynamical gauge fields and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.

Gluon condensate from lattice caculations: SU(3) pure gauge theory

International Nuclear Information System (INIS)

Kripfganz, J.

1981-01-01

A short distance expansion of Wilson loops is used to define and isolate vacuum expectation values of composite gluon operators. It is applied to available lattice Monte Carlo data for SU(3) pure gauge theory. The value obtained for the gluon condensate is consistent with the ITEP estimate. (author)

Optimization of renormalization group transformations in lattice gauge theory

International Nuclear Information System (INIS)

Lang, C.B.; Salmhofer, M.

1988-01-01

We discuss the dependence of the renormalization group flow on the choice of the renormalization group transformation (RGT). An optimal choice of the transformation's parameters should lead to a renormalized trajectory close to a few-parameter action. We apply a recently developed method to determine an optimal RGT to SU(2) lattice gauge theory and discuss the achieved improvement. (orig.)

Particle structure of gauge theories

International Nuclear Information System (INIS)

Fredenhagen, K.

1985-11-01

The implications of the principles of quantum field theory for the particle structure of gauge theories are discussed. The general structure which emerges is compared with that of the Z 2 Higgs model on a lattice. The discussion leads to several confinement criteria for gauge theories with matter fields. (orig.)

Lattice fermions

Energy Technology Data Exchange (ETDEWEB)

Randjbar-Daemi, S

1995-12-01

The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if {Gamma}/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs.

Lattice fermions

International Nuclear Information System (INIS)

Randjbar-Daemi, S.

1995-12-01

The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs

A multiscale view of propagators in gauge fields

Energy Technology Data Exchange (ETDEWEB)

Baeker, M

1995-07-01

The Iteratively Smoothing Unigrid (ISU) is presented and studied in detail. An appropriate definition of smoothness in the presence of disordered gauge fields is given on which the algorith is based. ISU uses an iterative process to determ is based. ISU uses an iterative process to determine the interpolation operators as the eigenvectors to the lowest eigenvalues on blocks of larger and larger sizes. We always used the algorith in two dim in two dimensions, usually with SU(2) gauge fields. The ISU algorith perform performs extreely well for the case of the covariant Laplace equation with arbitrarily large disorder. For the Dirac equation, critical slowing down is elimely well for the case of the covariant Laplace equation with arbitrarily large disorder. For the Dirac equation, critical slowing down is eliminated in the continuu lim limit, but when {beta} is kept fixed and the lattice size is increased the critical exponent is estiated to z{approx}1.6. (orig.) methods prove that the problem is due to the many eigenmodes of the Dirac operator that have low eigenvalues and can not be approximated well by the used localized interpolation operators. That the Laplace equation is solved efficiently is caused by the phenomenon of Localization: The lowest modes of the Laplace operator are strongly localized when the disorder of the gauge field is large. We also present an explanation of this phenomenon. For the Dirac operator in two dimension, no localization is found; the reasons for this are not known. It is explained in detail why localization helps to improve the convergence of the algorithm. After having analyzed the problems of the algorithm for the Dirac equation, we try to invent a cure. It consists of two parts: We change the shapes of the supports of the interpolation operators and we introduce the possibility of having more than one interpolation operators per block-lattice point. (Abstract Truncated)

Gauge fields

International Nuclear Information System (INIS)

Itzykson, C.

1978-01-01

In these notes the author provides some background on the theory of gauge fields, a subject of increasing popularity among particle physicists (and others). Detailed motivations and applications which are covered in the other lectures of this school are not presented. In particular the application to weak interactions is omitted by referring to the introduction given by J. Ilipoulos a year ago (CERN Report 76-11). The aim is rather to stress those aspects which suggest that gauge fields may play some role in a future theory of strong interactions. (Auth.)

Anomalous Lorentz and CPT violation from a local Chern-Simons-like term in the effective gauge-field action

Science.gov (United States)

Ghosh, K. J. B.; Klinkhamer, F. R.

2018-01-01

We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3 ×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U (1) gauge fields Aμ (x) which depend on all four spacetime coordinates (including the coordinate x4 ∈S1 of the compact dimension) and have vanishing components A4 (x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.

On a stochastic process associated to non-abelian gauge fields

International Nuclear Information System (INIS)

Vilela Mendes, R.

1989-01-01

A stochastic process is constructed from a ground state measure that generalizes to non-abelian fields the ground state of abelian (free) gauge fields without fermions. Using a latticized version one shows how the process leads to a well-defined quantum theory in the Schroedinger representation. An analysis of the qualitative behaviour of the theory seems to imply a quasi-free behaviour at short distances and a maximally disordered field strength configuration for the low-momentum component of the ground state. Scaling relations for the mass gap are inferred from the theory of small random perturbations of dynamical systems. (orig.)

SU(2) gauge theory in the maximally Abelian gauge without monopoles

International Nuclear Information System (INIS)

Shmakov, S.Yu.; Zadorozhnyj, A.M.

1995-01-01

We present an algorithm for simulation of SU(2) lattice gauge theory under the maximally Abelian (MA) gauge and first numerical results for the theory without Abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual Abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected. 12 refs., 1 tab

Anomalous gauge theories revisited

International Nuclear Information System (INIS)

Matsui, Kosuke; Suzuki, Hiroshi

2005-01-01

A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact U(1) link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear. (author)

Gauge field theories

International Nuclear Information System (INIS)

Leite Lopes, J.

1981-01-01

The book is intended to explain, in an elementary way, the basic notions and principles of gauge theories. Attention is centred on the Salem-Weinberg model of electro-weak interactions, as well as neutrino-lepton scattering and the parton model. Classical field theory, electromagnetic, Yang-Mills and gravitational gauge fields, weak interactions, Higgs mechanism and the SU(5) model of grand unification are also discussed. (U.K.)

Nonlocal gauge theories

International Nuclear Information System (INIS)

Partovi, M.H.

1982-01-01

From a generalization of the covariant derivative, nonlocal gauge theories are developed. These theories enjoy local gauge invariance and associated Ward identities, a corresponding locally conserved current, and a locally conserved energy-momentum tensor, with the Ward identities implying the masslessness of the gauge field as in local theories. Their ultraviolet behavior allows the presence as well as the absence of the Adler-Bell-Jackiw anomaly, the latter in analogy with lattice theories

Anisotropic quantum quench in the presence of frustration or background gauge fields: A probe of bulk currents and topological chiral edge modes

Science.gov (United States)

Killi, Matthew; Trotzky, Stefan; Paramekanti, Arun

2012-12-01

Bosons and fermions, in the presence of frustration or background gauge fields, can form many-body ground states that support equilibrium charge or spin currents. Motivated by the experimental creation of frustration or synthetic gauge fields in ultracold atomic systems, we propose a general scheme by which making a sudden anisotropic quench of the atom tunneling across the lattice and tracking the ensuing density modulations provides a powerful and gauge-invariant route to probing diverse equilibrium current patterns. Using illustrative examples of trapped superfluid Bose and normal Fermi systems in the presence of artificial magnetic fluxes on square lattices, and frustrated bosons in a triangular lattice, we show that this scheme to probe equilibrium bulk current order works independent of particle statistics. We also show that such quenches can detect chiral edge modes in gapped topological states, such as quantum Hall or quantum spin Hall insulators.

Universality and the approach to the continuum limit in lattice gauge theory

CERN Document Server

De Divitiis, G M; Guagnelli, M; Lüscher, Martin; Petronzio, Roberto; Sommer, Rainer; Weisz, P; Wolff, U; de Divitiis, G; Frezzotti, R; Guagnelli, M; Luescher, M; Petronzio, R; Sommer, R; Weisz, P; Wolff, U

1995-01-01

The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.

Surface representations of Wilson loop expectations in lattice gauge theory

International Nuclear Information System (INIS)

Brydges, D.C.; Giffen, C.; Durhuus, B.; Froehlich, J.

1986-01-01

Expectations of Wilson loops in lattice gauge theory with gauge group G=Z 2 , U(1) or SU(2) are expressed as weighted sums over surfaces with boundary equal to the loops labelling the observables. For G=Z 2 and U(1), the weights are all positive. For G=SU(2), the weights can have either sign depending on the Euler characteristic of the surface. Our surface (or flux sheet-) representations are partial resummations of the strong coupling expansion and provide some qualitative understanding of confinement. The significance of flux sheets with nontrivial topology for permanent confinement in the SU(2)-theory is elucidated. (orig.)

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Anomalous Lorentz and CPT violation from a local Chern–Simons-like term in the effective gauge-field action

Directory of Open Access Journals (Sweden)

K.J.B. Ghosh

2018-01-01

Full Text Available We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1 gauge fields Aμ(x which depend on all four spacetime coordinates (including the coordinate x4∈S1 of the compact dimension and have vanishing components A4(x (implying trivial holonomies in the 4-direction. Our calculation shows that the effective gauge-field action contains a local Chern–Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli–Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg–Wilson fermions.

On behaviour of Weyl's gauge field

International Nuclear Information System (INIS)

Yuan Zhong Zhang.

1990-05-01

We consider a system, consisting of a metric tensor g μυ , a scalar field φ, a Weyl's gauge field A μ and a scalar matter field Φ, which is invariant under general coordinate transformation and Weyl's gauge transformation. Two kinds of identities and field equations are given and discussed. A special space-time with g μυ =φ -2 η μυ is considered in a gauge-independent manner. We point out that in a correct treatment where g μυ is not regarded as an independent variable, an auxiliary condition for Weyl's gauge field cannot be obtained. Therefore Weyl's gauge field can be treated as a usual field of positive norm. (author). 11 refs

Analytic study of SU(3) lattice gauge theory

International Nuclear Information System (INIS)

Zheng Xite; Xu Yong

1989-01-01

The variational-cumulant expansion method has been extended to the case of lattice SU(3) Wilson model. The plaquette energy as an order paramenter has been calculated to the 2nd order expansion. No 1st order phase transition in the D = 4 case is found which is in agreement with the monte Carlo results, and the 1st order phase transition in the d = 5 case is clearly seen. The method can be used in the study of problems in LGT with SU(3) gauge group

Zero energy gauge fields and the phases of a gauge theory

International Nuclear Information System (INIS)

Guendelman, E.I.

1990-01-01

A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism

Z2 monopoles in the standard SU(2) lattice gauge theory model

International Nuclear Information System (INIS)

Mack, G.; Petkova, V.B.

1979-04-01

The standard SU(2) lattice gauge theory model without fermions may be considered as a Z 2 model with monopoles and fluctuating coupling constants. At low temperatures β -1 (= small bare coupling constant) the monopoles are confined. (orig.) [de

A lattice approach to spinorial quantum gravity

Science.gov (United States)

Renteln, Paul; Smolin, Lee

1989-01-01

A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

Abelian color cycles: A new approach to strong coupling expansion and dual representations for non-abelian lattice gauge theory

Energy Technology Data Exchange (ETDEWEB)

Gattringer, Christof, E-mail: christof.gattringer@uni-graz.at; Marchis, Carlotta, E-mail: carla.marchis@uni-graz.at

2017-03-15

We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over “abelian color cycles” (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).

Systematics of higher-spin gauge fields

International Nuclear Information System (INIS)

de Wit, B.; Freedman, D.Z.

1980-01-01

Free-field theories for symmetric tensor and tensor-spinor gauge fields have recently been obtained which describe massless particles of arbitrary integer or half-integer spin. An independent discussion of these field theories is given here, based on a hierarchy of generalized Christoffel symbols with simple gauge transformation properties. The necessity of certain constraints on gauge fields and parameters is easily seen. Wave equations and Lagrangians are expressed in terms of the Christoffel symbols, and the independent modes of the system are counted in covariant gauges. Minimal-coupling inconsistency and a combined system of higher-spin boson gauge fields interacting with relativistic particles is discussed

Adding gauge fields to Kaplan's fermions

International Nuclear Information System (INIS)

Blum, T.; Kaerkkaeinen, L.

1994-01-01

We experiment with adding dynamical gauge field to Kaplan (defect) fermions. In the case of U(1) gauge theory we use an inhomogeneous Higgs mechanism to restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d theory produce the correct 2d gauge dynamics. We measure fermion propagators with dynamical gauge fields. They posses the correct chiral structure. The fermions at the boundary of the support of the gauge field (waveguide) are non-chiral, and have a mass two times heavier than the chiral modes. Moreover, these modes cannot be excited by a source at the defect; implying that they are dynamically decoupled. We have also checked that the anomaly relation is fullfilled for the case of a smooth external gauge field. (orig.)

National software infrastructure for lattice gauge theory

International Nuclear Information System (INIS)

Brower, Richard C

2005-01-01

The current status of the SciDAC software infrastructure project for lattice gauge theory is summarized. This includes the the design of a QCD application programmers interface (API) that allows existing and future codes to be run efficiently on Terascale hardware facilities and to be rapidly ported to new dedicated or commercial platforms. The critical components of the API have been implemented and are in use on the US QCDOC hardware at BNL and on both the switched and mesh architecture Pentium 4 clusters at Fermi National Accelerator Laboratory (FNAL) and Thomas Jefferson National Accelerator Facility (JLab). Future software infrastructure requirements and research directions are also discussed

Extended pure Yang-Mills gauge theories with scalar and tensor gauge fields

International Nuclear Information System (INIS)

Gabrielli, E.

1991-01-01

The usual abelian gauge theory is extended to an interacting Yang-Mills-like theory containing vector, scalar and tensor gauge fields. These gauge fields are seen as components along the Clifford algebra basis of a gauge vector-spinorial field. Scalar fields φ naturally coupled to vector and tensor fields have been found, leading to a natural φ 4 coupling in the lagrangian. The full expression of the lagrangian for the euclidean version of the theory is given. (orig.)

Variational estimate of the vacuum state of the SU(2) lattice gauge theory with a disordered trial wave function

International Nuclear Information System (INIS)

Heys, D.W.; Stump, D.R.

1984-01-01

The variational principle is used to estimate the ground state of the Kogut-Susskind Hamiltonian of the SU(2) lattice gauge theory, with a trial wave function for which the magnetic fields on different plaquettes are uncorrelated. This trial function describes a disordered state. The energy expectation value is evaluated by a Monte Carlo method. The variational results are compared to similar results for a related Abelian gauge theory. Also, the expectation value of the Wilson loop operator is computed for the trial state, and the resulting estimate of the string tension is compared to the prediction of asymptotic freedom

Gauge field entanglement in Kitaev's honeycomb model

Science.gov (United States)

Dóra, Balázs; Moessner, Roderich

2018-01-01

A spin fractionalizes into matter and gauge fermions in Kitaev's spin liquid on the honeycomb lattice. This follows from a Jordan-Wigner mapping to fermions, allowing for the construction of a minimal entropy ground-state wave function on the cylinder. We use this to calculate the entanglement entropy by choosing several distinct partitionings. First, by partitioning an infinite cylinder into two, the -ln2 topological entanglement entropy is reconfirmed. Second, the reduced density matrix of the gauge sector on the full cylinder is obtained after tracing out the matter degrees of freedom. This allows for evaluating the gauge entanglement Hamiltonian, which contains infinitely long-range correlations along the symmetry axis of the cylinder. The matter-gauge entanglement entropy is (Ny-1 )ln2 , with Ny the circumference of the cylinder. Third, the rules for calculating the gauge sector entanglement of any partition are determined. Rather small correctly chosen gauge partitions can still account for the topological entanglement entropy in spite of long-range correlations in the gauge entanglement Hamiltonian.

On the presence of lower dimensional confinement mechanisms in 4d SU2 lattice gauge theory

International Nuclear Information System (INIS)

Hari Dass, N.D.

1983-11-01

The presence of an essentially two-dimensional confinement mechanism in 4d SU 2 gauge theory has been conjectured. The authors present an explicit realization of this conjecture valid up to β = 1.8 based on variational investigations of lattice gauge theories. (Auth.)

Gauge field models

International Nuclear Information System (INIS)

Becchi, C.; Rouet, A.; Stora, R.

1975-10-01

Stora's analysis is continued in discussing the nonabelian (Yang-Mills) gauge field models (G.F.M.). The gauge independence of the physical scattering operator is discussed in some details and the connection between its unitary and the Slavnov symmetry outlined. Only the models involving semisimple gauge groups are considered. This greatly simplifies the analysis of the possible quantum corrections to the Quantum Action Principle which is reduced to the study of the cohomology group of the Lie algebra characterizing the gauge theory. The discussion is at the classical level for the algebraic properties of the SU(2) Higgs-Kibble-Englert-Brout-Faddeev-Popov lagrangian and its invariance under Slavnov identity transformations is exhibited. The renormalization of the Slavnov identity in the G.M.F. involving semisimple gauge groups is studied. The unitary and gauge independence of the physical S operator in the SU(2) H.K. model is dealt with [fr

Light-induced gauge fields for ultracold atoms

Science.gov (United States)

Goldman, N.; Juzeliūnas, G.; Öhberg, P.; Spielman, I. B.

2014-12-01

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.

Light-induced gauge fields for ultracold atoms

International Nuclear Information System (INIS)

Goldman, N; Juzeliūnas, G; Öhberg, P; Spielman, I B

2014-01-01

Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms. (review article)

Lattice QCD

International Nuclear Information System (INIS)

Hasenfratz, P.

1983-01-01

The author presents a general introduction to lattice gauge theories and discusses non-perturbative methods in the gauge sector. He then shows how the lattice works in obtaining the string tension in SU(2). Lattice QCD at finite physical temperature is discussed. Universality tests in SU(2) lattice QCD are presented. SU(3) pure gauge theory is briefly dealt with. Finally, fermions on the lattice are considered. (Auth.)

Lattice Gauge Theories Within and Beyond the Standard Model

Energy Technology Data Exchange (ETDEWEB)

Gelzer, Zechariah John [Iowa U.

2017-01-01

The Standard Model of particle physics has been very successful in describing fundamental interactions up to the highest energies currently probed in particle accelerator experiments. However, the Standard Model is incomplete and currently exhibits tension with experimental data for interactions involving $B$~mesons. Consequently, $B$-meson physics is of great interest to both experimentalists and theorists. Experimentalists worldwide are studying the decay and mixing processes of $B$~mesons in particle accelerators. Theorists are working to understand the data by employing lattice gauge theories within and beyond the Standard Model. This work addresses the theoretical effort and is divided into two main parts. In the first part, I present a lattice-QCD calculation of form factors for exclusive semileptonic decays of $B$~mesons that are mediated by both charged currents ($B \\to \\pi \\ell \

The ϱ-ππ coupling constant in lattice gauge theory

Science.gov (United States)

Gottlieb, Steven; MacKenzie, Paul B.; Thacker, H. B.; Weingarten, Don

1984-01-01

We present a method for studying hadronic transitions in lattice gauge theory which requires computer time comparable to that required by recent hadron spectrum calculations. This method is applied to a calculation of the decay ϱ-->ππ. On leave from the Department of Physics, Indiana University, Bloomington, IN 47405, USA. Address after September 1, 1983: IBM, T.J. Watson Research Center, Yorktown Heights, NY 10598, USA.

Comparison of lattice gauge theories with gauge groups Z2 and SU(2)

International Nuclear Information System (INIS)

Mack, G.; Petkova, B.

1978-11-01

We study a model of a pure Yang Mills theory with gauge group SU(2) on a lattice in Euclidean space. We compare it with the model obtained by restricting varibales to 2 . An inequality relating expectation values of the Wilson loop integral in the two theories is established. It shows that confinement of static quarks is true in our SU(2) model whenever it holds for the corresponding 2 -model. The SU(2) model is shown to have high and low temperature phases that are distinguished by a qualitatively different behavior of the t'Hooft disorder parameter. (orig.) [de

Wess-Zumino-Witten term on the lattice

International Nuclear Information System (INIS)

Fujiwara, Takanori; Suzuki, Hiroshi; Matsui, Kosuke; Yamamoto, Masaru

2003-01-01

We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge anomaly generally implies that there is no basis of a Weyl fermion which leads to a single-valued expectation value in the fermion sector. The lattice Witten term, which carries information of a gauge path along which the gauge anomaly is integrated, is separated from the WZW term and the multivaluedness of the Witten term is shown to be related to the homotopy group π 2n+1 (G). We also discuss the global SU(2) anomaly on the basis of the WZW term. (author)

Introduction to gauge field theory

International Nuclear Information System (INIS)

Bailin, David; Love, Alexander

1986-01-01

The book is intended as an introduction to gauge field theory for the postgraduate student of theoretical particle physics. The topics discussed in the book include: path integrals, classical and quantum field theory, scattering amplitudes, feynman rules, renormalisation, gauge field theories, spontaneous symmetry breaking, grand unified theory, and field theories at finite temperature. (UK)

Renormalization of Supersymmetric QCD on the Lattice

Science.gov (United States)

Costa, Marios; Panagopoulos, Haralambos

2018-03-01

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

Holographic description of large N gauge theory

International Nuclear Information System (INIS)

Lee, Sung-Sik

2011-01-01

Based on the earlier work [S.-S. Lee, Nucl. Rev. B 832 (2010) 567], we derive a holographic dual for the D-dimensional U(N) lattice gauge theory from a first principle construction. The resulting theory is a lattice field theory of closed loops, dubbed as lattice loop field theory which is defined on a (D+1)-dimensional space. The lattice loop field theory is well defined non-perturbatively, and it becomes weakly coupled and local in the large N limit with a large 't Hooft coupling.

Deconfinement phase transition and finite-size scaling in SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Mogilevskij, O.A.

1988-01-01

Calculation technique for deconfinement phase transition parameters based on application of finite-size scaling theory is suggested. The essence of the technique lies in plotting of universal scaling function on the basis of numerical data obtained at different-size final lattices and discrimination of phase transition parameters for infinite lattice system. Finite-size scaling technique was developed as applied to spin system theory. β critical index for Polyakov loop and SU(2) deconfinement temperature of lattice gauge theory are calculated on the basis of finite-size scaling technique. The obtained value agrees with critical index of magnetization in Ising three-dimensional model

Independent SU(2)-loop variables and the reduced configuration space of SU(2)-lattice gauge theory

International Nuclear Information System (INIS)

Loll, R.

1992-01-01

We give a reduction procedure for SU(2)-trace variables and an explicit description of the reduced configuration sace of pure SU(2)-gauge theory on the hypercubic lattices in two, three and four dimensions, using an independent subset of the gauge-invariant Wilson loops. (orig.)

Critical behavior of the compact 3D U(1) gauge theory on isotropic lattices

International Nuclear Information System (INIS)

Borisenko, O; Fiore, R; Papa, A; Gravina, M

2010-01-01

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three-dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for N t = 8 on lattices with spatial extension ranging from L = 32 to 256. Our determination of the infinite volume critical point on the lattice with N t = 8 differs substantially from the pseudo-critical coupling at L = 32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index ν computed from the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with the XY value ν = 1/2. On the other hand, the index η shows large deviation from the expected universal value. The possible reasons for such behavior are discussed in detail

Gauge fields in a torsion field

International Nuclear Information System (INIS)

Rosu, Ion

2004-01-01

In this paper we analyse the motion and the field equations in a non-null curvature and torsion space. In this 4-n dimensional space, the connection coefficients are γ bc a = 1/2S bc a + 1/2T bc a, where S bc a is the symmetrical part and T bc a are the components of the torsion tensor. We will consider that all the fields depend on x = x α , α = 1,2,3,4 and do not depend on y = y k , k=1,2,...,n. The factor S bc a depends on the components of the metric tensor g αβ (x) and on the gauge fields A ν s 0 (x) and the components of the torsion depend only on the gauge fields A ν s 0 (x). We take into consideration the particular case for which the geodesic equations coincide with the motion equations in the presence of the gravitational and the gauge fields. In this case the field equations are Einstein equations in a 4-n dimensional space. We show that both the geodesic equations and the field equations can be obtained from a variational principle. (author)

Quantum Monte Carlo studies in Hamiltonian lattice gauge theory

International Nuclear Information System (INIS)

Hamer, C.J.; Samaras, M.; Bursill, R.J.

2000-01-01

Full text: The application of Monte Carlo methods to the 'Hamiltonian' formulation of lattice gauge theory has been somewhat neglected, and lags at least ten years behind the classical Monte Carlo simulations of Euclidean lattice gauge theory. We have applied a Green's Function Monte Carlo algorithm to lattice Yang-Mills theories in the Hamiltonian formulation, combined with a 'forward-walking' technique to estimate expectation values and correlation functions. In this approach, one represents the wave function in configuration space by a discrete ensemble of random walkers, and application of the time development operator is simulated by a diffusion and branching process. The approach has been used to estimate the ground-state energy and Wilson loop values in the U(1) theory in (2+1)D, and the SU(3) Yang-Mills theory in (3+1)D. The finite-size scaling behaviour has been explored, and agrees with the predictions of effective Lagrangian theory, and weak-coupling expansions. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak couplings. A drawback to this method is that it is necessary to introduce a 'trial' or 'guiding wave function' to guide the walkers towards the most probable regions of configuration space, in order to achieve convergence and accuracy. The 'forward-walking' estimates should be independent of this guidance, but in fact for the SU(3) case they turn out to be sensitive to the choice of trial wave function. It would be preferable to use some sort of Metropolis algorithm instead to produce a correct distribution of walkers: this may point in the direction of a Path Integral Monte Carlo approach

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

Gravitating SO (3,1) gauge field

International Nuclear Information System (INIS)

Aragone, C.; Restuccia, A.

1978-01-01

In this article, we postulate SO (3,1) as a local symmetry of any relativistic theory. This is equivalent to assuming the existence of a gauge field associated with this noncompact group. This SO (3,1) gauge field is the spinorial affinity which usually appears when we deal with weighting spinors, which, as is well known, cannot be coupled to the metric tensor field. Furthermore, according to the integral approach to gauge fields proposed by Yang, it is also recognized that in order to obtain models of gravity we have to introduce ordinary affinities as the gauge field associated with GL (4) (the local symmetry determined by the parallel transport). Thus if we assume both GL (4) and SO (3,1) as local independent symmetries we are led to analyze the dynamical gauge system constituted by the Einstein field interacting with the SO (3,1) Weyl--Yang gauge field. We think this system is a possible model of strong gravity. Once we give the first-order action for this Einstein--Weyl--Yang system we study whether the SO (3,1) gauge field could have a tetrad associated with it. It is also shown that both fields propagate along a unique characteristic cone. Algebraic and differential constraints are solved when the system evolves along a null coordinate. The unconstrained expression for the action of the system is found working in the Bondi gauge. That allows us to exhibit an explicit expression of the dynamical generator of the system. Its signature turns out to be nondefinite, due to the nondefinite contribution of the Weyl--Yang field, which has the typical spinorial behavior. A conjecture is made that such an unpleasant feature could be overcome in the quantized version of this model

Lattice QCD for nuclear physics

CERN Document Server

Meyer, Harvey

2015-01-01

With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun, and many new observables will be calculated at the new computational facilities.  The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems, and in particular to nuclear physics.  A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spect...

A space-time lattice version of scalar electrodynamics

International Nuclear Information System (INIS)

Kijowski, J.; Thielmann, A.

1993-10-01

A Minkowski-lattice version of quantum scalar electrodynamics is constructed. Quantum field is consequently described in a gauge-independent way, i.e. the algebra of quantum observables of the theory is generated by gauge-invariant operators assigned to zero-, one-, and two-dimensional elements of the lattice. The operators satisfy canonical commutation relations. Field dynamics is formulated in terms of difference equations imposed on the field operators. The dynamics is obtained from a discrete version of the path-integral. (author). 19 refs

Lattice fields and strong interactions

International Nuclear Information System (INIS)

Creutz, M.

1989-06-01

I review the lattice formulation of gauge theories and the use of numerical methods to investigate nonperturbative phenomena. These methods are directly applicable to studying hadronic matter at high temperatures. Considerable recent progress has been made in numerical algorithms for including dynamical fermions in such calculations. Dealing with a nonvanishing baryon density adds new unsolved challenges. 33 refs

From lattice BF gauge theory to area-angle Regge calculus

International Nuclear Information System (INIS)

Bonzom, Valentin

2009-01-01

We consider Riemannian 4D BF lattice gauge theory, on a triangulation of spacetime. Introducing the simplicity constraints which turn BF theory into simplicial gravity, some geometric quantities of Regge calculus, areas, and 3D and 4D dihedral angles, are identified. The parallel transport conditions are taken care of to ensure a consistent gluing of simplices. We show that these gluing relations, together with the simplicity constraints, contain the constraints of area-angle Regge calculus in a simple way, via the group structure of the underlying BF gauge theory. This provides a precise road from constrained BF theory to area-angle Regge calculus. Doing so, a framework combining variables of lattice BF theory and Regge calculus is built. The action takes a form a la Regge and includes the contribution of the Immirzi parameter. In the absence of simplicity constraints, the standard spin foam model for BF theory is recovered. Insertions of local observables are investigated, leading to Casimir insertions for areas and reproducing for 3D angles known results obtained through angle operators on spin networks. The present formulation is argued to be suitable for deriving spin foam models from discrete path integrals and to unravel their geometric content.

Towards a multigrid scheme in SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Gutbrod, F.

1992-12-01

The task of constructing a viable updating multigrid scheme for SU(2) lattice gauge theory is discussed in connection with the classical eigenvalue problem. For a nonlocal overrelaxation Monte Carlo update step, the central numerical problem is the search for the minimum of a quadratic approximation to the action under nonlocal constraints. Here approximate eigenfunctions are essential to reduce the numerical work, and these eigenfunctions are to be constructed with multigrid techniques. A simple implementation on asymmetric lattices is described, where the grids are restricted to 3-dimensional hyperplanes. The scheme is shown to be moderately successful in the early stages of the updating history (starting from a cold configuration). The main results of another, less asymmetric scheme are presented briefly. (orig.)

Computation of hybrid static potentials in SU(3 lattice gauge theory

Directory of Open Access Journals (Sweden)

Reisinger Christian

2018-01-01

Full Text Available We compute hybrid static potentials in SU(3 lattice gauge theory. We present a method to automatically generate a large set of suitable creation operators with defined quantum numbers from elementary building blocks. We show preliminary results for several channels and discuss, which structures of the gluonic flux tube seem to be realized by the ground states in these channels.

Emergent Gauge Fields in Holographic Superconductors

CERN Document Server

Domènech, Oriol; Pomarol, Alex; Salvio, Alberto; Silva, Pedro J

2010-01-01

Holographic superconductors have been studied so far in the absence of dynamical electromagnetic fields, namely in the limit in which they coincide with holographic superfluids. It is possible, however, to introduce dynamical gauge fields if a Neumann-type boundary condition is imposed on the AdS-boundary. In 3+1 dimensions, the dual theory is a 2+1 dimensional CFT whose spectrum contains a massless gauge field, signaling the emergence of a gauge symmetry. We study the impact of a dynamical gauge field in vortex configurations where it is known to significantly affect the energetics and phase transitions. We calculate the critical magnetic fields H_c1 and H_c2, obtaining that holographic superconductors are of Type II (H_c1 < H_c2). We extend the study to 4+1 dimensions where the gauge field does not appear as an emergent phenomena, but can be introduced, by a proper renormalization, as an external dynamical field. We also compare our predictions with those arising from a Ginzburg-Landau theory and identif...

'Baldin autumn' and gauge fields

International Nuclear Information System (INIS)

Konopleva, N.P.

2008-01-01

The paper is the reminiscences of the participant of the gauge field theory beginning and the first 'Baldin Autumn' conference in 1969. This conference was named 'Vector Mesons and Electromagnetic Interactions'. At that time, just the processes with vector mesons participation contained some experimental indications of new universal interactions existence. Vector dominance was the experimental evidence of physical reasons of the gauge field theory. In the course of time the gauge field theory form, which was under discussion thirty seven years ago, became generally recognized and experimentally corroborated. It led to construction of the well-known Standard Model of elementary particle interactions

Chiral fermions on the lattice

International Nuclear Information System (INIS)

Randjbar Daemi, S.; Strathdee, J.

1995-01-01

The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi-flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in D dimensions and show that they coincide with the bilinear part of the effective action of D-dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2-dimensional gravitation and Maxwell fields. (author). 15 refs

Gauge field copies

International Nuclear Information System (INIS)

Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.

1979-01-01

The construction of field strength copies without any gauge constraint is discussed. Several examples are given, one of which is not only a field strength copy but also (at the same time) a 'current copy'. (author) [pt

Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter

Science.gov (United States)

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

2017-02-01

We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2 +1 ) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z2 model in (2 +1 ) dimensions.

Digital Quantum Simulation of Z_{2} Lattice Gauge Theories with Dynamical Fermionic Matter.

Science.gov (United States)

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J Ignacio

2017-02-17

We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2+1) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z_{2} model in (2+1) dimensions.

Cutoff effects on energy-momentum tensor correlators in lattice gauge theory

International Nuclear Information System (INIS)

Meyer, Harvey B.

2009-01-01

We investigate the discretization errors affecting correlators of the energy-momentum tensor T μν at finite temperature in SU(N c ) gauge theory with the Wilson action and two different discretizations of T μν . We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time x 0 and spatial momentum p, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy ∫d 3 x T 00 has much larger discretization errors than the correlator of momentum ∫d 3 x T 0k . Secondly, the shear and diagonal stress correlators (T 12 and T kk ) require N τ ≥ 8 for the Tx 0 = 1/2 point to be in the scaling region and the cutoff effect to be less than 10%. We then show that their discretization errors on an anisotropic lattice with a σ /a τ = 2 are comparable to those on the isotropic lattice with the same temporal lattice spacing. Finally, we also study finite p correlators.

Quantum Operator Design for Lattice Baryon Spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Lichtl, Adam [Carnegie Mellon Univ., Pittsburgh, PA (United States)

2006-09-07

A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. The operators are assemblages of smeared and gauge-covariantly-displaced quark fields having a definite flavor structure. The importance of using smeared fields is dramatically demonstrated. It is found that quark field smearing greatly reduces the couplings to the unwanted high-lying short-wavelength modes, while gauge field smearing drastically reduces the statistical noise in the extended operators.

Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

International Nuclear Information System (INIS)

Shamir, Yigal; Svetitsky, Benjamin; DeGrand, Thomas

2008-01-01

We have carried out a Schrodinger functional calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the Schrodinger functional renormalized coupling is in the neighborhood of g 2 =2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.

Lattice Gauge Theory and the Origin of Mass

Energy Technology Data Exchange (ETDEWEB)

Kronfeld, Andreas S.

2013-08-01

Most of the mass of everyday objects resides in atomic nuclei/ the total of the electrons' mass adds up to less than one part in a thousand. The nuclei are composed of nucleons---protons and neutrons---whose nuclear binding energy, though tremendous on a human scale, is small compared to their rest energy. The nucleons are, in turn, composites of massless gluons and nearly massless quarks. It is the energy of these confined objects, via $M=E/c^2$, that is responsible for everyday mass. This article discusses the physics of this mechanism and the role of lattice gauge theory in establishing its connection to quantum chromodynamics.

Elastic Gauge Fields in Weyl Semimetals

Science.gov (United States)

Cortijo, Alberto; Ferreiros, Yago; Landsteiner, Karl; Hernandez Vozmediano, Maria Angeles

We show that, as it happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudo gauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated to these elastic gauge fields, we derive a non-zero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings. European Union structural funds and the Comunidad de Madrid MAD2D-CM Program (S2013/MIT-3007).

SU(N) lattice gauge theory with Villain's action

International Nuclear Information System (INIS)

Onofri, E.

1981-01-01

The pure gauge lattice theory with Villain's action exp[-A(U)] = GAMMAsub(j=1)sup(N) Σsub(n=-infinity)sup(+infinity) exp[-(N/lambda)(THETAsub(j) + 2nπ) 2 ], where THETA 1 ,..., THETAsub(N) are the invariant angles of U is an element of U(N) or SU(N) is considered. For the two-dimensional lattice the partition function Z(lambda,N) is calculated with the specific heat, the level density rhosub(N)(THETA) and Wilson's loops Wsub(n) = (1/N) (n = 1,2,3,...). The 1/N expansion of Z and Wsub(n) is convergent for sufficiently small |lambda/N| and its coefficients are analytic in lambda near the real axis (no ''Gross-Witten'' singularity to all orders in 1/N), but it is still not possible to commute the strong-coupling limit with the planar limit (lambda→infinity, N→infinity). The character expansion which is needed for strong-coupling calculations in four dimensions is also calculated. A comparison with Monte Carlo data (N=2) and a preliminary discussion of the large-N limit is given. (author)

Effects of the quark field on the ghost propagator of lattice Landau gauge QCD

International Nuclear Information System (INIS)

Furui, Sadataka; Nakajima, Hideo

2006-01-01

Infrared features of the ghost propagator of color-diagonal and color antisymmetric ghost propagator of quenched SU(2) and quenched SU(3) are compared with those of unquenched Kogut-Susskind fermion SU(3) lattice Landau gauge. We compare (i) the fluctuation of the ghost propagator (ii) the ghost condensate parameter v of the local composite operator (LCO) approach, and (iii) the Binder cumulant of color antisymmetric ghost propagator between quenched and unquenched configurations. The color-diagonal SU(3) ghost dressing function of unquenched configurations has weaker singularity than the quenched configurations. In both cases fluctuations become large in q c configuration samples is ∼0.002-0.04 GeV 2 while that of the SU(2) parallel tempering samples is consistent with 0. The Binder cumulant defined as U(q)=1-(1/3)( 4 >/( 2 >) 2 ), where φ-vector(q) is the color antisymmetric ghost propagator measured by the sample average of gauge fixed configurations via parallel tempering method, becomes ∼4/9 in all the momentum region. The Binder cumulant of the color antisymmetric ghost propagator of quenched SU(2) can be explained by the 3D Gaussian distribution, but that of the unquenched MILC c deviates slightly from that of the eight-dimensional Gaussian distribution. The stronger singularity and large fluctuation in the quenched configuration could be the cause of the deviation of the Kugo-Ojima confinement parameter c from 1, and the presence of ordering in the ghost propagator of unquenched configurations makes it closer to 1

Supersymmetric gauge field theories

International Nuclear Information System (INIS)

Slavnov, A.A.

1976-01-01

The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models

Critical behavior at the deconfinement phase phase transition of SU(2) lattice gauge theory in (2+1) dimensions

International Nuclear Information System (INIS)

Christensen, J.; Damgaard, P.H.

1991-01-01

The finite-temperature deconfinement phase transition of SU(2) lattice gauge theory in (2+1) dimensions is studied by Monte Carlo methods. Comparison is made with the expected form of correlation functions on both sides of the critical point. The critical behavior is compared with expectations based on universality arguments. Attempts are made to extract unbiased values of critical exponents on several lattices sizes. The behavior of Polyakov loops in higher representations of the gauge group is studied close to the phase transition. (orig.)

Gauge-invariant Yang-Mills fields and the role of Lorentz gauge condition

International Nuclear Information System (INIS)

Skachkov, N.B.; Shevchenko, O.Yu.

1985-01-01

A new class of gauge-invariant (G.I.) fields is constructed. The inversion formulae that express these fields through the G.I. strength tensor are obtained. It is shown that for the G.I. fields the Lorentz gauge condition appears as the secondary constraint. These fields coincide with the usual ones in some definite gauges. The Dyson-Schwinger equations for the G.I. spinor propagator are derived. It is found that in QED this propagator has a simple pole singularity (p-m) -1 in the infrared limit

Model of unified gauge fields

International Nuclear Information System (INIS)

Leite Lopes, J.

1998-04-01

In this work, we discuss the physical ideas which represents the basis for the unified gauge field model. Despite of the difficulties that we presently have for embodying in a natural manner muons and hadrons in that model, we have the feeling that we are on the way which seems to lead to the construction of a theory in which the Maxwell electromagnetic field and the Fermi weak interaction field are manifestations of a unique subjacent physical entity - the unified gauge fields. (author)

Phase structure of lattice gauge theories for non-abelian subgroups of SU(3)

International Nuclear Information System (INIS)

Grosse, H.; Kuehnelt, H.

1981-01-01

The authors study the phase structure of Euclidean lattice gauge theories in four dimensions for certain non-abelian subgroups of SU(3) by using Monte-Carlo simulations and strong coupling expansions. As the order of the group increases a splitting of one phase transition into two is observed. (Auth.)

Gauge field condensation in geometric quantum chromodynamics

International Nuclear Information System (INIS)

Guendelman, E.I.

1991-09-01

In odd number of dimensions, it is possible to construct general covariant gauge theories, where the metric is not an independent variable, but local function of the gauge fields. Starting from standardly defined gauge theory, upon functional integration of some variables, we could end up with such moodels. For models with SU(2) and SU(3) symmetry in three dimensions, gauge field condensation take place in the vacuum, which is nevertheless homogeneous and isotropic up to a gauge transformation, provided the space is flat. Introducing Higgs fields that spontaneously break the gauge symmetry, we get a breakdown of the homogenity and isotropy of the vacuum. Finally, we discuss how some of this ideas can be generalized to four and other even dimensions. (author)

Monte Carlo simulation of Su(2) lattice gauge theory with internal quark loops

International Nuclear Information System (INIS)

Azcoiti, V.; Nakamura, A.

1982-01-01

Dynamical effects of quark loops in lattice gauge theory with icosahedral group are studied. The standard Wilson action is employed and the fermionic part by a discretize pseudo fermionic method is calculated. The masses of π, rho, ω are computed and the average value of an effective fermionic action is evaluated

Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits

Energy Technology Data Exchange (ETDEWEB)

Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics

1975-03-01

General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.

The infrared behavior of lattice QCD Green's functions. A numerical study of lattice QCD in Landau gauge

International Nuclear Information System (INIS)

Sternbeck, A.

2006-01-01

Within the framework of lattice QCD we investigate different aspects of QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied. We demonstrate the ghost dressing function to systematically depend on the choice of Gribov copies at low momentum, while the influence on the gluon dressing function is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies. We show that the influence of dynamical Wilson fermions on the ghost propagator is negligible at the momenta available to us. On the contrary, fermions affect the gluon propagator at large and intermediate momenta. In addition, we analyze data for both propagators obtained on asymmetric lattices and compare these results with data obtained on symmetric lattices. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with different criteria for confinement. However, the running coupling constant, given as a renormalization-group-invariant combination of the gluon and ghost dressing functions, does not expose a finite infrared fixed point. Rather the data are in favor of an infrared vanishing coupling constant. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant. We present results of an investigation of the spectral properties of the Faddeev-Popov operator. For this we have calculated the low-lying eigenvalues and eigenmodes of the Faddeev-Popov operator. (orig.)

An improved single-plaquette gauge action

International Nuclear Information System (INIS)

Banerjee, D.; Bögli, M.; Holland, K.; Niedermayer, F.; Pepe, M.; Wenger, University; Wiese, UniversityJ.

2016-01-01

We describe and test a nonperturbatively improved single-plaquette lattice action for 4-d SU(2) and SU(3) pure gauge theory, which suppresses large fluctuations of the plaquette, without requiring the naive continuum limit for smooth fields. We tune the action parameters based on torelon masses in moderate cubic physical volumes, and investigate the size of cut-off effects in other physical quantities, including torelon masses in asymmetric spatial volumes, the static quark potential, and gradient flow observables. In 2-d O(N) models similarly constructed nearest-neighbor actions have led to a drastic reduction of cut-off effects, down to the permille level, in a wide variety of physical quantities. In the gauge theories, we find significant reduction of lattice artifacts, and for some observables, the coarsest lattice result is very close to the continuum value. We estimate an improvement factor of 40 compared to using the Wilson gauge action to achieve the same statistical accuracy and suppression of cut-off effects.

Derivation of the Finslerian gauge field equations

International Nuclear Information System (INIS)

Asanov, G.S.

1984-01-01

As is well known the simplest way of formulating the equations for the Yang-Mills gauge fields consists in taking the Lagrangian to be quadratic in the gauge tensor, whereas the application of such an approach to the gravitational field yields equations which are of essentially more complicated structure than the Einstein equations. On the other hand, in the gravitational field theory the Lagrangian can be constructed to be of forms which may be both quadratic and linear in the curvature tensor, whereas the latter possibility is absent in the current gauge field theories. In previous work it has been shown that the Finslerian structure of the space-time gives rise to certain gauge fields provided that the internal symmetries may be regarded as symmetries of a three-dimensional Riemannian space. Continuing this work we show that appropriate equations for these gauge fields can be formulated in both ways, namely on the basis of the quadratic Lagrangian or, if a relevant generalization of the Palatini method is applied, on the basis of a Lagrangian linear in the gauge field strength tensor. The latter possibility proves to result in equations which are similar to the Einstein equations, a distinction being that the Finslerian Cartan curvature tensor rather then the Riemann curvature tensor enters the equations. (author)

Four-dimensional Ashkin-Teller gauge theory

International Nuclear Information System (INIS)

Alcaraz, F.C.; Jacobs, L.

1983-01-01

The authors construct and analyze a lattice field theory of two Z 2 gauge fields which interact in a minimal gauge-invariant fashion. Although the theory presented here, a generalization of the two-dimensional Ashkin-Teller spin system, has no formal continuum limit, it is found that it has an electrodynamicslike phase similar to that observed in general Z/sub N/ theories for N> or =4. This model is probably the simplest generalization of the conventional Z 2 pure gauge theory which has a massless phase separated from the strong- and weak-coupling regions by lines of second-order phase transitions

Renormalization group aspects of 3-dimensional Pure U(1) lattice gauge theory

International Nuclear Information System (INIS)

Gopfert, M.; Mack, G.

1983-01-01

A few surprises in a recent study of the 3-dimensional pure U(1) lattice gauge theory model, from the point of view of the renormalization group theory, are discussed. Since the gauge group U(1) of this model is abelian, the model is subject to KramersWannier duality transformation. One obtains a ferromagnet with a global symmetry group Z. The duality transformation shows that the surface tension alpha of the model equals the strong tension of the U(1) gauge model. A theorem to represent the true asymptotic behaviour of alpha is derived. A second theorem considers the correlation functions. Discrepiancies between the theorems result in a solution that ''is regarded as a catastrophe'' in renormalization group theory. A lesson is drawn: To choose a good block spin in a renormalization group procedure, know what the low lying excitations of the theory are, to avoid integrating some of them by mischief

Elastic gauge fields and Hall viscosity of Dirac magnons

Science.gov (United States)

Ferreiros, Yago; Vozmediano, María A. H.

2018-02-01

We analyze the coupling of elastic lattice deformations to the magnon degrees of freedom of magnon Dirac materials. For a honeycomb ferromagnet we find that, as happens in the case of graphene, elastic gauge fields appear coupled to the magnon pseudospinors. For deformations that induce constant pseudomagnetic fields, the spectrum around the Dirac nodes splits into pseudo-Landau levels. We show that when a Dzyaloshinskii-Moriya interaction is considered, a topological gap opens in the system and a Chern-Simons effective action for the elastic degrees of freedom is generated. Such a term encodes a phonon Hall viscosity response, entirely generated by quantum fluctuations of magnons living in the vicinity of the Dirac points. The magnon Hall viscosity vanishes at zero temperature, and grows as temperature is raised and the states around the Dirac points are increasingly populated.

Stochastic quantization of field theories on the lattice and supersymmetrical models

International Nuclear Information System (INIS)

Aldazabal, Gerardo.

1984-01-01

Several aspects of the stochastic quantization method are considered. Specifically, field theories on the lattice and supersymmetrical models are studied. A non-linear sigma model is studied firstly, and it is shown that it is possible to obtain evolution equations written directly for invariant quantities. These ideas are generalized to obtain Langevin equations for the Wilson loops of non-abelian lattice gauge theories U (N) and SU (N). In order to write these equations, some different ways of introducing the constraints which the fields must satisfy are discussed. It is natural to have a strong coupling expansion in these equations. The correspondence with quantum field theory is established, and it is noticed that at all orders in the perturbation theory, Langevin equations reduce to Schwinger-Dyson equations. From another point of view, stochastic quantization is applied to large N matrix models on the lattice. As a result, a simple and systematic way of building reduced models is found. Referring to stochastic quantization in supersymmetric theories, a simple supersymmetric model is studied. It is shown that it is possible to write an evolution equation for the superfield wich leads to quantum field theory results in equilibrium. As the Langevin equation preserves supersymmetry, the property of dimensional reduction known for the quantum model is shown to be valid at all times. (M.E.L.) [es

Hardware matrix multiplier/accumulator for lattice gauge theory calculations

International Nuclear Information System (INIS)

Christ, N.H.; Terrano, A.E.

1984-01-01

The design and operating characteristics of a special-purpose matrix multiplier/accumulator are described. The device is connected through a standard interface to a host PDP11 computer. It provides a set of high-speed, matrix-oriented instructions which can be called from a program running on the host. The resulting operations accelerate the complex matrix arithmetic required for a class of Monte Carlo calculations currently of interest in high energy particle physics. A working version of the device is presently being used to carry out a pure SU(3) lattice gauge theory calculation using a PDP11/23 with a performance twice that obtainable on a VAX11/780. (orig.)

Inflationary dynamics of kinetically-coupled gauge fields

DEFF Research Database (Denmark)

Ferreira, Ricardo J. Z.; Ganc, Jonathan

2015-01-01

We investigate the inflationary dynamics of two kinetically-coupled massless U(1) gauge fields with time-varying kinetic-term coefficients. Ensuring that the system does not have strongly coupled regimes shrinks the parameter space. Also, we further restrict ourselves to systems that can be quant......We investigate the inflationary dynamics of two kinetically-coupled massless U(1) gauge fields with time-varying kinetic-term coefficients. Ensuring that the system does not have strongly coupled regimes shrinks the parameter space. Also, we further restrict ourselves to systems that can...... be quantized using the standard creation, annihilation operator algebra. This second constraint limits us to scenarios where the system can be diagonalized into the sum of two decoupled, massless, vector fields with a varying kinetic-term coefficient. Such a system might be interesting for magnetogenesis...... because of how the strong coupling problem generalizes. We explore this idea by assuming that one of the gauge fields is the Standard Model U(1) field and that the other dark gauge field has no particles charged under its gauge group. We consider whether it would be possible to transfer a magnetic field...

Measurability of non-abelium gauge fields

Energy Technology Data Exchange (ETDEWEB)

Ivanenko, D.D.; Obukhov, Yu.N.

New estimations of the accuracy of measurement of non-abeliar gauge field components are obtained on the base of qualitative analysis of the test body equations of motion. They generalize the Bohr and Rosenfeld results on the measurability of an electomagnetic field for the case of an arbitrary gauge group.

Magnetic monopoles, center vortices, confinement and topology of gauge fields

International Nuclear Information System (INIS)

Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schaefke, A.

2000-01-01

The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed

Magnetic Monopoles, Center Vortices, Confinement and Topology of Gauge Fields

OpenAIRE

Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Sch"afke, A.

1999-01-01

The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed.

On the overlap prescription for lattice regularization of chiral fermions

International Nuclear Information System (INIS)

Randjbar-Daemi, S.; Strathdee, J.

1995-12-01

Feynman rules for the vacuum amplitude of fermions coupled to external gauge and Higgs fields in a domain wall lattice model are derived using time-dependent perturbation theory. They have a clear and simple structure corresponding to 1-loop vacuum graphs. Their continuum approximations are extracted by isolating the infrared singularities and it is shown that, in each order, they reduce to vacuum contributions for chiral fermions. In this sense the lattice model is seen to constitute a valid regularization of the continuum theory of chiral fermions coupled to weak and slowly varying gauge and Higgs fields. The overlap amplitude, while not gauge invariant, exhibits a well defined (module phase conventions) response to gauge transformations of the background fields. This response reduces in the continuum limit to the expected chiral anomaly, independently of the phase convention. (author). 20 refs

On the overlap prescription for lattice regularization of chiral fermions

Energy Technology Data Exchange (ETDEWEB)

Randjbar-Daemi, S; Strathdee, J

1995-12-01

Feynman rules for the vacuum amplitude of fermions coupled to external gauge and Higgs fields in a domain wall lattice model are derived using time-dependent perturbation theory. They have a clear and simple structure corresponding to 1-loop vacuum graphs. Their continuum approximations are extracted by isolating the infrared singularities and it is shown that, in each order, they reduce to vacuum contributions for chiral fermions. In this sense the lattice model is seen to constitute a valid regularization of the continuum theory of chiral fermions coupled to weak and slowly varying gauge and Higgs fields. The overlap amplitude, while not gauge invariant, exhibits a well defined (module phase conventions) response to gauge transformations of the background fields. This response reduces in the continuum limit to the expected chiral anomaly, independently of the phase convention. (author). 20 refs.

Gauge-invariant intense-field approximations to all orders

International Nuclear Information System (INIS)

Faisal, F H M

2007-01-01

We present a gauge-invariant formulation of the so-called strong-field KFR approximations in the 'velocity' and 'length' gauges and demonstrate their equivalence in all orders. The theory thus overcomes a longstanding discrepancy between the strong-field velocity and the length-gauge approximations for non-perturbative processes in intense laser fields. (fast track communication)

World-sheet gauge fields in superstrings

International Nuclear Information System (INIS)

Porrati, M.; Tomboulis, E.T.

1989-01-01

We investigate the introduction of world-sheet 2-dimensional gauge fields in a manner consistent with world-sheet supersymmetry. We obtain the effective string action resulting from the exact integration over the world-sheet gauge fields to show that it generally describes string models with spontaneous breaking of gauge symmetries with continuous breaking parameters. We examine the question of spacetime supersymmetry spontaneous breaking, and show that breaking with continuous, in particular arbitrarily small breaking parameters does not occur; only breaking for discrete values of parameters is possible. (orig.)

Magnetic vortices in gauge/gravity duality

Energy Technology Data Exchange (ETDEWEB)

Strydom, Migael

2014-07-18

We study strongly-coupled phenomena using gauge/gravity duality, with a particular focus on vortex solutions produced by magnetic field and time-dependent problems in holographic models. The main result is the discovery of a counter-intuitive effect where a strong non-abelian magnetic field induces the formation of a triangular vortex lattice ground state in a simple holographic model. Gauge/gravity duality is a powerful theoretical tool that has been used to study strongly-coupled systems ranging from the quark-gluon plasma produced at particle colliders to condensed matter theories. The most important idea is that of duality: a strongly coupled quantum field theory can be studied by investigating the properties of a particular gravity background described by Einstein's equations. One gravity background we study in this dissertation is AdS-Schwarzschild with an SU(2) gauge field. We switch on the gauge field component that gives the field theory an external magnetic field. When the magnetic field is above a critical value, we find that the system is unstable, indicating a superconducting phase transition. We find the instability in two ways. Firstly, we do a quasinormal mode analysis, studying fluctuations about the background. Secondly, we rewrite the equations in Schroedinger form and numerically find that, as the magnetic field is increased, the potential deepens until it is capable of supporting a bound state. Next we show that the resulting superconducting ground state is a triangular vortex lattice. This is done by performing a perturbative expansion in a small parameter proportional to the condensate size. After solving the equations to third order, we use the holographic dictionary to calculate the total energy of different lattice solutions and identify the minimum energy state. In addition, we show that the result holds in an AdS-hard wall model as well, which is dual to a confining theory. Next we extend the simple gravity model to include a

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

Science.gov (United States)

Kurkela, Aleksi; Lappi, Tuomas; Peuron, Jarkko

2018-03-01

Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss's law is conserved.

Canonical Yang-Mills field theory with invariant gauge-families

International Nuclear Information System (INIS)

Yokoyama, Kan-ichi

1978-01-01

A canonical Yang-Mills field theory with indefinite metric is presented on the basis of a covariant gauge formalism for quantum electrodynamics. As the first step of the formulation, a many-gauge-field problem, in which many massless Abelian-gauge fields coexist, is treated from a new standpoint. It is shown that only a single pair of a gaugeon field and its associated one can govern the gauge structure of the whole system. The result obtained is further extended to cases of non-Abelian gauge theories. Gauge parameters for respective components of the Yang-Mills fields are introduced as a group vector. There exists a q-number local gauge transformation which connects relevant fields belonging to the same invariant gauge family with one another in a manifestly covariant way. In canonical quantization, the Faddeev-Popov ghosts are introduced in order to guarantee the existence of a desirable physical subspace with positive semi-definite metric. As to treatment of the Faddeev-Popov ghosts, Kugo and Ojima's approach is adopted. Three supplementary conditions which are consistent with one another constrain the physical subspace. (author)

Analysis and development of stochastic multigrid methods in lattice field theory

International Nuclear Information System (INIS)

Grabenstein, M.

1994-01-01

We study the relation between the dynamical critical behavior and the kinematics of stochastic multigrid algorithms. The scale dependence of acceptance rates for nonlocal Metropolis updates is analyzed with the help of an approximation formula. A quantitative study of the kinematics of multigrid algorithms in several interacting models is performed. We find that for a critical model with Hamiltonian H(Φ) absence of critical slowing down can only be expected if the expansion of (H(Φ+ψ)) in terms of the shift ψ contains no relevant term (mass term). The predictions of this rule was verified in a multigrid Monte Carlo simulation of the Sine Gordon model in two dimensions. Our analysis can serve as a guideline for the development of new algorithms: We propose a new multigrid method for nonabelian lattice gauge theory, the time slice blocking. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method, in accordance with the theoretical prediction. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four dimensional gauge field leads to kinematical problems. (orig.)

Constraints on Gauge Field Production during Inflation

DEFF Research Database (Denmark)

Nurmi, Sami; Sloth, Martin Snoager

2014-01-01

In order to gain new insights into the gauge field couplings in the early universe, we consider the constraints on gauge field production during inflation imposed by requiring that their effect on the CMB anisotropies are subdominant. In particular, we calculate systematically the bispectrum...... of the primordial curvature perturbation induced by the presence of vector gauge fields during inflation. Using a model independent parametrization in terms of magnetic non-linearity parameters, we calculate for the first time the contribution to the bispectrum from the cross correlation between the inflaton...

Gauge invariance of string fields

International Nuclear Information System (INIS)

Banks, T.; Peskin, M.E.

1985-10-01

Some work done to understand the appearance of gauge bosons and gravitons in string theories is reported. An action has been constructed for free (bosonic) string field theory which is invariant under an infinite set of gauge transformations which include Yang-Mills transformations and general coordinate transformations as special cases. 15 refs., 1 tab

Individual eigenvalue distributions of crossover chiral random matrices and low-energy constants of SU(2) × U(1) lattice gauge theory

Science.gov (United States)

Yamamoto, Takuya; Nishigaki, Shinsuke M.

2018-02-01

We compute individual distributions of low-lying eigenvalues of a chiral random matrix ensemble interpolating symplectic and unitary symmetry classes by the Nyström-type method of evaluating the Fredholm Pfaffian and resolvents of the quaternion kernel. The one-parameter family of these distributions is shown to fit excellently the Dirac spectra of SU(2) lattice gauge theory with a constant U(1) background or dynamically fluctuating U(1) gauge field, which weakly breaks the pseudoreality of the unperturbed SU(2) Dirac operator. The observed linear dependence of the crossover parameter with the strength of the U(1) perturbations leads to precise determination of the pseudo-scalar decay constant, as well as the chiral condensate in the effective chiral Lagrangian of the AI class.

Extrapolation of lattice gauge theories to the continuum limit

International Nuclear Information System (INIS)

Duncan, A.; Vaidya, H.

1978-01-01

The problem of extrapolating lattice gauge theories from the strong-coupling phase to the continuum critical point is studied for the Abelian (U(1)) and non-Abelian (SU(2)) theories in three (space--time) dimensions. A method is described for obtaining the asymptotic behavior, for large β, of such thermodynamic quantities and correlation functions as the free energy and Wilson loop function. Certain general analyticity and positivity properties (in the complex β-plane) are shown to lead, after appropriate analytic remappings, to a Stieltjes property of these functions. Rigorous theorems then guarantee uniform and monotone convergence of the Pade approximants, with exact pointwise upper and lower bounds. The first three Pade's are computed for both the free energy and the Wilson function. For the free energy, satisfactory agreement is with the asymptotic behavior computed by an explicit lattice calculation. The strong-coupling series for the Wilson function is found to be considerably more unstable in the lower order terms - correspondingly, convergence of the Pade's is found to be slower than in the free-energy case. It is suggested that higher-order calculations may allow a reasonably accurate determination of the string constant for the SU(2) theory. 14 references

Gauge field theory

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Slavnov, A.A.

1981-01-01

This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks [ru

Gauge invariant fractional electromagnetic fields

International Nuclear Information System (INIS)

Lazo, Matheus Jatkoske

2011-01-01

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.

Introduction to gauge field theory

International Nuclear Information System (INIS)

Bailin, D.; Love, A.

1986-01-01

This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications

Series expansions of the density of states in SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Denbleyker, A.; Du, Daping; Liu, Yuzhi; Meurice, Y.; Velytsky, A.

2008-01-01

We calculate numerically the density of states n(S) for SU(2) lattice gauge theory on L 4 lattices [S is the Wilson's action and n(S) measures the relative number of ways S can be obtained]. Small volume dependences are resolved for small values of S. We compare ln(n(S)) with weak and strong coupling expansions. Intermediate order expansions show a good overlap for values of S corresponding to the crossover. We relate the convergence of these expansions to those of the average plaquette. We show that, when known logarithmic singularities are subtracted from ln(n(S)), expansions in Legendre polynomials appear to converge and could be suitable to determine the Fisher's zeros of the partition function.

Non-Abelian gauge fields in two spatial dimensions

International Nuclear Information System (INIS)

Hagen, C.R.

1987-01-01

Generalizing an earlier work on the Abelian case the most general non-Abelian gauge theory in two spatial dimensions is derived. It is shown that local gauge invariance leads to a new term in the action which in turn requires that the gauge current operator have a part which is bilinear in the non-Abelian gauge field-strength tensor. Although a radiation (or axial) gauge quantization is possible, this approach is found not to yield the maximal set of commutation relations among the basic fields. The latter goal can be accomplished only by a rather unusual gauge choice which has not previously been studied. Quantization conditions on the coupling constant implied by invariance under large gauge transformations are also derived

Vacuum polarization and chiral lattice fermions

International Nuclear Information System (INIS)

Randjbar Daemi, S.; Strathdee, J.

1995-09-01

The vacuum polarization due to chiral fermions on a 4-dimensional Euclidean lattice is calculated according to the overlap prescription. The fermions are coupled to weak and slowly varying background gauge and Higgs fields, and the polarization tensor is given by second order perturbation theory. In this order the overlap constitutes a gauge invariant regularization of the fermion vacuum amplitude. Its low energy - long wavelength behaviour can be computed explicitly and we verify that it coincides with the Feynman graph result obtainable, for example, by dimensional regularization of continuum gauge theory. In particular, the Standard Model Callan-Symanzik, RG functions are recovered. Moreover, there are no residual lattice artefacts such as a dependence on Wilson-type mass parameters. (author). 16 refs

Gauge field vacuum structure in geometrical aspect

International Nuclear Information System (INIS)

Konopleva, N.P.

2003-01-01

Vacuum conception is one of the main conceptions of quantum field theory. Its meaning in classical field theory is also very profound. In this case the vacuum conception is closely connected with ideas of the space-time geometry. The global and local geometrical space-time conceptions lead to different vacuum definitions and therefore to different ways of physical theory construction. Some aspects of the gauge field vacuum structure are analyzed. It is shown that in the gauge field theory the vacuum Einstein equation solutions describe the relativistic vacuum as common vacuum of all gauge fields and its sources. Instantons (both usual and hyperbolical) are regarded as nongravitating matter, because they have zero energy-momentum tensors and correspond to vacuum Einstein equations

Plasmon mass scale and quantum fluctuations of classical fields on a real time lattice

Directory of Open Access Journals (Sweden)

Kurkela Aleksi

2018-01-01

Full Text Available Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Above the Debye scale the classical Yang-Mills (CYM theory can be matched smoothly to kinetic theory. First we study the limits of the quasiparticle picture of the CYM fields by determining the plasmon mass of the system using 3 different methods. Then we argue that one needs a numerical calculation of a system of classical gauge fields and small linearized fluctuations, which correspond to quantum fluctuations, in a way that keeps the separation between the two manifest. We demonstrate and test an implementation of an algorithm with the linearized fluctuation showing that the linearization indeed works and that the Gauss’s law is conserved.

A gauge field theory of fermionic continuous-spin particles

Energy Technology Data Exchange (ETDEWEB)

Bekaert, X., E-mail: xavier.bekaert@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science, Daejeon (Korea, Republic of); Najafizadeh, M., E-mail: mnajafizadeh@gmail.com [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of); Setare, M.R., E-mail: rezakord@ipm.ir [Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of)

2016-09-10

In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.

A gauge field theory of fermionic continuous-spin particles

International Nuclear Information System (INIS)

Bekaert, X.; Najafizadeh, M.; Setare, M.R.

2016-01-01

In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.

Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study

International Nuclear Information System (INIS)

Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.

2007-06-01

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)

The infrared behavior of lattice QCD Green's functions. A numerical study of lattice QCD in Landau gauge

Energy Technology Data Exchange (ETDEWEB)

Sternbeck, A.

2006-07-18

Within the framework of lattice QCD we investigate different aspects of QCD in Landau gauge using Monte Carlo simulations. In particular, we focus on the low momentum behavior of gluon and ghost propagators. The gauge group is SU(3). Different systematic effects on the gluon and ghost propagators are studied. We demonstrate the ghost dressing function to systematically depend on the choice of Gribov copies at low momentum, while the influence on the gluon dressing function is not resolvable. Also the eigenvalue distribution of the Faddeev-Popov operator is sensitive to Gribov copies. We show that the influence of dynamical Wilson fermions on the ghost propagator is negligible at the momenta available to us. On the contrary, fermions affect the gluon propagator at large and intermediate momenta. In addition, we analyze data for both propagators obtained on asymmetric lattices and compare these results with data obtained on symmetric lattices. We compare our data with results from studies of Dyson-Schwinger equations for the gluon and ghost propagators. We demonstrate that the infrared behavior of both propagators, as found in this thesis, is consistent with different criteria for confinement. However, the running coupling constant, given as a renormalization-group-invariant combination of the gluon and ghost dressing functions, does not expose a finite infrared fixed point. Rather the data are in favor of an infrared vanishing coupling constant. We also report on a first nonperturbative computation of the SU(3) ghost-gluon-vertex renormalization constant. We present results of an investigation of the spectral properties of the Faddeev-Popov operator. For this we have calculated the low-lying eigenvalues and eigenmodes of the Faddeev-Popov operator. (orig.)

Gauge bridges in classical field theory

International Nuclear Information System (INIS)

Jakobs, S.

2009-03-01

In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called ''gauge bridges''are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

On the topological structure of the vacuum in SU(2) and SU(3) lattice gauge theories

International Nuclear Information System (INIS)

Ishikawa, K.; Schierholz, G.; Schneider, H.; Teper, M.

1983-01-01

We present Monte Carlo measurements of the net topological charge of the vacuum in SU(2) and SU(3) lattice gauge theories. In both cases there is no evidence of any topological structure, and the values obtained are a factor of 0(100) smaller than expectations based on analyses of the U(1) problem. Moreover we find a strong sensitivity to the lattice size and to the boundary conditions imposed on the lattice. We comment on the physical significance of these results, establish criteria for the reliable performance of such calculations, and remark on the possibly detrimental impact of these findings on the calculation of hadron spectra

The H dibaryon on the lattice

International Nuclear Information System (INIS)

Wetzorke, I.; Karsch, F.

2002-08-01

We present our final results for the mass of the six quark flavor singlet state (J P =0 + , S=-2) called H dibaryon, which would be the lightest possible strangelet in the context of strange quark matter. The calculations are performed in quenched QCD on (8-24) 3 x 30 lattices with the (1,2) Symanzik improved gauge action and the clover fermion action. Furthermore the fuzzing technique for the fermion fields and smearing of the gauge fields is applied in order to enhance the overlap with the ground state. Depending on the lattice size we observe an H mass slightly above or comparable with the ΛΛ threshold for strong decay. Therefore a bound H dibaryon state seemed to be ruled out by our simulation. (orig.)

The H dibaryon on the lattice

International Nuclear Information System (INIS)

Wetzorke, I.; Karsch, F.

2003-01-01

We present our final results for the mass of the six quark flavor singlet state (J P = 0 + , S = -2) called H dibaryon, which would be the lightest possible strangelet in the context of strange quark matter. The calculations are performed in quenched QCD on (8 - 24) 3 x 30 lattices with the (1,2) Symanzik improved gauge action and the clover fermion action. Furthermore the fuzzing technique for the fermion fields and smearing of the gauge fields is applied in order to enhance the overlap with the ground state. Depending on the lattice size we observe an H mass slightly above or comparable with the AA threshold for strong decay. Therefore a bound H dibaryon state seemed to be ruled out by our simulation

Noncommutative gauge field theories: A no-go theorem

International Nuclear Information System (INIS)

Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

2001-06-01

Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)

Metric interpretation of gauge fields in noncommutative geometry

International Nuclear Information System (INIS)

Martinetti, P.

2007-01-01

We shall give an overview of the metric interpretation of gauge fields in noncommutative geometry, via Connes distance formula. Especially we shall focus on the Higgs fields in the standard model, and gauge fields in various models of fiber bundle. (author)

Hamiltonian formulation of QCD in the Schwinger gauge

International Nuclear Information System (INIS)

Schutte, D.

1989-01-01

The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed

Gauge invariant fractional electromagnetic fields

Energy Technology Data Exchange (ETDEWEB)

Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)

2011-09-26

Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.

Vacuum structure of pure gauge theories on the lattice

International Nuclear Information System (INIS)

Haymaker, R.W.; Singh, V.; Browne, D.; Wosiek, J.; Max-Planck-Institut fuer Physik und Astrophysik, Muenchen

1992-01-01

Results from simulations on two aspects of quark confinement in the pure gauge sector are presented. First is the calculation of the profile of the flux tube connecting a static q bar q pair in SU(2). By use of the Michael sum rules as a constraint, evidence is set forth that the energy density at the center of the flux tube goes to a constant as a function of quark- separation. Slow variation of the width and energy density is not ruled out. Secondly in the confined phase of lattice U(l), the curl of the magnetic monopole current is calculated, and it is shown that the dual London equation is satisfied and that the electric fluxoid is quantized

Linear b-gauges for open string fields

International Nuclear Information System (INIS)

Kiermaier, Michael; Zwiebach, Barton; Sen, Ashoke

2008-01-01

Motivated by Schnabl's gauge choice, we explore open string perturbation theory in gauges where a linear combination of antighost oscillators annihilates the string field. We find that in these linear b-gauges different gauge conditions are needed at different ghost numbers. We derive the full propagator and prove the formal properties which guarantee that the Feynman diagrams reproduce the correct on-shell amplitudes. We find that these properties can fail due to the need to regularize the propagator, and identify a large class of linear b-gauges for which they hold rigorously. In these gauges the propagator has a non-anomalous Schwinger representation and builds Riemann surfaces by adding strip-like domains. Projector-based gauges, like Schnabl's, are not in this class of gauges but we construct a family of regular linear b-gauges which interpolate between Siegel gauge and Schnabl gauge

Spin foam model for pure gauge theory coupled to quantum gravity

International Nuclear Information System (INIS)

Oriti, Daniele; Pfeiffer, Hendryk

2002-01-01

We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian Barrett-Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang-Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang-Mills scale

SU(N) gauge theory couplings on asymmetric lattices

International Nuclear Information System (INIS)

Karsch, F.

1982-01-01

The connection between euclidean and hamiltonian lattice QCD requires the use of asymmetric lattices, which in turn implies the necessity of two coupling parameters. We analyse the dependence of space- and time-like couplings gsub(sigma) and gsub(tau) on the different lattice spacings a and asub(tau) in space and time directions. Using the background field method we determine the derivatives of the couplings with respect to the asymmetry factor xi = a/asub(tau) in the weak coupling limit, obtaining for xi = 1 the values (deltag -2 sub(sigma)/deltaxi)sub(xi = 1) = 0.11403, N = 2, 0.20161, N = 3, (deltag -2 sub(tau)/deltaxi)sub(xi = 1) = -0.06759, N = 2, -0.13195, N = 3. We argue that the sum of these derivatives has to be equal to b 0 = 11N/48π 2 and determine the Λ parameter for asymmetric lattices. In the limit xi → infinity all our results agree with those of A. and P. Hasenfratz. (orig.)

Renormalization of gauge fields models

International Nuclear Information System (INIS)

Becchi, C.; Rouet, A.; Stora, R.

1974-01-01

A new approach to gauge field models is described. It is based on the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme making extensive use of the quantum action principle, and the Slavnov invariance. The quantum action principle being first summarized in the framework of the BPHZ is then applied to a global symmetry problem. The symmetry property of the gauge field Lagrangians in the tree approximation is exhibited, and the preservation of this property at the quantum level is discussed. The main results relative to the Abelian and SU(2) Higgs-Kibble models are briefly reviewed [fr

Gauge glass

International Nuclear Information System (INIS)

Nielsen, H.B.; Brene, N.

1984-12-01

The fundamental laws of nature may be truely random, or they may be so complicated that a random description is adequate. With this philosophy we examine various ways in which a lattice gauge theory (at the Planck scale) can be generalized. Without here giving up a regular lattice structure (which we really ought to do) we consider two generalizations. Making the action (quenched) random has the effect that the gauge group tends to break down and some gauge bosons become massive, unless the gauge group has special properties: no noncentral corners in the geometry of conjugacy classes and furthermore a connected center. Making the concept of gauge transformation more general has a symmetry breaking effect for groups with outer automorphisms. A study of SU 5 -breaking in the context of the first breakdown mechanism (D. Bennett, E. Buturovic and H. B. Nielsen) is shortly reviewed. (orig.)

Lattice approximation of gauge theories with Dirac Kaehler fermions

International Nuclear Information System (INIS)

Joos, H.

1988-01-01

A program which tries to overcome the systematic difficulties caused by the lattice fermion problem by the consideration of models which describe Dirac fields by differential forms is reported. In the first lecture the formalism is developped and applied to the formulation of geometric QCD and of a Geometric Standard Model. The second lecture treats the characteristic symmetry problems which appear in the lattice approximation of geometric field theories. In the last lecture strong coupling dynamics of geometric QCD are considered with the final aim of a derivation of the quark model for the hadron spectrum. (author) [pt

Some physico-geometrical remarks on gauge fields

International Nuclear Information System (INIS)

Ikeda, S.

1976-01-01

The gauge fields introduced to accomplish gauge invariance under Poincare and Weyl gauge transformations in general relativity are found a new to be absorbed into the covariant derivative operators. Some torsional properties associated with them are also discussed in connection with the principle of minimally coupling and the equivalence principle

Ground state metamorphosis for Yang-Mills fields on a finite periodic lattice

International Nuclear Information System (INIS)

Gonzalez-Arroyo, A.; Jurkiewicz, J.; Korthals-Altes, C.P.

1983-01-01

The authors study the weak coupling behaviour of the partition function of non-abelian gauge fields on a finite lattice. Periodic boundary conditions are imposed. Two different power laws in the coupling BETA -1 arise for the partition function, when the dimension d of space time is larger or smaller than a critical dimension d /SUB c/ . For SU(2) d /SUB c/ = 4 and they find at this dimension power behaviour corrected by log BETA. The phenomenon is of practical importance in Monte Carlo simulations of the twisted action

Light-cone gauge approach to arbitrary spin fields, currents and shadows

International Nuclear Information System (INIS)

Metsaev, R R

2014-01-01

Totally symmetric arbitrary spin fields in AdS space, conformal fields, conformal currents, and shadow fields in flat space are studied. Light-cone gauge formulations for such fields, currents and shadows are obtained. Use of the Poincaré parametrization of AdS space and ladder operators allows us to treat fields in flat and AdS spaces on an equal footing. Light-cone gauge realization of relativistic symmetries for fields, currents and shadows is also obtained. The light-cone gauge formulation for fields is obtained by using the gauge invariant Lagrangian which is presented in terms of modified de Donder divergence, while the light-cone gauge formulation for currents and shadows is obtained by using the gauge invariant approach to currents and shadows. This allows us to demonstrate explicitly how the ladder operators entering the gauge invariant formulation of fields, currents and shadows manifest themselves in the light-cone gauge formulation for fields, currents and shadows. (paper)

A recipe for constructing frustration-free Hamiltonians with gauge and matter fields in one and two dimensions

Science.gov (United States)

Bernabé Ferreira, Miguel Jorge; Ibieta Jimenez, Juan Pablo; Padmanabhan, Pramod; Teôtonio Sobrinho, Paulo

2015-12-01

State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space-time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described by an {A}-module with an inner product. Performing this construction on a triangulated manifold with a boundary we obtain transfer matrices which are decomposed into a product of local operators acting on vertices, links and plaquettes. The vertex and plaquette operators are similar to the ones appearing in the quantum double models (QDMs) of Kitaev. The link operator couples the gauge and the matter fields, and it reduces to the usual interaction terms in known models such as {{{Z}}}2 gauge theory with matter fields. The transfer matrices lead to Hamiltonians that are frustration-free and are exactly solvable. According to the choice of the initial input, that of the gauge group and a matter module, we obtain interesting models which have a new kind of ground state degeneracy that depends on the number of equivalence classes in the matter module under gauge action. Some of the models have confined flux excitations in the bulk which become deconfined at the surface. These edge modes are protected by an energy gap provided by the link operator. These properties also appear in ‘confined Walker-Wang’ models which are 3D models having interesting surface states. Apart from the gauge excitations there are also excitations in the matter sector which are immobile and can be thought of as defects like in the Ising model. We only consider bosonic matter fields in this paper.

On gauge fields with sources

International Nuclear Information System (INIS)

Torres del Castillo, G.F.; Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000 Mexico, D. F., Mexico)

1987-01-01

It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang--Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang--Mills--Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein--Yang--Mills--Weyl equations is also given

Abelian projection on the torus for general gauge groups

International Nuclear Information System (INIS)

Ford, C.; Tok, T.; Wipf, A.

1999-01-01

We consider Yang-Mills theories with general gauge groups G and twists of the four-torus. We find consistent boundary conditions for gauge fields in all instanton sectors. An extended abelian projection with respect to the Polyakov loop operator is presented, where A 0 is independent of time and in the Cartan subalgebra. Fundamental domains for the gauge fixed A 0 are constructed for arbitrary gauge groups. In the sectors with non-vanishing instanton number such gauge fixings are necessarily singular. The singularities can be restricted to Dirac strings joining magnetically charged defects. The magnetic charges of these monopoles take their values in the co-root lattice of the gauge group. We relate the magnetic charges of the defects and the windings of suitable Higgs fields about these defects to the instanton number

The string tension and the scaling behavior of SU(2) gauge theory on a random lattice

International Nuclear Information System (INIS)

Qui Zhaoming; Ren Haichang; Academia Sinica, Beijing; Wang Xiaoqun; Yang Zhixing; Zhao Enping

1987-01-01

The SU(2) gauge theory on an 8 4 random lattice has been studied by the Monte Carlo method. The string tensions have been evaluated. They display the expected scaling behavior for β = 1.2-1.3. The scale parameter Λ RAN has been determined approximately. (orig.)

Lattice Methods for Quantum Chromodynamics

CERN Document Server

DeGrand, Thomas

2006-01-01

Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually do

Gauge field theories an introduction with applications

CERN Document Server

Guidry, Mike

1991-01-01

Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises

SU (2) lattice gauge theory simulations on Fermi GPUs

International Nuclear Information System (INIS)

Cardoso, Nuno; Bicudo, Pedro

2011-01-01

In this work we explore the performance of CUDA in quenched lattice SU (2) simulations. CUDA, NVIDIA Compute Unified Device Architecture, is a hardware and software architecture developed by NVIDIA for computing on the GPU. We present an analysis and performance comparison between the GPU and CPU in single and double precision. Analyses with multiple GPUs and two different architectures (G200 and Fermi architectures) are also presented. In order to obtain a high performance, the code must be optimized for the GPU architecture, i.e., an implementation that exploits the memory hierarchy of the CUDA programming model. We produce codes for the Monte Carlo generation of SU (2) lattice gauge configurations, for the mean plaquette, for the Polyakov Loop at finite T and for the Wilson loop. We also present results for the potential using many configurations (50,000) without smearing and almost 2000 configurations with APE smearing. With two Fermi GPUs we have achieved an excellent performance of 200x the speed over one CPU, in single precision, around 110 Gflops/s. We also find that, using the Fermi architecture, double precision computations for the static quark-antiquark potential are not much slower (less than 2x slower) than single precision computations.

The H dibaryon on the lattice

Energy Technology Data Exchange (ETDEWEB)

Wetzorke, I. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Karsch, F. [Bielefeld Univ. (Germany). Fakultaet fuer Physik

2002-08-01

We present our final results for the mass of the six quark flavor singlet state (J{sup P}=0{sup +}, S=-2) called H dibaryon, which would be the lightest possible strangelet in the context of strange quark matter. The calculations are performed in quenched QCD on (8-24){sup 3} x 30 lattices with the (1,2) Symanzik improved gauge action and the clover fermion action. Furthermore the fuzzing technique for the fermion fields and smearing of the gauge fields is applied in order to enhance the overlap with the ground state. Depending on the lattice size we observe an H mass slightly above or comparable with the {lambda}{lambda} threshold for strong decay. Therefore a bound H dibaryon state seemed to be ruled out by our simulation. (orig.)

The H dibaryon on the lattice

Energy Technology Data Exchange (ETDEWEB)

Wetzorke, I.; Karsch, F

2003-05-01

We present our final results for the mass of the six quark flavor singlet state (J{sup P} = 0{sup +}, S = -2) called H dibaryon, which would be the lightest possible strangelet in the context of strange quark matter. The calculations are performed in quenched QCD on (8 - 24){sup 3} x 30 lattices with the (1,2) Symanzik improved gauge action and the clover fermion action. Furthermore the fuzzing technique for the fermion fields and smearing of the gauge fields is applied in order to enhance the overlap with the ground state. Depending on the lattice size we observe an H mass slightly above or comparable with the AA threshold for strong decay. Therefore a bound H dibaryon state seemed to be ruled out by our simulation.

Near-field photon wave mechanics in the Lorenz gauge

International Nuclear Information System (INIS)

Keller, Ole

2007-01-01

Optical near-field interactions are studied theoretically in the perspective of photon wave mechanics paying particular attention to the dynamics in the wave-vector time domain. A unitary transformation is used to replace the scalar and longitudinal photon variables by so-called near-field and gauge photon variables. Dynamical equations are established for these types of photon variables, and it is shown that these equations are invariant against gauge transformations within the Lorenz gauge. The near-field photon is absent in the free-field limit, and the gauge photon can be eliminated by a suitable gauge transformation. Implicit solutions for the near-field, gauge, and transverse photon variables are obtained and discussed. The general theory is applied to an investigation of transverse photon propagation in a uniform solid-state plasma dominated by the diamagnetic field-matter interaction. It is found that the diamagnetic response can be incorporated in a quantum mechanical wave equation for a massive transverse photon. The Compton wave number of the massive photon equals the plasma wave number of the electron system. A dynamical equation describing the emission of a massive transverse photon from a mesoscopic source embedded in the plasma is finally established

Hyperunified field theory and gravitational gauge-geometry duality

International Nuclear Information System (INIS)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

Hyperunified field theory and gravitational gauge-geometry duality

Energy Technology Data Exchange (ETDEWEB)

Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)

2018-01-15

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

Hyperunified field theory and gravitational gauge-geometry duality

Science.gov (United States)

Wu, Yue-Liang

2018-01-01

A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

Vortex operators in gauge field theories

International Nuclear Information System (INIS)

Polchinski, J.G.

1980-01-01

We study several related aspects of the t Hooft vortex operator. The first chapter reviews the current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator. The second chapter deals with the Abelian vortex operator written in terms of elementary fields and with the calculation of its Green's functions. The Dirac veto problem appears in a new guise. We present a two dimensional solvable model of a Dirac string. This leads us to a new solution of the veto problem; we discuss its extension to four dimensions. We then show how the Green's functions can be expressed more neatly in terms of Wu and Yang's geometrical idea of sections. In the third chapter we discuss the dependence of the Green's functions of the Wilson and t Hooft operators on the nature of the vacuum. In the fourth chapter we consider systems which have fields in the fundamental representation, so that there are no vortex operators. When these fields enter only weakly into the dynamics, as is the case in QCD and in real superconductors, we would expect to be able to define a vortex-like operator. We show that any such operator can no longer be local looplike, but must have commutators at long range. We can still find an operator with useful properties, its cluster property, though more complicated than that of the usual vortex operator, still appears to distinguish Higgs, confining and perturbative phases. To test this, we consider a U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint)

Strong coupling expansion for scattering phases in hamiltonian lattice field theories. Pt. 1. The (d+1)-dimensional Ising model

International Nuclear Information System (INIS)

Dahmen, Bernd

1994-01-01

A systematic method to obtain strong coupling expansions for scattering quantities in hamiltonian lattice field theories is presented. I develop the conceptual ideas for the case of the hamiltonian field theory analogue of the Ising model, in d space and one time dimension. The main result is a convergent series representation for the scattering states and the transition matrix. To be explicit, the special cases of d=1 and d=3 spatial dimensions are discussed in detail. I compute the next-to-leading order approximation for the phase shifts. The application of the method to investigate low-energy scattering phenomena in lattice gauge theory and QCD is proposed. ((orig.))

String field theory-inspired algebraic structures in gauge theories

International Nuclear Information System (INIS)

Zeitlin, Anton M.

2009-01-01

We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.

Gauge fields in algebraically special space-times

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1985-01-01

It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein--Yang--Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Baecklund transformations is demonstrated. All the results apply for an arbitrary gauge group

Gauge field copies and Higgs mechanism

International Nuclear Information System (INIS)

Gleiser, M.

1982-07-01

From the algebric classification of the possible solutions of the necessary and sufficient condition for the existence of gauge field copies in two possible classes the Higgs mechanism for the potential obtained from the difference between two copied potentials is applied. It is shown that for class I 'electric type' it is possible to construct a vector field that satisfies an electromagnetic wave equation. For class I 'magnetic type', a vector field that satisfies a non-linear equation as a consequence of the non-abelianity of the theory, is obtained. It is shown that for class II it's not possible to apply the Higgs mechanism. A possible physical interpretation for the 'gauge field copies' phenomenon, is obtained. (author) [pt

Gauge theory on a lattice, 1984: proceedings

International Nuclear Information System (INIS)

Zachos, C.; Celmaster, W.; Kovacs, E.; Sivers, D.

1984-06-01

In the past few years there have been rapid advances in understanding quantum field theory by making discrete approximations of the path integral functional. This approach offers a systematic alternative to perturbation theory and opens up the possibility of first-principles calculation of new classes of observables. Computer simulations based on lattice regularization have already provided intriguing insights into the long-distance behavior of quantum chromodynamics. The objective of the workshop was to bring together researchers using lattice techniques for a discussion of current projects and problems. These proceedings aim to communicate the results to a broader segment of the research community. Separate entries were made in the data base for 26 of the 31 papers presented. Five papers were previously included in the data base

More on random-lattice fermions

International Nuclear Information System (INIS)

Kieu, T.D.; Institute for Advanced Study, Princeton, NJ; Markham, J.F.; Paranavitane, C.B.

1995-01-01

The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sufficient condition to remove the fermion doublers. 8 refs., 3 figs

Extended Josephson Relation and Abrikosov lattice deformation

International Nuclear Information System (INIS)

Matlock, Peter

2012-01-01

From the point of view of time-dependent Ginzburg Landau (TDGL) theory, a Josephson-like relation is derived for an Abrikosov vortex lattice accelerated and deformed by applied fields. Beginning with a review of the Josephson Relation derived from the two ingredients of a lattice-kinematics assumption in TDGL theory and gauge invariance, we extend the construction to accommodate a time-dependent applied magnetic field, a Floating-Kernel formulation of normal current, and finally lattice deformation due to the electric field and inertial effects of vortex-lattice motion. The resulting Josephson-like relation, which we call an Extended Josephson Relation, applies to a much wider set of experimental conditions than the original Josephson Relation, and is explicitly compatible with the considerations of TDGL theory.

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

International Nuclear Information System (INIS)

Borisenko, O.; Chelnokov, V.; Cortese, G.; Gravina, M.; Papa, A.; Surzhikov, I.

2014-01-01

Three-dimensional Z(N) lattice gauge theories at zero temperature are studied for various values of N. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized Z(N) model for N=2,3,4,5,6,8. Numerical computations are used to simulate vector models for N=2,3,4,5,6,8,13,20 for lattices with linear extension up to L=96. We locate the critical points of phase transitions and establish their scaling with N. The values of the critical indices indicate that the models with N>4 belong to the universality class of the three-dimensional XY model. However, the exponent α derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Energy Technology Data Exchange (ETDEWEB)

Borisenko, O., E-mail: oleg@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Chelnokov, V., E-mail: chelnokov@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Cortese, G., E-mail: cortese@unizar.es [Instituto de Física Teórica UAM/CSIC, Cantoblanco, E-28049 Madrid (Spain); Departamento de Física Teórica, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Gravina, M., E-mail: gravina@cs.infn.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Papa, A., E-mail: papa@cs.infn.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Surzhikov, I., E-mail: i_van_go@inbox.ru [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine)

2014-02-15

Three-dimensional Z(N) lattice gauge theories at zero temperature are studied for various values of N. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized Z(N) model for N=2,3,4,5,6,8. Numerical computations are used to simulate vector models for N=2,3,4,5,6,8,13,20 for lattices with linear extension up to L=96. We locate the critical points of phase transitions and establish their scaling with N. The values of the critical indices indicate that the models with N>4 belong to the universality class of the three-dimensional XY model. However, the exponent α derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle.

END FIELD EFFECTS IN BEND ONLY COOLING LATTICES

International Nuclear Information System (INIS)

BEERG, J.S.; KIRK, H.; GARREN, A.

2003-01-01

Cooling lattices consisting only of bends (using either rotated pole faces or gradient dipoles to achieve focusing) often require large apertures and short magnets. One expects the effect of end fields to be significant in this case. In this paper we explore the effect of adding end fields to a working lattice design that originally lacked them. The paper describes the process of correcting the lattice design for the added end fields so as to maintain desirable lattice characteristics. It then compares the properties of the lattice with end fields relative to the lattice without them

Phase structure of 3D Z(N) lattice gauge theories at finite temperature: Large-N and continuum limits

International Nuclear Information System (INIS)

Borisenko, O.; Chelnokov, V.; Gravina, M.; Papa, A.

2014-01-01

We study numerically three-dimensional Z(N) lattice gauge theories at finite temperature, for N=5,6,8,12,13 and 20 on lattices with temporal extension N t =2,4,8. For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N. The data obtained enable us to verify the scaling near the continuum limit for the Z(N) models at finite temperatures

Phase structure of 3DZ(N) lattice gauge theories at finite temperature

International Nuclear Information System (INIS)

Borisenko, O.; Chelnokov, V.; Cortese, G.; Gravina, M.; Papa, A.; Surzhikov, I.

2013-01-01

We perform a numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4. Using the dual formulation of the models and a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the average action and the specific heat. Our results are consistent with the two transitions being of infinite order. Furthermore, they belong to the universality class of two-dimensional Z(N) vector spin models

T expansion and SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Horn, D.; Karliner, M.; Weinstein, M.

1985-01-01

This paper presents the results obtained by applying the t expansion to the case of an SU(2) lattice gauge theory in 3+1 space-time dimensions. We compute the vacuum energy density, specific heat, string tension sigma, mass M of the lowest-lying 0 ++ glueball, and the ratio R = M 2 /sigma. Our computations converge best for the energy density, specific heat, and R, and these quantities exhibit behavior which agrees with what we expect on general grounds and what is known from Euclidean Monte Carlo calculations. In particular we see a broad lump in the specific heat and determine √R to be √R = 3.5 +- 0.2, a value which lies in the ballpark of values obtained from Monte Carlo calculations. Our direct computations of the mass of the 0 ++ glueball and string tension cannot be easily compared to the results of Monte Carlo calculations, but appear to be consistent with what one would expect

Localization of abelian gauge fields on thick branes

Energy Technology Data Exchange (ETDEWEB)

Vaquera-Araujo, Carlos A. [Universidad de Colima, Facultad de Ciencias, CUICBAS, Colima (Mexico); Corradini, Olindo [Universidad Autonoma de Chiapas, Ciudad Universitaria, Facultad de Ciencias en Fisica y Matematicas, Tuxtla Gutierrez (Mexico); Universita di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Modena (Italy)

2015-02-01

In this work, we explore a mechanism for abelian gauge field localization on thick branes based on a five-dimensional Stueckelberg-like action. A normalizable zero mode is found through the identification of a suitable coupling function between the brane and the gauge field. The same mechanism is studied for the localization of the abelian Kalb-Ramond field. (orig.)

Vortex operators in gauge field theories

International Nuclear Information System (INIS)

Polchinski, J.

1980-07-01

Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures

Perturbative formulation of pure space-like axial gauge QED with infrared divergences regularized by residual gauge fields

International Nuclear Information System (INIS)

Nakawaki, Yuji; McCartor, Gary

2006-01-01

We construct a new perturbative formulation of pure space-like axial gauge QED in which the inherent infrared divergences are regularized by residual gauge fields. For this purpose, we carry out our calculations in the coordinates x μ =(x + , x - , x 1 , x 2 ), where x + =x 0 sinθ + x 3 cosθ and x - = x 0 cosθ - x 3 sinθ. Here, A=A 0 cosθ + A 3 sinθ = n·A=0 is taken as the gauge fixing condition. We show in detail that, in perturbation theory, infrared divergences resulting from the residual gauge fields cancel infrared divergences resulting from the physical parts of the gauge field. As a result, we obtain the gauge field propagator proposed by Mandelstam and Leibbrandt. By taking the limit θ→π/4, we are able to construct a light-cone formulation that is free from infrared divergences. With that analysis complete, we next calculate the one-loop electron self-energy, something not previously done in the light-cone quantization and light-cone gauge. (author)

Linked cluster expansion in the SU(2) lattice Higgs model at strong gauge coupling

International Nuclear Information System (INIS)

Wagner, C.E.M.

1989-01-01

A linked cluster expansion is developed for the β=0 limit of the SU(2) Higgs model. This method, when combined with strong gauge coupling expansions, is used to obtain the phase transition surface and the behaviour of scalar and vector masses in the lattice regularized theory. The method, in spite of the low order of truncation of the series applied, gives a reasonable agreement with Monte Carlo data for the phase transition surface and a qualitatively good picture of the behaviour of Higgs, glueball and gauge vector boson masses, in the strong coupling limit. Some limitations of the method are discussed, and an intuitive picture of the different behaviour for small and large bare self-coupling λ is given. (orig.)

Fractional Quantum Field Theory: From Lattice to Continuum

Directory of Open Access Journals (Sweden)

Vasily E. Tarasov

2014-01-01

Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.

Criticality and novel quantum liquid phases in Ginzburg-Landau theories with compact and non-compact gauge fields

Energy Technology Data Exchange (ETDEWEB)

Smiseth, Jo

2005-07-01

The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)

Non-Abelian tensor gauge fields and higher-spin extension of standard model

International Nuclear Information System (INIS)

Savvidy, G.

2006-01-01

We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Calculating the Jet Transport Coefficient q-hat in Lattice Gauge Theory

International Nuclear Information System (INIS)

Majumder, Abhijit

2013-01-01

The formalism of jet modification in the higher twist approach is modified to describe a hard parton propagating through a hot thermalized medium. The leading order contribution to the transverse momentum broadening of a high energy (near on-shell) quark in a thermal medium is calculated. This involves a factorization of the perturbative process of scattering of the quark from the non-perturbative transport coefficient. An operator product expansion of the non-perturbative operator product which represents q -hat is carried out and related via dispersion relations to the expectation of local operators. These local operators are then evaluated in quenched SU(2) lattice gauge theory

On the hyperbolicity of Einstein's and other gauge field equations

International Nuclear Information System (INIS)

Friedrich, H.

1985-01-01

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)

Phase structure of 3D Z(N) lattice gauge theories at finite temperature: Large-N and continuum limits

Energy Technology Data Exchange (ETDEWEB)

Borisenko, O., E-mail: oleg@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Chelnokov, V., E-mail: chelnokov@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Gravina, M., E-mail: gravina@fis.unical.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Papa, A., E-mail: papa@fis.unical.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy)

2014-11-15

We study numerically three-dimensional Z(N) lattice gauge theories at finite temperature, for N=5,6,8,12,13 and 20 on lattices with temporal extension N{sub t}=2,4,8. For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N. The data obtained enable us to verify the scaling near the continuum limit for the Z(N) models at finite temperatures.

Reduction of a Z(3) gauge theory on the flat lattices to the spin-1 BEG model

International Nuclear Information System (INIS)

Ananikian, N.S.; Shcherbakov, R.R.

1995-01-01

The Z(3) gauge model with double plaquette representation of the action on the flat triangular and square lattices is constructed. It is reduced to the spin-1 Blume-Emery-Griffiths (BEG) model. An Ising-type critical line of a second-order phase transition is found. ((orig.))

Vacuum structure of the SU(3) gauge field theory in the Coulomb gauge

International Nuclear Information System (INIS)

Yee, J.H.; Viswanathan, K.S.

1978-01-01

The SU(3) gauge field is studied in the Coulomb gauge. The Gribov ambiguities arising in the Coulomb gauge are analysed. Restricting to a class of spherically symmetric vacua it is shown that there exist non-trivial vacua characterized by a topological number eta=0, +-1/2, and +-2. This must be contrasted with the spherically symmetric SU(2) vacua which are characterized by eta=0, +-1/2. (Auth.)

Two-time physics with gravitational and gauge field backgrounds

International Nuclear Information System (INIS)

Bars, Itzhak

2000-01-01

It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d dimensions (one time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the world line formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1)+1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target (d+2)-dimensional spacetime. The gravitational background obeys a closed homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher (d+2)-dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden

Strongly coupled gauge theories: What can lattice calculations teach us?

CERN Multimedia

CERN. Geneva

2015-01-01

Electroweak symmetry breaking and the dynamical origin of the Higgs boson are central questions today. Strongly coupled systems predicting the Higgs boson as a bound state of a new gauge-fermion interaction are candidates to describe beyond Standard Model physics. The phenomenologically viable models are strongly coupled, near the conformal boundary, requiring non-perturbative studies to reveal their properties. Lattice studies show that many of the beyond-Standard Model candidates have a relatively light isosinglet scalar state that is well separated from the rest of the spectrum. When the scale is set via the vev of electroweak symmetry breaking, a 2 TeV vector resonance appears to be a general feature of many of these models with several other resonances that are not much heavier.

Differential geometry of group lattices

International Nuclear Information System (INIS)

Dimakis, Aristophanes; Mueller-Hoissen, Folkert

2003-01-01

In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained

Representations of l-p-i functionals in gauge field theories

International Nuclear Information System (INIS)

Bordag, M.; Kaschluhn, L.; Matveev, V.A.; Robaschik, D.

1981-01-01

A representation of the functions which solve by construction the Slavnov-Taylor identities and contain independent coefficient functions is given. These solutions show the different role of the gauge field which acts in some respect as an ordinary field. The Slavnov-Taylor identities are solved for axial gauge conditions in non-Abelian gauge field theory and in quantum electrodynamics

Non-Abelian gauge field theory in scale relativity

International Nuclear Information System (INIS)

Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry

2006-01-01

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description

Gauge field theories

International Nuclear Information System (INIS)

Pokorski, S.

1987-01-01

Quantum field theory forms the present theoretical framework for the understanding of the fundamental interactions of particle physics. This book examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. The author discusses field-theoretical techniques and encourages the reader to perform many of the calculations presented. This book includes a brief introduction to perturbation theory, the renormalization programme, and the use of the renormalization group equation. Several topics of current research interest are covered, including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry

Phase-structure of SU(3) lattice gauge-higgs model

International Nuclear Information System (INIS)

Gerdt, V.P.; Mitrjushkin, V.K.; Zadorozhny, A.M.

1985-01-01

Phase structure is investigated of SU(3) symmetric gauge-Higgs theory with a defrost radial mode. The Higgs fields are considered in the fundamental representation of SU(3) group. It is shown that the phase structures of SU(3) and SU(2) symmetric coincide qualitatively

Amorphous gauge glass theory

International Nuclear Information System (INIS)

Nielsen, H.B.; Bennett, D.L.

1987-08-01

Assuming that a lattice gauge theory describes a fundamental attribute of Nature, it should be pointed out that such a theory in the form of a gauge glass is a weaker assumption than a regular lattice model in as much as it is not constrained by the imposition of translational invariance; translational invariance is, however, recovered approximately in the long wavelength or continuum limit. (orig./WL)

Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory. Spectral calculations with matrix product states

Energy Technology Data Exchange (ETDEWEB)

Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2017-07-20

We propose an explicit formulation of the physical subspace for a 1+1 dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.

Efficient Basis Formulation for (1+1-Dimensional SU(2 Lattice Gauge Theory: Spectral Calculations with Matrix Product States

Directory of Open Access Journals (Sweden)

Mari Carmen Bañuls

2017-11-01

Full Text Available We propose an explicit formulation of the physical subspace for a (1+1-dimensional SU(2 lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.

Efficient Basis Formulation for (1 +1 )-Dimensional SU(2) Lattice Gauge Theory: Spectral Calculations with Matrix Product States

Science.gov (United States)

Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio; Jansen, Karl; Kühn, Stefan

2017-10-01

We propose an explicit formulation of the physical subspace for a (1 +1 )-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.

Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory. Spectral calculations with matrix product states

International Nuclear Information System (INIS)

Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan; Cichy, Krzysztof; Adam Mickiewicz Univ., Poznan; Jansen, Karl

2017-01-01

We propose an explicit formulation of the physical subspace for a 1+1 dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely general, and might be potentially suited for the design of future quantum simulators. Additionally, it allows for addressing the theory numerically with matrix product states. We apply this technique to explore the spectral properties of the model and the effect of truncating the gauge degrees of freedom to a small finite dimension. In particular, we determine the scaling exponents for the vector mass. Furthermore, we also compute the entanglement entropy in the ground state and study its scaling towards the continuum limit.

Calibration and characterization of Bayard-Alpert gauges operating in high magnetic fields

International Nuclear Information System (INIS)

Pickles, W.L.; Hunt, A.L.

1985-11-01

Standard Bayard-Alpert gauges have been successfully operated for several months in the 0.3 to 0.7 T magnetic fields near the plasma edge of the Tandem Mirror Experiment-Upgrade (TMX-U). The gauges clearly measure gas pressure and maintain calibration within 10% during operation. The gauge filaments are tungsten and are heated with DC. The gauge housing allows operation in the low density plasma outside the limiter radius by thermalizing the neutral gas that enters the gauge and by preventing plasma from entering the gauge. Changing the orientation of the gauge with respect to the magnetic field changes the gauge calibration, or effective sensitivity, by as much as a factor of 100. Only some orientations of the filament collector plane with respect to the magnetic field direction allow calibrated operation as a pressure gauge. This range of angles is approximately from 20 to 50 degrees. The gauge is oriented to produce the desired sensitivity, then calibrated for the magnetic field effects for that position. The correction to sensitivity for magnet field is not strongly species dependent. The gauge species sensitivities for CH 4 , Xe,and Kr measured in the high magnetic fields were found to be close to the published values measured in no magnetic field

Multigrid methods for the computation of propagators in gauge fields

International Nuclear Information System (INIS)

Kalkreuter, T.

1992-11-01

In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. We discuss proper averaging operations for bosons and for staggered fermions. An efficient algorithm for computing C numerically is presented. The averaging kernels C can be used not only in deterministic multigrid computations, but also in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies of gauge theories. Actual numerical computations of kernels and propagators are performed in compact four-dimensional SU(2) gauge fields. (orig./HSI)

Axial-gauge formulation of a three-dimensional field theory

International Nuclear Information System (INIS)

Hagen, C.R.

1985-01-01

Since the non-Abelian version of a recently formulated gauge theory in two spatial dimensions gives rise to a nonlinear constraint upon the fields in the radiation-gauge approach, one is motivated to attempt a description in terms of the axial gauge. This is accomplished in the Abelian version of the model, with results similar to those encountered in the radiation gauge. The non-Abelian case is then formally solved in the same gauge, it being subsequently shown, however, that the theory is not covariant. It is argued on the basis of perturbation theory that such noncovariance is a real effect which is not readily circumvented by modification of the field transformation properties

Quarks, gluons and lattices

International Nuclear Information System (INIS)

Krojts, M.

1987-01-01

The book by the known american physicist-theoretist M.Kreuts represents the first monography in world literature, where a new perspective direction in elementary particle physics and quantum field theory - lattice formulation of gauge theories is stated systematically. Practically all main ideas of this direction are given. Material is stated in systematic and understandable form

Dual geometric-gauge field aspects of gravity

International Nuclear Information System (INIS)

Huei Peng; Wang, K.

1992-01-01

We propose that the geometric and standard gauge field aspects of gravity are equally essential for a complete description of gravity and can be reconciled. We show that this dualism of gravity resolves the dimensional Newtonian constant problem in both quantum gravity and unification schemes involving gravity (i.e., the Newtonian constant is no longer the coupling constant in the gauge aspect of gravity) and reveals the profound similarity between gravity and other fields. 23 refs., 3 tabs

Four-loop result in SU(3) lattice gauge theory by a stochastic method: lattice correction to the condensate

International Nuclear Information System (INIS)

Di Renzo, F.; Onofri, E.; Marchesini, G.; Marenzoni, P.

1994-01-01

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak-coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables U μ (x) →exp {A μ (x)/√(β)} into the Langevin algorithm and the observables and to perform the expansion in β -1/2 . The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (β -4 ) which extends by one loop the previously known series. ((orig.))

Towards a unified picture for gauge and Higgs fields

International Nuclear Information System (INIS)

Mecklenburg, W.

1981-01-01

A scheme for a geometrical unification of gauge and Higgs fields, previously given for SU 2 , is generalized to include arbitrary semisimple gauge groups. Gauge and physical Higgs fields appear as different components of the same tensor in a high dimensional manifold, the higher dimensions being comprised by the group coordinates. Their respective inhomogeneous transformation behaviour is derived from the same principle. The number of Higgs fields is restricted. The form of the Higgs potential is fixed and the mass of the Higgs particle is predicted in terms of the vector boson mass. (author)

Gauge fields and inflation

Science.gov (United States)

Maleknejad, A.; Sheikh-Jabbari, M. M.; Soda, J.

2013-07-01

The isotropy and homogeneity of the cosmic microwave background (CMB) favors “scalar driven” early Universe inflationary models. However, gauge fields and other non-scalar fields are far more common at all energy scales, in particular at high energies seemingly relevant to inflation models. Hence, in this review we consider the role and consequences, theoretical and observational, that gauge fields can have during the inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the level of cosmic perturbations. There have been two main classes of models with gauge fields in the background, models which show violation of the cosmic no-hair theorem and those which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem. Models in which gauge fields are only turned on at the cosmic perturbation level, may source primordial magnetic fields. We also review specific observational features of these models on the CMB and/or the primordial cosmic magnetic fields. Our discussions will be mainly focused on the inflation period, with only a brief discussion on the post inflationary (p)reheating era. Large field models: The initial value of the inflaton field is large, generically super-Planckian, and it rolls slowly down toward the potential minimum at smaller φ values. For instance, chaotic inflation is one of the representative models of this class. The typical potential of large-field models has a monomial form as V(φ)=V0φn. A simple analysis using the dynamical equations reveals that for number of e-folds Ne larger than 60, we require super-Planckian initial field values,5φ0>3M. For these models typically ɛ˜η˜Ne-1. Small field models: Inflaton field is initially small and slowly evolves toward the potential minimum at larger φ values. The small field models are characterized by the following potential V(φ)=V0(1-(), which corresponds to a Taylor expansion about the origin, but more realistic

Massive Abelian gauge fields coupled with nonconserved currents

International Nuclear Information System (INIS)

Nakazato, Hiromichi; Namiki, Mikio; Yamanaka, Yoshiya; Yokoyama, Kan-ichi.

1985-04-01

A massive Abelian gauge field coupled with a nonconserved mass-changing current is described within the framework of canonical quantum theory with indefinite metric. In addition to the conventional Lagrange multiplier fields, another ghost field is introduced to preserve gauge invariance and unitarity of a physical S-matrix in the case of the nonconserved current. The renormalizability of the theory is explicitly shown in the sense of superpropagator approach for nonpolynomial Lagrangian theories. (author)

String tensions for lattice gauge theories in 2+1 dimensions

International Nuclear Information System (INIS)

Ambjoern, J.; Hey, A.J.G.; Otto, S.

1982-01-01

Compact U(1) and SU(2) lattice gauge theories in 3 euclidean dimensions are studied by standard Monte Carlo techniques. The question of extracting reliable string tensions from these theories is examined in detail, including a comparison of the Monte Carlo Wilson loop data with weak coupling predictions and a careful error analysis: our conclusions are rather different from those of previous investigations of these theories. In the case of U(1) theory, we find that only a tiny range of β values can possibly be relevant for extracting a string tension and we are unable to convincingly demonstrate the expected exponential dependence of the string tension on β. For the SU(2) theory we are able to determine, albeit with rather large errors, a string tension from a study of Wilson loops. (orig.)

Lattice theory for nonspecialists

International Nuclear Information System (INIS)

Hari Dass, N.D.

1984-01-01

These lectures were delivered as part of the academic training programme at the NIKHEF-H. These lectures were intended primarily for experimentalists, and theorists not specializing in lattice methods. The goal was to present the essential spirit behind the lattice approach and consequently the author has concentrated mostly on issues of principle rather than on presenting a large amount of detail. In particular, the author emphasizes the deep theoretical infra-structure that has made lattice studies meaningful. At the same time, he has avoided the use of heavy formalisms as they tend to obscure the basic issues for people trying to approach this subject for the first time. The essential ideas are illustrated with elementary soluble examples not involving complicated mathematics. The following subjects are discussed: three ways of solving the harmonic oscillator problem; latticization; gauge fields on a lattice; QCD observables; how to solve lattice theories. (Auth.)

Topological insulators in cold-atom gases with non-Abelian gauge fields: the role of interactions

Energy Technology Data Exchange (ETDEWEB)

Orth, Peter Philipp [Institut fuer Theorie der Kondensierten Materie, Karlsruher Institut fuer Technologie, 76128 Karlsruhe (Germany); Cocks, Daniel; Buchhold, Michael; Hofstetter, Walter [Institut fuer Theoretische Physik, Goethe Universitaet, 60438 Frankfurt am Main (Germany); Rachel, Stephan [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Le Hur, Karyn [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Center for Theoretical Physics, Ecole Polytechnique, 91128 Palaiseau Cedex (France)

2012-07-01

With the recent technological advance of creating (non)-Abelian gauge fields for ultracold atoms in optical lattices, it becomes possible to study the interplay of topological phases and interactions in these systems. Specifically, we consider a spinful and time-reversal invariant version of the Hofstadter problem. In addition, we allow for a hopping term which does not preserve S{sub z} spin symmetry and a staggered sublattice potential. Without interactions, the parameters can be tuned such that the system is a topological insulator. Using a combination of analytical techniques and the powerful real-space dynamical mean-field (R-DMFT) method, we discuss the effect of interactions and determine the interacting phase diagram.

Definition and general properties of the transfer matrix in continuum limit improved lattice gauge theories

International Nuclear Information System (INIS)

Luescher, M.; Weisz, P.

1984-02-01

When operators of dimension 6 are added to the standard Wilson action in lattice gauge theories, physical positivity is lost in general. We show that a transfer matrix can nevertheless be defined. Its properties are, however, unusual: complex eigenvalues may occur (leading to damped oscillatory behaviour of correlation functions), and there are always contributions in the spectral decomposition of two-point functions that come with a negative weight. (orig.)

Magnetic monopoles and the dual London equation in SU(3) lattice gauge theory

International Nuclear Information System (INIS)

Skala, P.; Faber, M.; Zach, M.

1996-01-01

The dual superconductor model of confinement in non-Abelian gauge theories is studied in a gauge invariant formulation. We propose a method for the determination of magnetic monopole currents in non-Abelian gauge theories which does not need a projection to Abelian degrees of freedom. With this definition we are able to determine the distribution of magnetic currents and electric fields for the gluonic flux tube between a pair of static charges. Further we check the validity of the dual London equation in a gauge invariant formulation. (orig.)

Physical principles, geometrical aspects, and locality properties of gauge field theories

International Nuclear Information System (INIS)

Mack, G.; Hamburg Univ.

1981-01-01

Gauge field theories, particularly Yang - Mills theories, are discussed at a classical level from a geometrical point of view. The introductory chapters are concentrated on physical principles and mathematical tools. The main part is devoted to locality problems in gauge field theories. Examples show that locality problems originate from two sources in pure Yang - Mills theories (without matter fields). One is topological and the other is related to the existence of degenerated field configurations of the infinitesimal holonomy groups on some extended region of space or space-time. Nondegenerate field configurations in theories with semisimple gauge groups can be analysed with the help of the concept of a local gauge. Such gauges play a central role in the discussion. (author)

Continuum limit of QED2 on a lattice

International Nuclear Information System (INIS)

Weingarten, D.H.; Challifour, J.L.

1979-01-01

A path integral is defined for the vacuum expectation values of Euclidean QED 2 on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews--Salam formula for vacuum expectation values. For a combination of gauge and fermion fields G on a lattice with spacing proportional to N -+ , Nelement ofZ + , the Matthews--Salam formula for the vacuum expectation /sub N/ has the form /sub n/=∫ dμW/sub N/(G, f), where dμ is an N-independent measure on a random electromagnetic field f and W/sub N/(G,f) is an N-dependent function of f determined by G. For a class of G we prove that as N→infinity, W/sub N/(G,f) has a limit W (G,f) except possibly for a set of f of measure zero. In subsequent articles it will be shown that ∫ dμW (G,f) exists and lim/sub N/→infinity /sub N/ =∫ dμW

Elimination of spurious lattice fermion solutions and noncompact lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Lee, T.D.

1997-09-22

It is well known that the Dirac equation on a discrete hyper-cubic lattice in D dimension has 2{sup D} degenerate solutions. The usual method of removing these spurious solutions encounters difficulties with chiral symmetry when the lattice spacing l {ne} 0, as exemplified by the persistent problem of the pion mass. On the other hand, we recall that in any crystal in nature, all the electrons do move in a lattice and satisfy the Dirac equation; yet there is not a single physical result that has ever been entangled with a spurious fermion solution. Therefore it should not be difficult to eliminate these unphysical elements. On a discrete lattice, particle hop from point to point, whereas in a real crystal the lattice structure in embedded in a continuum and electrons move continuously from lattice cell to lattice cell. In a discrete system, the lattice functions are defined only on individual points (or links as in the case of gauge fields). However, in a crystal the electron state vector is represented by the Bloch wave functions which are continuous functions in {rvec {gamma}}, and herein lies one of the essential differences.

A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field

Directory of Open Access Journals (Sweden)

Suhendro I.

2008-01-01

Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold S4 via the connection, with the general- ized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.

Perturbative analysis for Kaplan's lattice chiral fermions

International Nuclear Information System (INIS)

Aoki, S.; Hirose, H.

1994-01-01

Perturbation theory for lattice fermions with domain wall mass terms is developed and is applied to investigate the chiral Schwinger model formulated on the lattice by Kaplan's method. We calculate the effective action for gauge fields to one loop, and find that it contains a longitudinal component even for anomaly-free cases. From the effective action we obtain gauge anomalies and Chern-Simons currents without ambiguity. We also show that the current corresponding to the fermion number has a nonzero divergence and it flows off the wall into the extra dimension. Similar results are obtained for a proposal by Shamir, who used a constant mass term with free boundaries instead of domain walls

Quantized gauge field

International Nuclear Information System (INIS)

Arodz, H.

1987-01-01

The two formulations of quantum theory of the free electromagnetic field are presented. In the Coulomb gauge approach the independent dynamical variables have been identified and then, in order to quantize the theory, it has been sufficient to apply the straightforward canonical quantization. In the Gupta-Bleuler approach the auxilliary theory is first considered. The straightforward canonical quantization of it leads to the quantum theory defined in the space G with indefinite norm. 15 refs. (author)

Local observables in non-Abelian gauge theories

International Nuclear Information System (INIS)

Sharatchandra, H.S.

1981-09-01

Labelling of the physical states of a non-Abelian gauge theory on a lattice in terms of local observables in considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter field is also included. The non-local variables required when space is multiply-connected, are specified. Non-Abelian version of the Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail. (orig.)

An improved geometric algorithm for calculating the topology of lattice gauge fields

International Nuclear Information System (INIS)

Pugh, D.J.R.; Teper, M.; Oxford Univ.

1989-01-01

We implement the algorithm of Phillips and Stone on a hypercubic, periodic lattice and show that at currently accessible couplings the SU(2) topological charge so calculated is dominated by short-distance fluctuations. We propose and test an improvement to rid the measure of such lattice artifacts. We find that the improved algorithm produces a topological susceptibility that is consistent with that obtained by the alternative cooling method, thus resolving the controversial discrepancy between geometric and cooling methods. We briefly discuss the reasons for this and point out that our improvement is likely to be particularly effective when applied to the case of SU(3). (orig.)

Fortran code for SU(3) lattice gauge theory with and without MPI checkerboard parallelization

Science.gov (United States)

Berg, Bernd A.; Wu, Hao

2012-10-01

.5. Nature of problem: Physics of pure SU(3) Quantum Field Theory (QFT). This is relevant for our understanding of Quantum Chromodynamics (QCD). It includes the glueball spectrum, topological properties and the deconfining phase transition of pure SU(3) QFT. For instance, Relativistic Heavy Ion Collision (RHIC) experiments at the Brookhaven National Laboratory provide evidence that quarks confined in hadrons undergo at high enough temperature and pressure a transition into a Quark-Gluon Plasma (QGP). Investigations of its thermodynamics in pure SU(3) QFT are of interest. Solution method: Markov Chain Monte Carlo (MCMC) simulations of SU(3) Lattice Gauge Theory (LGT) with the Wilson action. This is a regularization of pure SU(3) QFT on a hypercubic lattice, which allows approaching the continuum SU(3) QFT by means of Finite Size Scaling (FSS) studies. Specifically, we provide updating routines for the Cabibbo-Marinari heatbath with and without checkerboard parallelization. While the first is suitable for pedagogical purposes and small scale projects, the latter allows for efficient parallel processing. Targetting the geometry of RHIC experiments, we have implemented a Double-Layered Torus (DLT) lattice geometry, which has previously not been used in LGT MCMC simulations and enables inside and outside layers at distinct temperatures, the lower-temperature layer acting as the outside boundary for the higher-temperature layer, where the deconfinement transition goes on. Restrictions: The checkerboard partition of the lattice makes the development of measurement programs more tedious than is the case for an unpartitioned lattice. Presently, only one measurement routine for Polyakov loops is provided. Unusual features: We provide three different versions for the send/receive function of the MPI library, which work for different operating system +compiler +MPI combinations. This involves activating the correct row in the last three rows of our latmpi.par parameter file. The

Radiative Improvement of the Lattice Nonrelativistic QCD Action Using the Background Field Method and Application to the Hyperfine Splitting of Quarkonium States

International Nuclear Information System (INIS)

Hammant, T. C.; Horgan, R. R.; Monahan, C. J.; Hart, A. G.; Hippel, G. M. von

2011-01-01

We present the first application of the background field method to nonrelativistic QCD (NRQCD) on the lattice in order to determine the one-loop radiative corrections to the coefficients of the NRQCD action in a manifestly gauge-covariant manner. The coefficients of the σ·B term in the NRQCD action and the four-fermion spin-spin interaction are computed at the one-loop level; the resulting shift of the hyperfine splitting of bottomonium is found to bring the lattice predictions in line with experiment.

Non-planar diagrams in the large N limit of U(N) and SU(N) lattice gauge theories

International Nuclear Information System (INIS)

Weingarten, D.

1980-01-01

It is shown that the limit as N → infinitely with g 2 N fixed of the strong coupling expansion for the vacuum expectation values of a U(N) or SU(N) lattice gauge theory is not given by a sum of planar diagrams. This contradicts a result claimed by De Wit and 't Hooft. (orig.)

Transverse Lattice Approach to Light-Front Hamiltonian QCD

CERN Document Server

Dalley, S

1999-01-01

We describe a non-perturbative procedure for solving from first principles the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime dimensions (D>2), based on enforcing Lorentz covariance of observables. A transverse lattice regulator and colour-dielectric link fields are employed, together with an associated effective potential. We argue that the light-front vacuum is necessarily trivial for large enough lattice spacing, and clarify why this leads to an Eguchi-Kawai dimensional reduction of observables to 1+1-dimensions in the infinite N limit. The procedure is then tested by explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a first approximation to the lattice effective potential. We identify a scaling trajectory which produces Lorentz covariant behaviour for the lightest glueballs. The predicted masses, in units of the measured string tension, are in agreement with recent results from conventional Euclidean lattice simulations. In addition, we obtain the poten...

Mean-field lattice trees

NARCIS (Netherlands)

Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.

1999-01-01

We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an

Gauge fields in nonlinear group realizations involving two-dimensional space-time symmetry

International Nuclear Information System (INIS)

Machacek, M.E.; McCliment, E.R.

1975-01-01

It is shown that gauge fields may be consistently introduced into a model Lagrangian previously considered by the authors. The model is suggested by the spontaneous breaking of a Lorentz-type group into a quasiphysical two-dimensional space-time and one internal degree of freedom, loosely associated with charge. The introduction of zero-mass gauge fields makes possible the absorption via the Higgs mechanism of the Goldstone fields that appear in the model despite the fact that the Goldstone fields do not transform as scalars. Specifically, gauge invariance of the Yang-Mills type requires the introduction of two sets of massless gauge fields. The transformation properties in two-dimensional space-time suggest that one set is analogous to a charge doublet that behaves like a second-rank tensor in real four-dimensional space time. The other set suggests a spin-one-like charge triplet. Via the Higgs mechanism, the first set absorbs the Goldstone fields and acquires mass. The second set remains massless. If massive gauge fields are introduced, the associated currents are not conserved and the Higgs mechanism is no longer fully operative. The Goldstone fields are not eliminated, but coupling between the Goldstone fields and the gauge fields does shift the mass of the antisymmetric second-rank-tensor gauge field components

RIKEN BNL RESEARCH CENTER WORKSHOP ON GAUGE-INVARIANT VARIABLES IN GAUGE THEORIES, VOLUME 20

Energy Technology Data Exchange (ETDEWEB)

VAN BAAL,P.; ORLAND,P.; PISARSKI,R.

2000-06-01

This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.

On the value and origin of the chiral condensate in quenched SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Hands, S.J.; Teper, M.; Oxford Univ.

1990-01-01

We present results of a numerical calculation of the chiral condensate in quenched SU(2) lattice gauge theory. The calculation proceeds by evaluating the spectral density distribution function for small eigenvalues on both the original lattice and after a factor-of-two blocking. It is performed on lattices as large as 20 4 and for couplings as small as β=4/g 2 =2.6. The fitted values of the condensate as a function of β show good evidence for scaling and universality when compared with string tension measurements at the same value. At the smallest lattice spacings considered, we find evidence that a separation of length scales between ultraviolet fluctuations and those responsible for chiral symmetry breaking has occurred. A more qualitative study yields a significant correlation between the small modes vertical stroken> responsible for the non-zero value of and topological activity as revealed by the expectation value 5 x1/n(>, and hence provides evidence for a topological origin of chiral symmetry breaking. Our interpretation is supported by a subsidiary calculation of the topological susceptibility of the vacuum. (orig.)

Central extensions of some Abelian finite gauge groups

International Nuclear Information System (INIS)

Combe, Ph.; Rodriguez, R.; Sirugue, M.; Sirugue-Collin, M.

1981-01-01

The authors describe central extensions of Abelian finite gauge groups on lattices which are permutation invariant. Moreover some remarks are made on the gauge models on lattice associated with these non-commutative central extensions. (Auth.)

Anomalous coupling of scalars to gauge fields

International Nuclear Information System (INIS)

Brax, Philippe; Davis, Anne-Christine; Seery, David; Weltman, Amanda

2010-10-01

We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)

Anomalous coupling of scalars to gauge fields

Energy Technology Data Exchange (ETDEWEB)

Brax, Philippe [CEA, IPhT, CNRS, URA 2306, Gif-sur-Yvette (France). Inst. de Physique Theorique; Burrage, Clare [Geneve Univ. (Switzerland). Dept. de Physique Theorique; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Davis, Anne-Christine [Centre for Mathematical Sciences, Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics; Seery, David [Sussex Univ., Brighton (United Kingdom). Dept. of Physics and Astronomy; Weltman, Amanda [Cape Town Univ., Rondebosch (South Africa). Astronomy, Cosmology and Gravity Centre

2010-10-15

We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)

Estimating q-hat in Quenched Lattice SU(2) Gauge Theory

International Nuclear Information System (INIS)

Majumder, Abhijit

2013-01-01

The propagation of a virtual quark in a thermal medium is considered. The non-perturbative jet transport coefficient q -hat is estimated in quark less SU(2) lattice gauge theory. The light like correlator which defines q -hat , defined in the regime where the jet has small virtuality compared to its energy, is analytically related to a series of local operators in the deep Euclidean region, where the jet's virtuality is of the same order as its energy. It is demonstrated that in this region, for temperatures in the range of T=400–600 MeV, and for jet energies above 20 GeV, the leading term in the series is dominant over the next-to-leading term and thus yields an estimate of the value of q -hat . In these proceedings we discuss the details of the numerical calculation

Massive and massless gauge fields of any spin and symmetry

International Nuclear Information System (INIS)

Hussain, F.; Jarvis, P.D.

1988-05-01

An analysis of the BRST approach to massive and massless gauge fields of any spin and symmetry is presented. Previous results on massless gauge fields are extended to totally antisymmetric massless tensors and Kaehler-Dirac particles. Two methods for arriving at a BRST invariant, massive theory from the corresponding massless one are discussed. The first allows for an interpretation in terms of dimensional reduction, while the second keeps the BRST operator of the massless theory, but employs gauge invariant fields. (author). 10 refs

Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.

Entanglement entropy for 2D gauge theories with matters

Science.gov (United States)

Aoki, Sinya; Iizuka, Norihiro; Tamaoka, Kotaro; Yokoya, Tsuyoshi

2017-08-01

We investigate the entanglement entropy in 1 +1 -dimensional S U (N ) gauge theories with various matter fields using the lattice regularization. Here we use extended Hilbert space definition for entanglement entropy, which contains three contributions; (1) classical Shannon entropy associated with superselection sector distribution, where sectors are labeled by irreducible representations of boundary penetrating fluxes, (2) logarithm of the dimensions of their representations, which is associated with "color entanglement," and (3) EPR Bell pairs, which give "genuine" entanglement. We explicitly show that entanglement entropies (1) and (2) above indeed appear for various multiple "meson" states in gauge theories with matter fields. Furthermore, we employ transfer matrix formalism for gauge theory with fundamental matter field and analyze its ground state using hopping parameter expansion (HPE), where the hopping parameter K is roughly the inverse square of the mass for the matter. We evaluate the entanglement entropy for the ground state and show that all (1), (2), (3) above appear in the HPE, though the Bell pair part (3) appears in higher order than (1) and (2) do. With these results, we discuss how the ground state entanglement entropy in the continuum limit can be understood from the lattice ground state obtained in the HPE.

Nonabelian gauge fields in the background of magnetic strings

International Nuclear Information System (INIS)

Wieczorek, E.

1993-01-01

Quantized nonabelian gauge fields are studied in the external classical background of a linear magnetic string. The determination of the gauge field propagator demands a specification of the string by suitable physical limiting procedures. The vacuum energy density is obtained after transforming the background problem into a Casimir problem. (orig.)

Problems of an external field in non-Abelian gauge theory