Analytic operator approach to fermionic lattice field theories

International Nuclear Information System (INIS)

Duncan, A.

1985-01-01

An analytic Lanczos algorithm previously used to extract the spectrum of bosonic lattice field theories in the continuum region is extended to theories with fermions. The method is illustrated in detail for the (1+1)-dimensional Gross-Neveu model. All parameters in the model (coupling, lattice size N, number of fermion flavors Nsub(F), etc.) appear explicitly in analytic formulas for matrix elements of the hamiltonian. The method is applied to the calculation of the collective field vacuum expectation value and the mass gap, and excellent agreement obtained with explicit results available from the large Nsub(F) solution of the model. (orig.)

Lattice Field Theory with the Sign Problem and the Maximum Entropy Method

Directory of Open Access Journals (Sweden)

Masahiro Imachi

2007-02-01

Full Text Available Although numerical simulation in lattice field theory is one of the most effective tools to study non-perturbative properties of field theories, it faces serious obstacles coming from the sign problem in some theories such as finite density QCD and lattice field theory with the θ term. We reconsider this problem from the point of view of the maximum entropy method.

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

Statistical mechanics of lattice Boson field theory

International Nuclear Information System (INIS)

1976-01-01

A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3 and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region

Statistical mechanics of lattice boson field theory

International Nuclear Information System (INIS)

Baker, G.A. Jr.

1977-01-01

A lattice approximation to Euclidean, boson quantum field theory is expressed in terms of the thermodynamic properties of a classical statistical mechanical system near its critical point in a sufficiently general way to permit the inclusion of an anomalous dimension of the vacuum. Using the thermodynamic properties of the Ising model, one can begin to construct nontrivial (containing scattering) field theories in 2, 3, and 4 dimensions. It is argued that, depending on the choice of the bare coupling constant, there are three types of behavior to be expected: the perturbation theory region, the renormalization group fixed point region, and the Ising model region. 24 references

Fermion Bag Approach to Lattice Hamiltonian Field Theories

Science.gov (United States)

Huffman, Emilie

2018-03-01

Using a model in the Gross-Neveu Ising universality class, we show how the fermion bag idea can be applied to develop algorithms to Hamiltonian lattice field theories. We argue that fermion world lines suggest an alternative method to the traditional techniques for calculating ratios of determinants in a stable manner. We show the power behind these ideas by extracting the physics of the model on large lattices.

Conformal field theories, representations and lattice constructions

International Nuclear Information System (INIS)

Dolan, L.; Montague, P.

1996-01-01

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z 2 -twisted theories, H(Λ) and H(Λ) respectively, which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct lattices Λ C and Lambda C by analogous constructions from a doubly-even binary code C. In the case when C is self-dual, the corresponding lattices are also. Similarly, H(Λ) and H(Λ) are self-dual if and only if Λ is. We show that H(Λ C ) has a natural triality structure, which induces an isomorphism H(Λ C )≡H(Λ C ) and also a triality structure on H(Λ C ). For C the Golay code, Λ C is the Leech lattice, and the triality on H(Λ C ) is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories H(Λ) and H(Λ) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code. (orig.). With 8 figs., 2 tabs

The Toda lattice hierarchy and deformation of conformal field theories

International Nuclear Information System (INIS)

Fukuma, M.

1990-01-01

In this paper, the authors point out that the Toda lattice hierarchy known in soliton theory is relevant for the description of the deformations of conformal field theories while the KP hierarchy describes unperturbed conformal theories. It is shown that the holomorphic parts of the conserved currents in the perturbed system (the Toda lattice hierarchy) coincide with the conserved currents in the KP hierarchy and can be written in terms of the W-algebraic currents. Furthermore, their anti-holomorphic counterparts are obtained

Lattice models and conformal field theories

International Nuclear Information System (INIS)

Saleur, H.

1988-01-01

Theoretical studies concerning the connection between critical physical systems and the conformal theories are reviewed. The conformal theory associated to a critical (integrable) lattice model is derived. The obtention of the central charge, critical exponents and torus partition function, using renormalization group arguments, is shown. The quantum group structure, in the integrable lattice models, and the theory of Visaro algebra representations are discussed. The relations between off-critical integrable models and conformal theories, in finite geometries, are studied

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

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.)

Mean field with corrections in lattice gauge theory

International Nuclear Information System (INIS)

Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.

1981-12-01

A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)

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.)

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...

Mayer expansions for Euclidean lattice field theory: Convergence properties and relation with perturbation theory

International Nuclear Information System (INIS)

Pordt, A.

1985-10-01

The author describes the Mayer expansion in Euclidean lattice field theory by comparing it with the statistical mechanics of polymer systems. In this connection he discusses the Borel summability and the analyticity of the activities on the lattice. Furthermore the relations between renormalization and the Mayer expansion are considered. (HSI)

Monte Carlo numerical study of lattice field theories

International Nuclear Information System (INIS)

Gan Cheekwan; Kim Seyong; Ohta, Shigemi

1997-01-01

The authors are interested in the exact first-principle calculations of quantum field theories which are indeed exact ones. For quantum chromodynamics (QCD) at low energy scale, a nonperturbation method is needed, and the only known such method is the lattice method. The path integral can be evaluated by putting a system on a finite 4-dimensional volume and discretizing space time continuum into finite points, lattice. The continuum limit is taken by making the lattice infinitely fine. For evaluating such a finite-dimensional integral, the Monte Carlo numerical estimation of the path integral can be obtained. The calculation of light hadron mass in quenched lattice QCD with staggered quarks, 3-dimensional Thirring model calculation and the development of self-test Monte Carlo method have been carried out by using the RIKEN supercomputer. The motivation of this study, lattice QCD formulation, continuum limit, Monte Carlo update, hadron propagator, light hadron mass, auto-correlation and source size dependence are described on lattice QCD. The phase structure of the 3-dimensional Thirring model for a small 8 3 lattice has been mapped. The discussion on self-test Monte Carlo method is described again. (K.I.)

Continuum gauge fields from lattice gauge fields

International Nuclear Information System (INIS)

Goeckeler, M.; Kronfeld, A.S.; Schierholz, G.; Wiese, U.J.

1993-01-01

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the U(1) theory in two dimensions, where it leads to simple results. (orig.)

Lattice gauge theory using parallel processors

International Nuclear Information System (INIS)

Lee, T.D.; Chou, K.C.; Zichichi, A.

1987-01-01

The book's contents include: Lattice Gauge Theory Lectures: Introduction and Current Fermion Simulations; Monte Carlo Algorithms for Lattice Gauge Theory; Specialized Computers for Lattice Gauge Theory; Lattice Gauge Theory at Finite Temperature: A Monte Carlo Study; Computational Method - An Elementary Introduction to the Langevin Equation, Present Status of Numerical Quantum Chromodynamics; Random Lattice Field Theory; The GF11 Processor and Compiler; and The APE Computer and First Physics Results; Columbia Supercomputer Project: Parallel Supercomputer for Lattice QCD; Statistical and Systematic Errors in Numerical Simulations; Monte Carlo Simulation for LGT and Programming Techniques on the Columbia Supercomputer; Food for Thought: Five Lectures on Lattice Gauge Theory

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.)

Canonical simulations with worldlines: An exploratory study in ϕ24 lattice field theory

Science.gov (United States)

Orasch, Oliver; Gattringer, Christof

2018-01-01

In this paper, we explore the perspectives for canonical simulations in the worldline formulation of a lattice field theory. Using the charged ϕ4 field in two dimensions as an example, we present the details of the canonical formulation based on worldlines and outline the algorithmic strategies for canonical worldline simulations. We discuss the steps for converting the data from the canonical approach to the grand canonical picture which we use for cross-checking our results. The canonical approach presented here can easily be generalized to other lattice field theories with a worldline representation.

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

New techniques and results for worldline simulations of lattice field theories

Science.gov (United States)

Giuliani, Mario; Orasch, Oliver; Gattringer, Christof

2018-03-01

We use the complex ø4 field at finite density as a model system for developing further techniques based on worldline formulations of lattice field theories. More specifically we: 1) Discuss new variants of the worm algorithm for updating the ø4 theory and related systems with site weights. 2) Explore the possibility of canonical simulations in the worldline formulation. 3) Study the connection of 2-particle condensation at low temperature to scattering parameters of the theory.

Grassmann methods in lattice field theory and statistical mechanics

International Nuclear Information System (INIS)

Bilgici, E.; Gattringer, C.; Huber, P.

2006-01-01

Full text: In two dimensions models of loops can be represented as simple Grassmann integrals. In our work we explore the generalization of these techniques to lattice field theories and statistical mechanic systems in three and four dimensions. We discuss possible strategies and applications for representations of loop and surface models as Grassmann integrals. (author)

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

Introduction to lattice gauge theories

International Nuclear Information System (INIS)

La Cock, P.

1988-03-01

A general introduction to Lattice Gauge Theory (LGT) is given. The theory is discussed from first principles to facilitate an understanding of the techniques used in LGT. These include lattice formalism, gauge invariance, fermions on the lattice, group theory and integration, strong coupling methods and mean field techniques. A review of quantum chromodynamics on the lattice at finite temperature and density is also given. Monte Carlo results and analytical methods are discussed. An attempt has been made to include most relevant data up to the end of 1987, and to update some earlier reviews existing on the subject. 224 refs., 33 figs., 14 tabs

Chiral effective field theory on the lattice at next-to-leading order

International Nuclear Information System (INIS)

Borasoy, B.; Epelbaum, E.; Krebs, H.; Meissner, U.G.; Lee, D.

2008-01-01

We study nucleon-nucleon scattering on the lattice at next-to-leading order in chiral effective field theory. We determine phase shifts and mixing angles from the properties of two-nucleon standing waves induced by a hard spherical wall in the center-of-mass frame. At fixed lattice spacing we test model independence of the low-energy effective theory by computing next-to-leading-order corrections for two different leading-order lattice actions. The first leading-order action includes instantaneous one-pion exchange and same-site contact interactions. The second leading-order action includes instantaneous one-pion exchange and Gaussian-smeared interactions. We find that in each case the results at next-to-leading order are accurate up to corrections expected at higher order. (orig.)

Dielectric lattice gauge theory

International Nuclear Information System (INIS)

Mack, G.

1983-06-01

Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)

Dielectric lattice gauge theory

International Nuclear Information System (INIS)

Mack, G.

1984-01-01

Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)element ofG that are attached to the links b = (x+esub(μ), x) of the lattice and take their values in the linear space G which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)sigmasub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportional sigmasub(i)sigmasub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder-Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson-loop expectation values show an area law decay, if the euclidean action has certain qualitative features which imply that PHI=0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)

A lattice formulation of chiral gauge theories

International Nuclear Information System (INIS)

Bodwin, G.T.

1995-12-01

The authors present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken in which the lattice spacing associated with the fermion field is taken to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. They also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration

Renormalization group and finite size effects in scalar lattice field theories

International Nuclear Information System (INIS)

Bernreuther, W.; Goeckeler, M.

1988-01-01

Binder's phenomenological renormalization group is studied in the context of the O(N)-symmetric euclidean lattice φ 4 theory in dimensions d ≤ 4. By means of the field theoretical formulation of the renormalization group we analyse suitable ratios of Green functions on finite lattices in the limit where the dimensionless lattice length L >> 1 and where the dimensionless bare mass approaches the critical point of the corresponding infinite volume model. If the infrared-stable fixed point which controls this limit is a simple zero of the β-function we are led to formulae which allow the extraction of the critical exponents ν and η. For the gaussian fixed point in four dimensions, discussed as a known example for a multiple zero of the β-function, we derive for these ratios the leading logarithmic corrections to mean field scaling. (orig.)

Lattice topological field theory on nonorientable surfaces

International Nuclear Information System (INIS)

Karimipour, V.; Mostafazadeh, A.

1997-01-01

The lattice definition of the two-dimensional topological quantum field theory [Fukuma et al., Commun. Math. Phys. 161, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that there is a one-to-one correspondence between real associative *-algebras and the topological state sum invariants defined on such surfaces. The partition and n-point functions on all two-dimensional surfaces (connected sums of the Klein bottle or projective plane and g-tori) are defined and computed for arbitrary *-algebras in general, and for the group ring A=R[G] of discrete groups G, in particular. copyright 1997 American Institute of Physics

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

Second order phase transition in two dimensional sine-Gordon field theory - lattice model

International Nuclear Information System (INIS)

Babu Joseph, K.; Kuriakose, V.C.

1978-01-01

Two dimensional sine-Gordon (SG) field theory on a lattice is studied using the single-site basis variational method of Drell and others. The nature of the phase transition associated with the spontaneous symmetry breakdown in a SG field system is clarified to be of second order. A generalisation is offered for a SG-type field theory in two dimensions with a potential of the form [cossup(n)((square root of lambda)/m)phi-1].(author)

Scattering theory for lattice phi4sub(D+1) theory

International Nuclear Information System (INIS)

Garczynski, W.

1983-01-01

Feynman rules are derived for a lattice version of the phi 4 sub(D+1) theory. The lattice values are transcribed, via a quasicontinual representation, into a continuous, non-local in spatial variables field theory, which is then quantized by the path integral method. (orig.)

Bogoliubov transformations and fermion condensates in lattice field theories

International Nuclear Information System (INIS)

Caracciolo, Sergio; Palumbo, Fabrizio; Viola, Giovanni

2009-01-01

We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian

Statistical mechanics view of quantum chromodynamics: Lattice gauge theory

International Nuclear Information System (INIS)

Kogut, J.B.

1984-01-01

Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made

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.)

Lattice gauge theory

International Nuclear Information System (INIS)

Mack, G.

1982-01-01

After a description of a pure Yang-Mills theory on a lattice, the author considers a three-dimensional pure U(1) lattice gauge theory. Thereafter he discusses the exact relation between lattice gauge theories with the gauge groups SU(2) and SO(3). Finally he presents Monte Carlo data on phase transitions in SU(2) and SO(3) lattice gauge models. (HSI)

Towards a coupled-cluster treatment of SU(N) lattice gauge field theory

NARCIS (Netherlands)

Bishop, Raymond F.; Ligterink, N.E.; Walet, Niels R.

2006-01-01

A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the

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

Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field

Science.gov (United States)

Figueroa, Daniel G.; Shaposhnikov, Mikhail

2018-01-01

Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U (1) gauge sector, a (x)FμνF˜μν, reproducing the continuum limit to order O (dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K =FμνF˜μν that admits a lattice total derivative representation K = Δμ+ Kμ, reproducing to order O (dxμ2) the continuum expression K =∂μKμ ∝ E → ṡ B → . If we consider a homogeneous field a (x) = a (t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.

Lattice implementation of Abelian gauge theories with Chern–Simons number and an axion field

Directory of Open Access Journals (Sweden)

Daniel G. Figueroa

2018-01-01

Full Text Available Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark–gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U(1 gauge sector, a(xFμνF˜μν, reproducing the continuum limit to order O(dxμ2 and obeying the following properties: (i the system is gauge invariant and (ii shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K=FμνF˜μν that admits a lattice total derivative representation K=Δμ+Kμ, reproducing to order O(dxμ2 the continuum expression K=∂μKμ∝E→⋅B→. If we consider a homogeneous field a(x=a(t, the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern–Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking in Abelian gauge theories at finite temperature. When a(x=a(x→,t is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O(dxμ2 accuracy. We discuss an iterative scheme allowing to overcome this difficulty.

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

Fermion bag approach to Hamiltonian lattice field theories in continuous time

Science.gov (United States)

Huffman, Emilie; Chandrasekharan, Shailesh

2017-12-01

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3 d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η =0.54 (6 ) and ν =0.88 (2 ) using lattices up to N =2304 sites. We argue that even sizes up to N =10 ,000 sites should be accessible with supercomputers available today.

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 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.)

Fields on a random lattice

International Nuclear Information System (INIS)

Itzykson, C.

1983-10-01

We review the formulation of field theory and statistical mechanics on a Poissonian random lattice. Topics discussed include random geometry, the construction of field equations for arbitrary spin, the free field spectrum and the question of localization illustrated in the one dimensional case

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

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)

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

International Nuclear Information System (INIS)

Bonora, L.; Colatto, L.P.; Constantinidis, C.P.

1996-05-01

In analogy with the Liouville case, we study the sl 3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W 3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra. (author). 16 refs

Phi4 lattice field theory as an asymptotic expansion about the Ising limit

International Nuclear Information System (INIS)

Caginalp, G.

1980-01-01

For a d-dimensional phi 4 lattice field theory consisting of N spins, an asymptotic expansion of expectations about the Ising limit is established in inverse powers of the bare coupling constant lambda. In the thermodynamic limit (N→infinity), the expansion is expected to be valid in the noncritical region of the Ising system

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

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

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

Saddle-points of a two dimensional random lattice theory

International Nuclear Information System (INIS)

Pertermann, D.

1985-07-01

A two dimensional random lattice theory with a free massless scalar field is considered. We analyse the field theoretic generating functional for any given choice of positions of the lattice sites. Asking for saddle-points of this generating functional with respect to the positions we find the hexagonal lattice and a triangulated version of the hypercubic lattice as candidates. The investigation of the neighbourhood of a single lattice site yields triangulated rectangles and regular polygons extremizing the above generating functional on the local level. (author)

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.)

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.))

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.

Quantum-field theories as representations of a single $^\\ast$-algebra

OpenAIRE

Raab, Andreas

2013-01-01

We show that many well-known quantum field theories emerge as representations of a single $^\\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field theories, and string theories. We prove that such theories can be approximated on lattices, and we give a rigorous definition of the continuum limit of lattice quantum field theories.

Perfect 3-dimensional lattice actions for 4-dimensional quantum field theories at finite temperature

International Nuclear Information System (INIS)

Kerres, U.; Mack, G.; Palma, G.

1994-12-01

We propose a two-step procedure to study the order of phase transitions at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional perfect lattice action by a block spin transformation. It has finite temperature dependent coefficients. In this way the UV-problem and the infrared problem is separated in a clean way. In the second step the effective 3-dimensional lattice theory is treated in a nonperturbative way, either by the Feynman-Bololiubov method (solution of a gap equation), by real space renormalization group methods, or by computer simulations. In this paper we outline the principles for φ 4 -theory and scalar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformation to the nonabelian case, but this will not be discussed here. (orig.)

A first look at Quasi-Monte Carlo for lattice field theory problems

International Nuclear Information System (INIS)

Jansen, K.; Leovey, H.; Griewank, A.; Nube, A.; Humboldt-Universitaet, Berlin; Mueller-Preussker, M.

2012-11-01

In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like N -1/2 , where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to N -1 . We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.

A first look at quasi-Monte Carlo for lattice field theory problems

International Nuclear Information System (INIS)

Jansen, K; Nube, A; Leovey, H; Griewank, A; Mueller-Preussker, M

2013-01-01

In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like N −1/2 , where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to N −1 . We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling

A first look at Quasi-Monte Carlo for lattice field theory problems

Energy Technology Data Exchange (ETDEWEB)

Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leovey, H.; Griewank, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Nube, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Mueller-Preussker, M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

2012-11-15

In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like N{sup -1/2}, where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to N{sup -1}. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.

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.

Variational method for field theories on the lattice and the spectrum of the phi4 theory in 1+1 dimensions

International Nuclear Information System (INIS)

Abad, J.; Esteve, J.G.; Pacheco, A.F.

1985-01-01

An approximation technique to construct the low-lying energy eigenstates of any bosonic field theory on the lattice is proposed. It is based on the SLAC blocking method, after performing a finite-spin approximation to the individual degrees of freedom of the problem. General expressions for any polynomial self-interacting theory are given. Numerical results for phi 2 and phi 4 theories in 1+1 dimensions are offered; they exhibit a fast convergence rate. The complete low-lying energy spectrum of the phi 4 theory in 1+1 dimensions is calculated

Lattice regularized chiral perturbation theory

International Nuclear Information System (INIS)

Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.

2004-01-01

Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term

Dynamical lattice theory

International Nuclear Information System (INIS)

Chodos, A.

1978-01-01

A version of lattice gauge theory is presented in which the shape of the lattice is not assumed at the outset but is a consequence of the dynamics. Other related features which are not specified a priori include the internal and space-time symmetry groups and the dimensionality of space-time. The theory possesses a much larger invariance group than the usual gauge group on a lattice, and has associated with it an integer k 0 analogous to the topological quantum numer of quantum chromodynamics. Families of semiclassical solutions are found which are labeled by k 0 and a second integer x, but the analysis is not carried far enough to determine which space-time and internal symmetry groups characterize the lowest-lying states of the theory

Einstein causal quantum fields on lattices with discrete Lorentz invariance

International Nuclear Information System (INIS)

Baumgaertel, H.

1986-01-01

Results on rigorous construction of quantum fields on the hypercubic lattice Z 4 considered as a lattice in the Minkowski space R 4 are presented. Two associated fields are constructed: The first one having on the lattice points of Z 4 is causal and Poincare invariant in the discrete sense. The second one is an interpolating field over R 4 which is pointlike, translationally covariant and spectral in such a manner that the 'real' lattices field is the restriction of the interpolating field to Z 4 . Furthermore, results on a rigorous perturbation theory of such fields are mentioned

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.

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.

31st International Symposium on Lattice Field Theory

CERN Document Server

2013-01-01

The annual lattice symposium brings together a global community of researchers from theoretical particle physics and beyond, who employ numerical and computational methods to study the properties of strongly interacting physical systems, above all Quantum Chromodynamics (QCD), the theory describing the interactions of quarks and gluons. Topics include studies of the spectrum and structure of hadrons, lattice studies of matter under extreme conditions, hadronic contributions to weak decay amplitudes, as well as recent developments in simulation algorithms and computer hardware. The 2013 conference in Mainz was attended by over 500 participants from all over the globe, making it the biggest in this series so far. This proceedings volume is dedicated to the memory of Nobel Laureate Kenneth G. Wilson (June 8, 1936 - June 15, 2013).

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

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

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.)

Fourier acceleration in lattice gauge theories. I. Landau gauge fixing

International Nuclear Information System (INIS)

Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.

1988-01-01

Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations

Matrix product states for lattice field theories

Energy Technology Data Exchange (ETDEWEB)

Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences

2013-10-15

The term Tensor Network States (TNS) refers to a number of families of states that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbativemanner. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.

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

Local structure theory: calculation on hexagonal arrays, and interaction of rule and lattice

International Nuclear Information System (INIS)

Gutowitz, H.A.; Victor, J.D.

1989-01-01

Local structure theory calculations are applied to the study of cellular automata on the two-dimensional hexagonal lattice. A particular hexagonal lattice rule denoted (3422) is considered in detail. This rule has many features in common with Conway's Life. The local structure theory captures many of the statistical properties of this rule; this supports hypotheses raised by a study of Life itself. As in Life, the state of a cell under (3422) depends only on the state of the cell itself and the sum of states in its neighborhood at the previous time step. This property implies that evolution rules which operate in the same way can be studied on different lattices. The differences between the behavior of these rules on different lattices are dramatic. The mean field theory cannot reflect these differences. However, a generalization of the mean field theory, the local structure theory, does account for the rule-lattice interaction

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

On diffeomorphism invariance for lattice theories

International Nuclear Information System (INIS)

Corichi, A.; Zapata, J.

1997-01-01

We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider 2+1 gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known - for both the continuum and the lattice - and can be compared. (orig.)

Non-perturbative field theory/field theory on a lattice

International Nuclear Information System (INIS)

Ambjorn, J.

1988-01-01

The connection between the theory of critical phenomena in statistical mechanics and the renormalization of field theory is briefly outlined. The way of using this connection is described to get information about non-perturbative quantities in QCD and about more intelligent ways of doing the Monte Carlo (MC) simulations. The (MC) method is shown to be a viable one in high energy physics, but it is not a good substitute for an analytic understanding. MC-methods will be very valuable both for getting out hard numbers and for testing the correctness of new ideas

Studies in quantum field theory

International Nuclear Information System (INIS)

Bender, C.M.; Mandula, J.E.; Shrauner, J.E.

1982-01-01

Washington University is currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large orders; quark condensation in QCD; chiral symmetry breaking; the l/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD

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.)

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...

Defects in higher-dimensional quantum field theory. Relations to AdS/CFT-correspondence and Kondo lattices

Energy Technology Data Exchange (ETDEWEB)

Schmidt, R.

2007-03-15

The present work is addressed to defects and boundaries in quantum field theory considering the application to AdS/CFT correspondence. We examine interactions of fermions with spins localised on these boundaries. Therefore, an algebra method is emphasised adding reflection and transmission terms to the canonical quantisation prescription. This method has already been applied to bosons in two space-time dimensions before. We show the possibilities of such reflection-transmission algebras in two, three, and four dimensions. We compare with models of solid state physics as well as with the conformal field theory approach to the Kondo effect. Furthermore, we discuss ansatzes of extensions to lattice structures. (orig.)

Homogenization theory in reactor lattices

International Nuclear Information System (INIS)

Benoist, P.

1986-02-01

The purpose of the theory of homogenization of reactor lattices is to determine, by the mean of transport theory, the constants of a homogeneous medium equivalent to a given lattice, which allows to treat the reactor as a whole by diffusion theory. In this note, the problem is presented by laying emphasis on simplicity, as far as possible [fr

Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

International Nuclear Information System (INIS)

Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki

2009-01-01

Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

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.)

Representation theory of lattice current algebras

International Nuclear Information System (INIS)

Alekseev, A.Yu.; Eidgenoessische Technische Hochschule, Zurich; Faddeev, L.D.; Froehlich, L.D.; Schomerus, V.; Kyoto Univ.

1996-04-01

Lattice current algebras were introduced as a regularization of the left-and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U q (G). Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts. (orig.)

Effective field theories

International Nuclear Information System (INIS)

Mack, G.; Kalkreuter, T.; Palma, G.; Speh, M.

1992-05-01

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low utraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically, the idea is to integrate out the high frequency components of fields. This requires the choice of a 'blockspin', i.e. the specification af a low frequency field as a function of the fundamental fields. These blockspins will be fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspin in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels A from coarse to fine grid in addition to the averaging kernels C which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The special case of a 'lattice' with a single site (the constraint effective potential) is of particular interest. In a higgs model, the effective action reduces in this case to the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data. (orig.)

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.)

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

Dynamical Mean Field Approximation Applied to Quantum Field Theory

CERN Document Server

Akerlund, Oscar; Georges, Antoine; Werner, Philipp

2013-12-04

We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...

Strong coupling expansion for scattering phases in hamiltonian lattice field theories. Pt. 2. SU(2) gauge theory in (2+1) dimensions

International Nuclear Information System (INIS)

Dahmen, B.

1994-12-01

A recently proposed method for a strong coupling analysis of scattering phenomena in hamiltonian lattice field theories is applied to the SU(2) Yang-Mills model in (2 + 1) dimensions. The calculation is performed up to second order in the hopping parameter. All relevant quantities that characterize the collision between the lightest glueballs in the elastic region - cross section, phase shifts, resonance parameters - are determined. (orig.)

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.

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.

Higgs-Yukawa model in chirally-invariant lattice field theory

CERN Document Server

Bulava, John; Jansen, Karl; Kallarackal, Jim; Knippschild, Bastian; Lin, C.-J.David; Nagai, Kei-Ichi; Nagy, Attila; Ogawa, Kenji

2013-01-01

Non-perturbative numerical lattice studies of the Higgs-Yukawa sector of the standard model with exact chiral symmetry are reviewed. In particular, we discuss bounds on the Higgs boson mass at the standard model top quark mass, and in the presence of heavy fermions. We present a comprehensive study of the phase structure of the theory at weak and very strong values of the Yukawa coupling as well as at non-zero temperature.

Higgs-Yukawa model in chirally-invariant lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Bulava, John [CERN, Geneva (Switzerland). Physics Department; Gerhold, Philipp; Kallarackal, Jim; Nagy, Attila [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Knippschild, Bastian [National Taiwan Univ., Taipei (China). Dept. of Physics; Lin, C.J. David [National Chiao-Tung Univ., Hsinchu (China). Inst. of Physics; National Centre for Theoretical Sciences, Hsinchu (China). Div. of Physics; Nagai, Kei-Ichi [Nagoya Univ., Nagoya, Aichi (Japan). Kobayashi-Maskawa Institute; Ogawa, Kenji [Chung-Yuan Christian Univ., Chung-Li (China). Dept. of Physics

2012-10-15

Non-perturbative numerical lattice studies of the Higgs-Yukawa sector of the standard model with exact chiral symmetry are reviewed. In particular, we discuss bounds on the Higgs boson mass at the standard model top quark mass, and in the presence of heavy fermions. We present a comprehensive study of the phase structure of the theory at weak and very strong values of the Yukawa coupling as well as at non-zero temperature.

Continuum (scaling) limits of lattice field theories (triviality of lambda/phi/4 in D greater than or equal to dimensions)

International Nuclear Information System (INIS)

Frohlich, J.

1983-01-01

The author describes some recent techniques for constructing the continuum (= scaling) limit of lattice field theories, including the one- and two- component lambda/less than or equal to→/phi// 4 theories and the Ising and rotator models in a space (- imaginary time) of dimension d >greater than or equal to 4. These techniques should have applications to other related models, like the selfavoiding random walk in five or more dimensions and bond percolation in seven or more dimensions. Some plausible conjectures concerning the Gaussian nature of the scaling limit of the d greater than or equal to 2 dimensional rotator model and the d greater than or equal to 4 dimensional U(1) lattice gauge theory in the low temperature (weak coupling) phase are described

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.

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.

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

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

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

Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory

Energy Technology Data Exchange (ETDEWEB)

Alarcon, Jose Manuel [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Thomas Jefferson National Accelerator Facility, Theory Center, Newport News, VA (United States); Du, Dechuan; Laehde, Timo A.; Li, Ning; Lu, Bing-Nan; Luu, Thomas [Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany); Klein, Nico [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Lee, Dean [North Carolina State University, Department of Physics, Raleigh, NC (United States); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Institute for Advanced Simulation, Institut fuer Kernphysik, and Juelich Center for Hadron Physics, Forschungszentrum Juelich, Juelich (Germany); Forschungszentrum Juelich, JARA - High Performance Computing, Juelich (Germany)

2017-05-15

We present a systematic study of neutron-proton scattering in Nuclear Lattice Effective Field Theory (NLEFT), in terms of the computationally efficient radial Hamiltonian method. Our leading-order (LO) interaction consists of smeared, local contact terms and static one-pion exchange. We show results for a fully non-perturbative analysis up to next-to-next-to-leading order (NNLO), followed by a perturbative treatment of contributions beyond LO. The latter analysis anticipates practical Monte Carlo simulations of heavier nuclei. We explore how our results depend on the lattice spacing a, and estimate sources of uncertainty in the determination of the low-energy constants of the next-to-leading-order (NLO) two-nucleon force. We give results for lattice spacings ranging from a = 1.97 fm down to a = 0.98 fm, and discuss the effects of lattice artifacts on the scattering observables. At a = 0.98 fm, lattice artifacts appear small, and our NNLO results agree well with the Nijmegen partial-wave analysis for S-wave and P-wave channels. We expect the peripheral partial waves to be equally well described once the lattice momenta in the pion-nucleon coupling are taken to coincide with the continuum dispersion relation, and higher-order (N3LO) contributions are included. We stress that for center-of-mass momenta below 100 MeV, the physics of the two-nucleon system is independent of the lattice spacing. (orig.)

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

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

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.

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

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.)

Propositional systems in local field theories

International Nuclear Information System (INIS)

Banai, M.

1980-07-01

The authors investigate propositional systems for local field theories, which reflect intrinsically the uncertainties of measurements made on the physical system, and satisfy the isotony and local commutativity postulates of Haag and Kastler. The spacetime covariance can be implemented in natural way in these propositional systems. New techniques are introduced to obtain these propositional systems: the lattice-valued logics. The decomposition of the complete orthomodular lattice-valued logics shows that these logics are more general than the usual two-valued ones and that in these logics there is enough structure to characterize the classical and quantum, non relativistic and relativistic local field theories in a natural way. The Hilbert modules give the natural inner product ''spaces'' (modules) for the realization of the lattice-valued logics. (author)

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

Quantum theory of two-dimensional generalized Toda lattice on bounded spatial interval

International Nuclear Information System (INIS)

Leznov, A.N.

1982-01-01

The quantization method of exactly solvable dynamical systems worked out in another paper is applied to a two-dimensional model described by the equations of generalized Toda lattice with a periodicity condition over spatial variable. The Heisenberg operators of the model are finite polynomials over the coupling constant g 2 , whose coefficients functionally depend on operators of noninteracting fields. The model has a direct relation with the string theories and reduces formally when L→infinity to two-dimensional quantum field theory described by the equations of generalized Toda lattice the formal solution of which has been found in Refs

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.)

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

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.)

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).

Chiral perturbation theory for lattice QCD

Energy Technology Data Exchange (ETDEWEB)

Baer, Oliver

2010-07-21

The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)

Chiral perturbation theory for lattice QCD

International Nuclear Information System (INIS)

Baer, Oliver

2010-01-01

The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)

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

Lattice formulations of reggeon interactions

International Nuclear Information System (INIS)

Brower, R.C.; Ellis, J.; Savit, R.; Zinn-Justin, J.

1976-01-01

A class of lattice analogues to reggeon field theory is examined. First the transition from a continuum to a lattice field theory is discussed, emphasizing the necessity of a Wick rotation and the consideration of symmetry properties. Next the theory is transformed to a discrete system with two spins at each lattice site, and the problems of the triple-reggeon interaction and the reggeon energy gap are discussed. It is pointed out that transferring the theory from the continuum to a lattice necesarily introduces new relevant operators not normally present in reggeon field theory. (Auth.)

The renormalization group study of the effective theory of lattice QED

International Nuclear Information System (INIS)

Sugiyama, Y.

1988-01-01

The compact U(1) lattice gauge theory with massless fermions (Lattice QED) is studied through the effective model analytically, using the renormalization group method. The obtained effective model is the local boson field system with non-local interactions. The authors study the existence of non-trivial fixed point and its scaling behavior. This fixed point seems to be tri-critical. Such fixed point is interpreted in terms of the original Lattice QED model, and the results are consistent with the Monte Calro study

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.)

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.)

Nonlocal continuum field theories

CERN Document Server

2002-01-01

Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Blossier, Benoit [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Paris-XI Univ., 91 - Orsay (France). Lab. de Physique Theorique; Morte, Michele della [CERN, Geneva (Switzerland). Physics Dept.]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Hippel, Georg von; Sommer, Rainer [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Mendes, Tereza [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)]|[Sao Paulo Univ. (Brazil). IFSC

2009-02-15

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E{sub N+1}-E{sub n}) t). The gap E{sub N+1}-E{sub n} can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m{sub b} in HQET. (orig.)

On the generalized eigenvalue method for energies and matrix elements in lattice field theory

International Nuclear Information System (INIS)

Blossier, Benoit; Mendes, Tereza; Sao Paulo Univ.

2009-02-01

We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as exp(-(E N+1 -E n ) t). The gap E N+1 -E n can be made large by increasing the number N of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order 1/m b in HQET. (orig.)

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.)

N = 1 SU(2) supersymmetric Yang-Mills theory on the lattice with light dynamical Wilson gluinos

International Nuclear Information System (INIS)

Demmouche, Kamel

2009-01-01

The supersymmetric Yang-Mills (SYM) theory with one supercharge (N=1) and one additional Majorana matter-field represents the simplest model of supersymmetric gauge theory. Similarly to QCD, this model includes gauge fields, gluons, with color gauge group SU(N c ) and fermion fields, describing the gluinos. The non-perturbative dynamical features of strongly coupled supersymmetric theories are of great physical interest. For this reason, many efforts are dedicated to their formulation on the lattice. The lattice regularization provides a powerful tool to investigate non-perturbatively the phenomena occurring in SYM such as confinement and chiral symmetry breaking. In this work we perform numerical simulations of the pure SU(2) SYM theory on large lattices with small Majorana gluino masses down to about m g approx 115 MeV with lattice spacing up to a ≅0.1 fm. The gluino dynamics is simulated by the Two-Step Multi-Boson (TSMB) and the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithms. Supersymmetry (SUSY) is broken explicitly by the lattice and the Wilson term and softly by the presence of a non-vanishing gluino mass m g ≠0. However, the recovery of SUSY is expected in the infinite volume continuum limit by tuning the bare parameters to the SUSY point in the parameter space. This scenario is studied by the determination of the low-energy mass spectrum and by means of lattice SUSY Ward-Identities (WIs). (orig.)

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

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.)

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

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.

[Studies in quantum field theory

International Nuclear Information System (INIS)

1990-01-01

During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity

Effective-field theory on the kinetic Ising model

International Nuclear Information System (INIS)

Shi Xiaoling; Wei Guozhu; Li Lin

2008-01-01

As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h 0 /ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT)

[Topics in field theory and string theory

International Nuclear Information System (INIS)

1990-01-01

In the past year, I have continued to investigate the relations between conformal field theories and lattice statistical mechanical models, and in particular have been studying two dimensional models coupled to quantum gravity. I have continued as well to consider possible extension of these results to higher dimensions and potential applications in other contexts

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

Energy Technology Data Exchange (ETDEWEB)

Deviren, Bayram [Institute of Science, Erciyes University, Kayseri 38039 (Turkey); Canko, Osman [Department of Physics, Erciyes University, Kayseri 38039 (Turkey); Keskin, Mustafa [Department of Physics, Erciyes University, Kayseri 38039 (Turkey)], E-mail: keskin@erciyes.edu.tr

2008-09-15

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior.

Effective-field theory of the Ising model with three alternative layers on the honeycomb and square lattices

International Nuclear Information System (INIS)

Deviren, Bayram; Canko, Osman; Keskin, Mustafa

2008-01-01

The Ising model with three alternative layers on the honeycomb and square lattices is studied by using the effective-field theory with correlations. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the adjacent spins of the nearest-neighbor layers are coupled either ferromagnetically or anti-ferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the thermal variations of the magnetizations and present the phase diagrams. The phase diagrams contain the paramagnetic, ferromagnetic and anti-ferromagnetic phases, and the system also exhibits a tricritical behavior

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.)

Exact vacuum energy of orbifold lattice theories

International Nuclear Information System (INIS)

Matsuura, So

2007-01-01

We investigate the orbifold lattice theories constructed from supersymmetric Yang-Mills matrix theories (mother theories) with four and eight supercharges. We show that the vacuum energy of these theories does not receive any quantum correction perturbatively

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

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...

Conformal field theory, triality and the Monster group

International Nuclear Information System (INIS)

Dolan, L.; Goddard, P.; Montague, P.

1990-01-01

From an even self-dual N-dimensional lattice, Λ, it is always possible to construct two (chiral) conformal field theories, an untwisted theory H (Λ), and a Z 2 -twisted theory H (Λ), constructed using the reflection twist. (N must be a multiple of 8 and the theories are modular invariant if it is a multiple of 24.) Similarly, from a doubly-even self-dual binary code C, it is possible to construct two even self-dual lattices, an untwisted one Λ C and a twisted one anti Λ C . It is shown that H(Λ C ) always has a triality structure, and that this triality induces first an isomorphism H(anti Λ C )≅H(Λ C ) and, through this, a triality of H(anti Λ C ). In the case where C is the Golay code, anti Λ C is the Leech lattice and the induced triality is the extra symmetry necessary to generate the Monster group from (an extension of) Conway's group. Thus it is demonstrated that triality is a generic symmetry. The induced isomorphism accounts for all 9 of the coincidences between the 48 conformal field theories H(Λ) and H(Λ) with N=24. (orig.)

Scaling laws and triviality bounds in the lattice Φ4 theory. Pt. 1

International Nuclear Information System (INIS)

Luescher, M.; Weisz, P.

1987-01-01

The lattice Φ 4 theory in four space-time dimensions is most likely 'trivial', i.e. its continuum limit is a free field theory. However, for small but positive lattice spacing a and at energies well below the cutoff mass Λ=1/a, the theory effectively behaves like a continuum theory with particle interactions, which may be appreciable. By a combination of known analytical methods, we here determine the maximal value of the renormalized coupling at zero momentum as a function of Λ/m, where m denotes the mass of the scalar particle in the theory. Moreover, a complete solution of the model is obtained in the sense that all low energy amplitudes can be computed with reasonable estimated accuracy for arbitrarily chosen bare coupling and mass in the symmetric phase region. (orig.)

[Studies in quantum field theory: Progress report, April 1, 1991--March 31, 1992

International Nuclear Information System (INIS)

Bender, C.M.

1992-01-01

Professors Bender, Bernard, and Shrauner, Assistant Professors Ogilvie and Goltermann, Research Assistant Professors Visser and Petcher, and Research Associate Rivas are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: lattice gauge calculations of masses and weak matrix elements; strong-coupling approximation; low-energy effective field theories; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; the nature of perturbation theory in large order; quark condensation in QCD; chiral fermion theories on the lattice; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including QCD; studies of the early universe and inflation; quantum gravity. This work is described in detail in the body of this proposal

Bell-type quantum field theories

International Nuclear Information System (INIS)

Duerr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghi, Nino

2005-01-01

In his paper (1986 Beables for quantum field theory Phys. Rep. 137 49-54) John S Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a vertical bar Ψ vertical bar 2 -distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; we call such processes Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to 'second quantization'. As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field. (topical review)

Differentiability and continuity of quantum fields on a lattice

International Nuclear Information System (INIS)

deLyra, J.L.; Foong, S.K.; Gallivan, T.E.

1991-01-01

The differentiability and continuity properties of quantized bosonic fields on a lattice are examined. It is shown for free fields that, in the continuum limit, the dominant configurations in the functional integral become discontinuous when the spacetime dimension is greater than 1. It is argued that the same is true for interacting fields. This is unlike the one-dimensional case of quantum mechanics, in which the dominant configurations are continuous but not differentiable. As a consequence of this discontinuity, classically equivalent actions may produce inequivalent quantum field theories upon functional-integral quantization

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.)

Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

Directory of Open Access Journals (Sweden)

Alex Thomson

2018-01-01

Full Text Available Quantum fluctuations of the Néel state of the square lattice antiferromagnet are usually described by a CP^{1} theory of bosonic spinons coupled to a U(1 gauge field, and with a global SU(2 spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS order, and upon including spin-singlet charge-2 Higgs fields, deconfined phases with Z_{2} topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in π flux in each square lattice plaquette. Fluctuations about this π-flux state are described by (2+1-dimensional quantum chromodynamics (QCD_{3} with a SU(2 gauge group and N_{f}=2 flavors of massless Dirac fermions. It has recently been argued by Wang et al. [Deconfined Quantum Critical Points: Symmetries and Dualities, Phys. Rev. X 7, 031051 (2017.PRXHAE2160-330810.1103/PhysRevX.7.031051] that this QCD_{3} theory describes the Néel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD_{3} and obtain fermionic dual descriptions of the phases with Z_{2} topological order obtained earlier using the bosonic CP^{1} theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1 gauge theory of the VBS state. The global phase diagram of these phases contains multicritical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.

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

Upper bound on the cutoff in lattice electroweak theory

International Nuclear Information System (INIS)

Veselov, A.I.; Zubkov, M.A.

2008-01-01

We investigate numerically lattice Weinberg-Salam model without fermions for realistic values of the fine structure constant and the Weinberg angle. We also analyze the data of the previous numerical investigations of lattice Electroweak theory. We have found that moving along the line of constant physics when the lattice spacing a is decreased, one should leave the physical Higgs phase of the theory at a certain value of a. Our estimate of the minimal value of the lattice spacing is a c = [430 ± 40 GeV] -1 .

The coupled cluster theory of quantum lattice systems

International Nuclear Information System (INIS)

Bishop, R.; Xian, Yang

1994-01-01

The coupled cluster method is widely recognized nowadays as providing an ab initio method of great versatility, power, and accuracy for handling in a fully microscopic and systematic way the correlations between particles in quantum many-body systems. The number of successful applications made to date within both chemistry and physics is impressive. In this article, the authors review recent extensions of the method which now provide a unifying framework for also dealing with strongly interacting infinite quantum lattice systems described by a Hamiltonian. Such systems include both spin-lattice models (such as the anisotropic Heisenberg or XXZ model) exhibiting interesting magnetic properties, and electron lattice models (such as the tJ and Hubbard models), where the spins or fermions are localized on the sites of a regular lattice; as well as lattice gauge theories [such as the Abelian U(1) model of quantum electrodynamics and non-Abelian SU(n) models]. Illustrative results are given for both the XXZ spin lattice model and U(1) lattice gauge theory

The 2-D lattice theory of Flower Constellations

Science.gov (United States)

Avendaño, Martín E.; Davis, Jeremy J.; Mortari, Daniele

2013-08-01

The 2-D lattice theory of Flower Constellations, generalizing Harmonic Flower Constellations (the symmetric subset of Flower Constellations) as well as the Walker/ Mozhaev constellations, is presented here. This theory is a new general framework to design symmetric constellations using a 2× 2 lattice matrix of integers or by its minimal representation, the Hermite normal form. From a geometrical point of view, the phasing of satellites is represented by a regular pattern (lattice) on a two-Dimensional torus. The 2-D lattice theory of Flower Constellations does not require any compatibility condition and uses a minimum set of integer parameters whose meaning are explored throughout the paper. This general minimum-parametrization framework allows us to obtain all symmetric distribution of satellites. Due to the J_2 effect this design framework is meant for circular orbits and for elliptical orbits at critical inclination, or to design elliptical constellations for the unperturbed Keplerian case.

Supercomputers and quantum field theory

International Nuclear Information System (INIS)

Creutz, M.

1985-01-01

A review is given of why recent simulations of lattice gauge theories have resulted in substantial demands from particle theorists for supercomputer time. These calculations have yielded first principle results on non-perturbative aspects of the strong interactions. An algorithm for simulating dynamical quark fields is discussed. 14 refs

YANG-MILLS FIELDS AND THE LATTICE.

Energy Technology Data Exchange (ETDEWEB)

CREUTZ,M.

2004-05-18

The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss some of the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.

Introduction to lattice theory with computer science applications

CERN Document Server

Garg, Vijay K

2015-01-01

A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author's intent

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.

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.)

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

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

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

Dynamic scattering theory for dark-field electron holography of 3D strain fields.

Science.gov (United States)

Lubk, Axel; Javon, Elsa; Cherkashin, Nikolay; Reboh, Shay; Gatel, Christophe; Hÿtch, Martin

2014-01-01

Dark-field electron holography maps strain in crystal lattices into reconstructed phases over large fields of view. Here we investigate the details of the lattice strain-reconstructed phase relationship by applying dynamic scattering theory both analytically and numerically. We develop efficient analytic linear projection rules for 3D strain fields, facilitating a straight-forward calculation of reconstructed phases from 3D strained materials. They are used in the following to quantify the influence of various experimental parameters like strain magnitude, specimen thickness, excitation error and surface relaxation. © 2013 Elsevier B.V. All rights reserved.

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

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.

Classification of networks of automata by dynamical mean field theory

International Nuclear Information System (INIS)

Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.

1990-01-01

Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)

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.)

Dynamic scattering theory for dark-field electron holography of 3D strain fields

International Nuclear Information System (INIS)

Lubk, Axel; Javon, Elsa; Cherkashin, Nikolay; Reboh, Shay; Gatel, Christophe; Hÿtch, Martin

2014-01-01

Dark-field electron holography maps strain in crystal lattices into reconstructed phases over large fields of view. Here we investigate the details of the lattice strain–reconstructed phase relationship by applying dynamic scattering theory both analytically and numerically. We develop efficient analytic linear projection rules for 3D strain fields, facilitating a straight-forward calculation of reconstructed phases from 3D strained materials. They are used in the following to quantify the influence of various experimental parameters like strain magnitude, specimen thickness, excitation error and surface relaxation. - Author-Highlights: • We derive a simple dynamic scattering formalism for dark field electron holography based on a perturbative two-beam theory. • The formalism facilitates the projection of 3D strain fields by a simple weighting integral. • The weighted projection depends analytically on the diffraction order, the excitation error and the specimen thickness. • The weighting integral formalism represents an important prerequisite towards the development of tomographic strain reconstruction techniques

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.)

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

Continuum limit and improved action in lattice theories. Pt. 1

International Nuclear Information System (INIS)

Symanzik, K.

1983-03-01

Corrections to continuum theory results stemming from finite lattice-spacing can be diminished systematically by use of lattice actions that include also suitable irrelevant terms. We describe in detail the principles of such constructions at the example of PHI 4 theory. (orig.)

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

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.)

Wilson lines in quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Cherednikov, Igor Olegovich [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.; Joint Institute of Nuclear Research, Moscow (Russian Federation). Bogoliubov Lab. of Theoretical Physics; Mertens, Tom; Veken, Frederik F. van der [Antwerpen Univ., Antwerp (Belgium). Fysica Dept.

2014-07-01

Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

Wilson lines in quantum field theory

International Nuclear Information System (INIS)

Cherednikov, Igor Olegovich; Joint Institute of Nuclear Research, Moscow; Mertens, Tom; Veken, Frederik F. van der

2014-01-01

Wilson lines (also known as gauge links or eikonal lines) can be introduced in any gauge field theory. Although the concept of the Wilson exponentials finds an enormously wide range of applications in a variety of branches of modern quantum field theory, from condensed matter and lattice simulations to quantum chromodynamics, high-energy effective theories and gravity, there are surprisingly few books or textbooks on the market which contain comprehensive pedagogical introduction and consecutive exposition of the subject. The objective of this book is to get the potential reader acquainted with theoretical and mathematical foundations of the concept of the Wilson loops in the context of modern quantum field theory, to teach him/her to perform independently some elementary calculations with Wilson lines, and to familiarize him/her with the recent development of the subject in different important areas of research. The target audience of the book consists of graduate and postgraduate students working in various areas of quantum field theory, as well as researchers from other fields.

On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories

Science.gov (United States)

Belletête, J.; Gainutdinov, A. M.; Jacobsen, J. L.; Saleur, H.; Vasseur, R.

2017-12-01

The relationship between bulk and boundary properties is one of the founding features of (rational) conformal field theory (CFT). Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice models. We focus on models based on the Temperley-Lieb algebra, and use the concept of ‘braid translation’, which is a natural way, in physical terms, to ‘close’ an open spin chain by adding an interaction between the first and last spins using braiding to ‘bring’ them next to each other. The interaction thus obtained is in general non-local, but has the key feature that it is expressed solely in terms of the algebra for the open spin chain—the ‘ordinary’ Temperley-Lieb algebra and its blob algebra generalization. This is in contrast with the usual periodic spin chains which involve only local interactions, and are described by the periodic Temperley-Lieb algebra. We show that for the restricted solid-on-solid models, which are known to be described by minimal unitary CFTs (with central charge ccontent in terms of the irreducibles is the same, as well as the spectrum, but the detailed structure (like logarithmic coupling) is profoundly different. This carries over to the continuum limit. The situation is similar for the sl(2\\vert 1) case. The problem of relating bulk and boundary lattice models for LCFTs thus remains open.

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.

Vortex structure in abelian-projected lattice gauge theory

International Nuclear Information System (INIS)

Ambjoern, J.; Giedt, J.; Greensite, J.

2000-01-01

We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice has at most a global Z 2 symmetry in the confined phase, rather than the global U(1) symmetry that might be expected in a dual superconductor or monopole Coulomb gas picture. Implications for monopole and center vortex theories of confinement are discussed

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

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

Associative-algebraic approach to logarithmic conformal field theories

International Nuclear Information System (INIS)

Read, N.; Saleur, Hubert

2007-01-01

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non-semisimple associative algebras appearing in their lattice regularizations (as discussed in a companion paper [N. Read, H. Saleur, Enlarged symmetry algebras of spin chains, loop models, and S-matrices, cond-mat/0701259]). Here we work out in detail two examples of theories derived as the continuum limit of XXZ spin-1/2 chains, which are related to spin chains with supersymmetry algebras gl(n|n) and gl(n+1 vertical bar n), respectively, with open (or free) boundary conditions in all cases. These theories can also be viewed as vertex models, or as loop models. Their continuum limits are boundary conformal field theories (CFTs) with central charge c=-2 and c=0 respectively, and in the loop interpretation they describe dense polymers and the boundaries of critical percolation clusters, respectively. We also discuss the case of dilute (critical) polymers as another boundary CFT with c=0. Within the supersymmetric formulations, these boundary CFTs describe the fixed points of certain nonlinear sigma models that have a supercoset space as the target manifold, and of Landau-Ginzburg field theories. The submodule structures of indecomposable representations of the Virasoro algebra appearing in the boundary CFT, representing local fields, are derived from the lattice. A central result is the derivation of the fusion rules for these fields

Lattice Methods and the Nuclear Few- and Many-Body Problem

Science.gov (United States)

Lee, Dean

This chapter builds upon the review of lattice methods and effective field theory of the previous chapter. We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.

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)

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

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

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

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.)

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.

Nucleon Polarisabilities and Effective Field Theories

Science.gov (United States)

Griesshammer, Harald W.

2017-09-01

Low-energy Compton scattering probes the nucleon's two-photon response to electric and magnetic fields at fixed photon frequency and multipolarity. It tests the symmetries and strengths of the interactions between constituents, and with photons. For convenience, this energy-dependent information is often compressed into the two scalar dipole polarisabilities αE 1 and βM 1 at zero photon energy. These are fundamental quantities, and important for the proton charge radius puzzle and the Lamb shift of muonic hydrogen. Combined with emerging lattice QCD computations, they provide stringent tests for our understanding of hadron structure. Extractions of the proton and neutron polarisabilities from all published elastic data below 300 MeV in Chiral Effective Field Theory with explicit Δ (1232) are now available. This talk emphasises χEFT as natural bridge between lattice QCD and ongoing or approved efforts at HI γS, MAMI and MAX-lab. Chiral lattice extrapolations from mπ > 200 MeV to the physical point compare well to lattice computations. Combining χEFT with high-intensity experiments with polarised targets and polarised beams will extract not only scalar polarisabilities, but in particular the four so-far poorly explored spin-polarisabilities. These parametrise the stiffness of the spin in external electro-magnetic fields (nucleonic bi-refringence/Faraday effect). New chiral predictions for proton, deuteron and 3He observables show intriguing sensitivities on spin and neutron polarisabilities. Data consistency and a model-independent quantification of residual theory uncertainties by Bayesian analysis are also discussed. Proton-neutron differences explore the interplay between chiral symmetry breaking and short-distance Physics. Finally, I address their impact on the neutron-proton mass difference, big-bang nucleosynthesis, and their relevance for anthropic arguments. Supported in part by DOE DE-SC0015393 and George Washington University.

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.)

Some topics in quantum field theory

International Nuclear Information System (INIS)

Symanzik, K.

1981-10-01

After a few general remarks on lattice theory, I describe the relation of lattice to continuum theory on the basis of perturbation theory, and deduce herefrom the principles of constructing 'improved' lattice actions. Then I briefly describe some recent perturbative and nonperturbative results in continuum theory. Finally, I point out a few recent approaches of more speculative nature that appear to merit particular attention. In the appendix, a few standard formulae from renormalization group analysis are collected for reference. (orig./HSI)

Phase diagram and Chiral Magnetic Effect in Dirac Semimetals from Lattice Simulation

Directory of Open Access Journals (Sweden)

Boyda D.L.

2018-01-01

Full Text Available Dirac Semimetals Na3Bi and Cd3As2 are recently discovered materials, which low energy electronic spectrum is described by two flavours of massless 3+1D fermions. In order to study electronic properties of these materials we formulated lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reproduces effective theory of Dirac semimetals. Using the lattice field theory we study the phase diagram of Dirac semimetals in the plane effective coupling constant - Fermi velocity anisotropy. We also measure conductivity of Dirac Semimetals within lattice field theory in external magnetic field. Our results confirm the existence of Chiral Magnetic Effect in Dirac Semimetals.

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...

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

Why QCD lattice theory is important to spin physicists

International Nuclear Information System (INIS)

Rebbi, C.

1982-01-01

The lattice formulation of a quantum field theory allows calculations in the regime of strong coupling, by expansion techniques, and for intermediate coupling, by Monte Carlo simulations. These computations are especially valuable in the case of Quantum Chromodynamics (QCD), where several of the most important problems are not amenable to a perturbative analysis. Monte carlo simulations, in particular, have recently emerged as a very powerful tool and have been used to evaluate a variety of important physical quantities, such as the string tension, the deconfinement temperature, the scale of the interquark potential, glueball masses and masses in the quark model spectrum. If we consider those problems of strong interactions where spin plays an important role, it is unlikely, for the moment at least, that the lattice formulation may be of relevance where the phenomena being investigated involve propagations over extended domains of space-time; thus, for instance, it is impossible to perform a meaningful simulation of a scattering experiment on the lattice. But we are at the stage where Monte Carlo calculations begin to provide relevant information on spectroscopic properties related to spin. These are briefly discussed

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.

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

Energy Technology Data Exchange (ETDEWEB)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2017-07-15

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

International Nuclear Information System (INIS)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda

2017-07-01

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

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.

Discrete field theories and spatial properties of strings

International Nuclear Information System (INIS)

Klebanov, I.; Susskind, L.

1988-10-01

We use the ground-state wave function in the light-cone gauge to study the spatial properties of fundamental strings. We find that, as the cut-off in the parameter space is removed, the strings are smooth and have a divergent size. Guided by these properties, we consider a large-N lattice gauge theory which has an unstable phase where the size of strings diverges. We show that this phase exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero for this equivalence to hold. Thus, exact rotation and translation invariance is restored in a discrete space. This suggests that the number of fundamental short-distance degrees of freedom in string theory is much smaller than in a conventional field theory. 11 refs., 4 figs

Effective field theory and integrability in two-dimensional Mott transition

International Nuclear Information System (INIS)

Bottesi, Federico L.; Zemba, Guillermo R.

2011-01-01

Highlights: → Mott transition in 2d lattice fermion model. → 3D integrability out of 2D. → Effective field theory for Mott transition in 2d. → Double Chern-Simons. → d-Density waves. - Abstract: We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a quantum group symmetry as a consequence of a recently found solution of the Zamolodchikov tetrahedron equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U q (sl(2)-circumflex)xU q (sl(2)-circumflex), with deformation parameter q = -1. Based on this result, the low-energy effective field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k = 1 (with the standard normalization). By further employing the effective filed theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.

On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory

International Nuclear Information System (INIS)

Catterall, Simon

2007-01-01

We study a discretization of N = 2 super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of twisted fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence supporting a restoration of (twisted) rotational invariance in the same limit. Finally we have examined the distribution of scalar field eigenvalues and find evidence for power law tails extending out to large eigenvalue. We argue that these tails indicate that the classical moduli space does not survive in the quantum theory

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.)

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.

Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges

International Nuclear Information System (INIS)

Cohen, Andrew G.; Kaplan, David B.; Katz, Emanuel; Uensal, Mithat

2003-01-01

We formulate a euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions. (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.

Microscopic theory for coupled atomistic magnetization and lattice dynamics

Science.gov (United States)

Fransson, J.; Thonig, D.; Bessarab, P. F.; Bhattacharjee, S.; Hellsvik, J.; Nordström, L.

2017-12-01

A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known interatomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double-antiferromagnetic materials, as well as charge density waves induced by a nonuniform spin structure, are given. In the final parts, coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and a damped driven mechanical oscillator for the ionic motion. It is important to notice, however, that these equations comprise contributions that couple these descriptions into one unified formulation. Finally, Kubo-like expressions for

Proceedings of the international colloquium on modern quantum field theory II

International Nuclear Information System (INIS)

Das, S.R.; Mandal, G.; Mukhi, S.; Wadia, S.R.

1995-01-01

In the second International Colloquium on Modern Quantum Field Theory an attempt was made to cover a broad spectrum of topics in theoretical physics that included string theory, quantum gravity, statistical mechanics, condensed matter theory, complexity, lattice gauge theory and epistemological aspects of quantum mechanics. Papers relevant to INIS in the published proceedings are indexed separately

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

Testing the Standard Model and Fundamental Symmetries in Nuclear Physics with Lattice QCD and Effective Field Theory

Energy Technology Data Exchange (ETDEWEB)

Walker-Loud, Andre [College of William and Mary, Williamsburg, VA (United States)

2016-10-14

The research supported by this grant is aimed at probing the limits of the Standard Model through precision low-energy nuclear physics. The work of the PI (AWL) and additional personnel is to provide theory input needed for a number of potentially high-impact experiments, notably, hadronic parity violation, Dark Matter direct detection and searches for permanent electric dipole moments (EDMs) in nucleons and nuclei. In all these examples, a quantitative understanding of low-energy nuclear physics from the fundamental theory of strong interactions, Quantum Chromo-Dynamics (QCD), is necessary to interpret the experimental results. The main theoretical tools used and developed in this work are the numerical solution to QCD known as lattice QCD (LQCD) and Effective Field Theory (EFT). This grant is supporting a new research program for the PI, and as such, needed to be developed from the ground up. Therefore, the first fiscal year of this grant, 08/01/2014-07/31/2015, has been spent predominantly establishing this new research effort. Very good progress has been made, although, at this time, there are not many publications to show for the effort. After one year, the PI accepted a job at Lawrence Berkeley National Laboratory, so this final report covers just a single year of five years of the grant.

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.

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.)

Orbital effect of the magnetic field in dynamical mean-field theory

Science.gov (United States)

Acheche, S.; Arsenault, L.-F.; Tremblay, A.-M. S.

2017-12-01

The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.

Matching fields and lattice points of simplices

OpenAIRE

Loho, Georg; Smith, Ben

2018-01-01

We show that the Chow covectors of a linkage matching field define a bijection of lattice points and we demonstrate how one can recover the linkage matching field from this bijection. This resolves two open questions from Sturmfels & Zelevinsky (1993) on linkage matching fields. For this, we give an explicit construction that associates a bipartite incidence graph of an ordered partition of a common set to all lattice points in a dilated simplex. Given a triangulation of a product of two simp...

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

Proceedings of the 5. Jorge Andre Swieca Summer School Field Theory and Particle Physics

International Nuclear Information System (INIS)

Eboli, O.J.P.; Gomes, M.; Santoro, A.

1989-01-01

Lectures on quantum field theories and particle physics are presented. The part of quantum field theories contains: constrained dynamics; Schroedinger representation in field theory; application of this representation to quantum fields in a Robertson-Walker space-time; Berry connection; problem of construction and classification of conformal field theories; lattice models; two-dimensional S matrices and conformal field theory for unifying perspective of Yang-Baxter algebras; parasupersymmetric quantum mechanics; introduction to string field theory; three dimensional gravity and two-dimensional parafermionic model. The part of particle physics contains: collider physics; strong interactions and use of strings in strong interactions. (M.C.K.)

Chiral soliton lattice and charged pion condensation in strong magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Brauner, Tomáš [Faculty of Science and Technology, University of Stavanger,N-4036 Stavanger (Norway); Yamamoto, Naoki [Department of Physics, Keio University,Yokohama 223-8522 (Japan)

2017-04-21

The Chiral Soliton Lattice (CSL) is a state with a periodic array of topological solitons that spontaneously breaks parity and translational symmetries. Such a state is known to appear in chiral magnets. We show that CSL also appears as a ground state of quantum chromodynamics at nonzero chemical potential in a magnetic field. By analyzing the fluctuations of the CSL, we furthermore demonstrate that in strong but achievable magnetic fields, charged pions undergo Bose-Einstein condensation. Our results, based on a systematic low-energy effective theory, are model-independent and fully analytic.

Topics in field theory

International Nuclear Information System (INIS)

Velasco, E.S.

1986-01-01

This dissertation deals with several topics of field theory. Chapter I is a brief outline of the work presented in the next chapters. In chapter II, the Gauss-Bonnet-Chern theorem for manifolds with boundary is computed using the path integral representation of the Witten index for supersymmetric quantum mechanical systems. In chapter III the action of N = 2 (Poincare) supergravity is obtained in terms of N = 1 superfields. In chapter IV, N = 2 supergravity coupled to the (abelian) vector multiplet is projected into N - 1 superspace. There, the resulting set of constraints is solved in terms of unconstrained prepotential and the action in terms of N = 1 superfields is constructed. In chapter V the set of constraints for N = 2 conformal supergravity is projected into N = 1 superspace and solved in terms of N = 1 conformal supergravity fields a d matter prepotentials. In chapter VI the role of magnetic monopoles in the phase structure of the change one fixed length abelian Higgs model ins the latticer is investigated using analytic and numerical methods. The technique of monopole suppression is used to determine the phase transition lines that are monopole driven. Finally in chapter VII, the role of the charge of the Higgs field in the abelian Higgs model in the lattice is investigated

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.

Time evolution of linearized gauge field fluctuations on a real-time lattice

Energy Technology Data Exchange (ETDEWEB)

Kurkela, A. [CERN, Theoretical Physics Department, Geneva (Switzerland); University of Stavanger, Faculty of Science and Technology, Stavanger (Norway); Lappi, T. [University of Jyvaeskylae, Department of Physics, P.O. Box 35, Jyvaeskylae (Finland); University of Helsinki, Helsinki Institute of Physics, P.O. Box 64, Helsinki (Finland); Peuron, J. [University of Jyvaeskylae, Department of Physics, P.O. Box 35, Jyvaeskylae (Finland)

2016-12-15

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. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law. (orig.)

Time evolution of linearized gauge field fluctuations on a real-time lattice

CERN Document Server

Kurkela, Aleksi; Peuron, Jarkko

2016-01-01

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. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss's law.

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.

Two-dimensional models in statistical mechanics and field theory

International Nuclear Information System (INIS)

Koberle, R.

1980-01-01

Several features of two-dimensional models in statistical mechanics and Field theory, such as, lattice quantum chromodynamics, Z(N), Gross-Neveu and CP N-1 are discussed. The problems of confinement and dynamical mass generation are also analyzed. (L.C.) [pt

Computing: Lattice work

International Nuclear Information System (INIS)

Bowler, Ken

1990-01-01

One of the major recent developments in particle theory has been the use of very high performance computers to obtain approximate numerical solutions of quantum field theories by formulating them on a finite space-time lattice. The great virtue of this new technique is that it avoids the straitjacket of perturbation theory and can thus attack new, but very fundamental problems, such as the calculation of hadron masses in quark-gluon field theory (quantum chromodynamics - QCD)

An overview of lattice QCD

International Nuclear Information System (INIS)

Woloshyn, R.M.

1988-03-01

The basic concepts of the Lagrangian formulation of lattice field theory are discussed. The Wilson and staggered schemes for dealing with fermions on the lattice are described. Some recent results for hadron masses and vector and axial vector current matrix elements in lattice QCD are reviewed. (Author) (118 refs., 16 figs.)

The Alternation Hierarchy for the Theory of µ-lattices

DEFF Research Database (Denmark)

Santocanale, Luigi

2002-01-01

independent of φ. In this paper we give a proof that the alternation hierarchy for the theory of µ-lattices is strict, meaning that such a constant does not exist if µ-term are built up from the basic lattice operations and are interpreted as expected. The proof relies on the explicit characterization of free...

Particle linear theory on a self-gravitating perturbed cubic Bravais lattice

International Nuclear Information System (INIS)

Marcos, B.

2008-01-01

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.

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.)

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

Statistical approach to quantum field theory. An introduction

International Nuclear Information System (INIS)

Wipf, Andreas

2013-01-01

Based on course-tested notes and pedagogical in style. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Contains end-of-chapter problems and listings of short, useful computer programs. Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an ''experimental'' tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as

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

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.

Nf=2 Lattice QCD and Chiral Perturbation Theory

International Nuclear Information System (INIS)

Scorzato, L.; Farchioni, F.; Hofmann, P.; Jansen, K.; Montvay, I.; Muenster, G.; Papinutto, M.; Scholz, E.E.; Shindler, A.; Ukita, N.; Urbach, C.; Wenger, U.; Wetzorke, I.

2006-01-01

By employing a twisted mass term, we compare recent results from lattice calculations of N f =2 dynamical Wilson fermions with Wilson Chiral Perturbation Theory (WChPT). The final goal is to determine some com- binations of Gasser-Leutwyler Low Energy Constants (LECs). A wide set of data with different lattice spacings (a ∼ 0.2 - 0.12 fm), different gauge actions (Wilson plaquette, DBW2) and different quark masses (down to the lowest pion mass allowed by lattice artifacts and including negative quark masses) provide a strong check of the applicability of WChPT in this regime and the scaling behaviours in the continuum limit

Topological charge on the lattice: a field theoretical view of the geometrical approach

International Nuclear Information System (INIS)

Rastelli, L.; Rossi, P.; Vicari, E.

1997-01-01

We construct sequences of ''field theoretical'' lattice topological charge density operators which formally approach geometrical definitions in 2D CP N-1 models and 4D SU(N) Yang-Mills theories. The analysis of these sequences of operators suggests a new way of looking at the geometrical method, showing that geometrical charges can be interpreted as limits of sequences of field theoretical (analytical) operators. In perturbation theory, renormalization effects formally tend to vanish along such sequences. But, since the perturbative expansion is asymptotic, this does not necessarily lead to well-behaved geometrical limits. It indeed leaves open the possibility that non-perturbative renormalizations survive. (orig.)

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

Current density functional theory in a continuum and lattice Lagrangians: Application to spontaneously broken chiral ground states

International Nuclear Information System (INIS)

Rasolt, M.; Vignale, G.

1992-03-01

We formulate the current-density functional theory for systems in arbitrarily strong magnetic fields. A set of self-consistent equations comparable to the Kohn-Sham equations for ordinary density functional theory is derived, and proved to be gauge-invariant and to satisfy the continuity equation. These equations of Vignale and Rasolt involve the gauge field corresponding to the external magnetic field as well as a new gauge field generated entirely from the many-body interactions. We next extend this gauge theory (following Rasolt and Vignale) to a lattice Lagrangian believed to be appropriate to a tight-binding Hamiltonian in the presence of an external magnetic field. We finally examine the nature of the ground state of a strongly nonuniform electron gas in the presence of this many-body self-induced gauge field

Multi-graviton theory, a latticized dimension and the cosmological constant

International Nuclear Information System (INIS)

Kan, Nahomi; Shiraishi, Kiyoshi

2003-01-01

Beginning with the Pauli-Fierz theory, we construct a model for multi-graviton theory. Couplings between gravitons belonging to nearest-neighbour 'theory spaces' lead to a discrete mass spectrum. Our model coincides with the Kaluza-Klein theory whose fifth dimension is latticized. We evaluate one-loop vacuum energy in models with a circular latticized extra dimension as well as with compact continuous dimensions. We find that the vacuum energy can take a positive value, if the dimension of the continuous spacetime is 6, 10, .... Moreover, since the amount of vacuum energy can be an arbitrary small value depending on the choice of parameters in the model, our models are useful for explaining the small positive dark energy in the present universe

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.)

Novel interpolative perturbation theory for quantum anharmonic oscillators in one and three dimensions and the ground state of a lattice model of the phi4 field theory

International Nuclear Information System (INIS)

Ginsburg, C.A.

1977-01-01

A new method for approximating the eigenfunctions and eigenvalues of anharmonic oscillators. An attempt was made to develop an analytic method which provides simple formulae for all values of the parameters as the W.K.B. approximation and perturbation theory do for certain limiting case, and which has the convergence properties associated with the computer methods. The procedure is based upon combining knowledge of the asymptotic behavior of the wave function for large and small values of the coordinate(s) to obtain approximations valid for all values of coordinate(s) and all strengths of the anharmonicity. A systematic procedure for improving these approximations is developed. Finally the groundstate of a lattice model of the phi 4 field theory which consists of an infinite number of coupled anharmonic oscillators. A first order calculation yields a covariant expression for the groundstate eigenvalue with the physical mass, m, given by a characteristic polynomial which involves the bare mass, μ, the lattice spacing, l, and the coupling constant, lambda. For l > 0, μ can be adjusted (a mass renormalization) 0 < m < infinity. As l → 0 lambda (l) (a charge renormalization) is adjusted so that lambda/sup 1/3//l → eta, a constant, as l → 0. Then eta can be chosen so that m can take any experimental value

Scattering of decuplet baryons in chiral effective field theory

Energy Technology Data Exchange (ETDEWEB)

Haidenbauer, J. [Institut fuer Kernphysik, Institute for Advanced Simulation and Juelich Center for Hadron Physics, Juelich (Germany); Petschauer, S.; Kaiser, N.; Weise, W. [Technische Universitaet Muenchen, Physik Department, Garching (Germany); Meissner, Ulf G. [Institut fuer Kernphysik, Institute for Advanced Simulation and Juelich Center for Hadron Physics, Juelich (Germany); Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany)

2017-11-15

A formalism for treating the scattering of decuplet baryons in chiral effective field theory is developed. The minimal Lagrangian and potentials in leading-order SU(3) chiral effective field theory for the interactions of octet baryons (B) and decuplet baryons (D) for the transitions BB → BB, BB <-> DB, DB → DB, BB <-> DD, DB <-> DD, and DD → DD are provided. As an application of the formalism we compare with results from lattice QCD simulations for ΩΩ and NΩ scattering. Implications of our results pertinent to the quest for dibaryons are discussed. (orig.)

Role of elasticity forces in thermodynamics of intercalation compounds : Self-consistent mean-field theory and Monte Carlo simulations

NARCIS (Netherlands)

Kalikmanov, V.I.; De Leeuw, S.W.

2002-01-01

We propose a self-consistent mean-field lattice-gas theory of intercalation compounds based on effective interactions between interstitials in the presence of the host atoms. In addition to short-range screened Coulomb repulsions, usually discussed in the lattice gas models, the present theory takes

Superspace approach to lattice supersymmetry

International Nuclear Information System (INIS)

Kostelecky, V.A.; Rabin, J.M.

1984-01-01

We construct a cubic lattice of discrete points in superspace, as well as a discrete subgroup of the supersymmetry group which maps this ''superlattice'' into itself. We discuss the connection between this structure and previous versions of lattice supersymmetry. Our approach clarifies the mathematical problems of formulating supersymmetric lattice field theories and suggests new methods for attacking them

Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory

Science.gov (United States)

Riello, Aldo

2018-01-01

I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.

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.)

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

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

Introduction to Vortex Lattice Theory

Directory of Open Access Journals (Sweden)

Santiago Pinzón

2015-10-01

Full Text Available Panel methods have been widely used in industry and are well established since the 1970s for aerodynamic analysis and computation. The Vortex Lattice Panel Method presented in this study comes across a sophisticated method that provides a quick solution time, allows rapid changes in geometry and suits well for aerodynamic analysis. The aerospace industry is highly competitive in design efficiency, and perhaps one of the most important factors on airplane design and engineering today is multidisciplinary optimization.  Any cost reduction method in the design cycle of a product becomes vital in the success of its outcome. The subsequent sections of this article will further explain in depth the theory behind the vortex lattice method, and the reason behind its selection as the method for aerodynamic analysis during preliminary design work and computation within the aerospace industry. This article is analytic in nature, and its main objective is to present a mathematical summary of this widely used computational method in aerodynamics.

Quantum field theories on algebraic curves. I. Additive bosons

International Nuclear Information System (INIS)

Takhtajan, Leon A

2013-01-01

Using Serre's adelic interpretation of cohomology, we develop a 'differential and integral calculus' on an algebraic curve X over an algebraically closed field k of constants of characteristic zero, define algebraic analogues of additive multi-valued functions on X and prove the corresponding generalized residue theorem. Using the representation theory of the global Heisenberg algebra and lattice Lie algebra, we formulate quantum field theories of additive and charged bosons on an algebraic curve X. These theories are naturally connected with the algebraic de Rham theorem. We prove that an extension of global symmetries (Witten's additive Ward identities) from the k-vector space of rational functions on X to the vector space of additive multi-valued functions uniquely determines these quantum theories of additive and charged bosons.

δ expansion for a quantum field theory in the nonperturbative regime

International Nuclear Information System (INIS)

Bender, C.M.; Milton, K.A.; Pinsky, S.S.; Simmons, L.M. Jr.

1990-01-01

The δ expansion, a recently proposed nonperturbative technique in quantum field theory, is used to calculate the dimensionless renormalized coupling constant of a λ(var-phi 2 ) 1+δ quantum field theory in d-dimensional space-time at the critical point defined by λ→∞ with the renormalized mass held fixed. The calculation is performed to leading order in δ and compared with previous lattice strong-coupling calculations. The numerical results are good and provide new evidence that the theory in four dimensions is free for all δ

Statistical mechanics and field theory

International Nuclear Information System (INIS)

Samuel, S.A.

1979-05-01

Field theory methods are applied to statistical mechanics. Statistical systems are related to fermionic-like field theories through a path integral representation. Considered are the Ising model, the free-fermion model, and close-packed dimer problems on various lattices. Graphical calculational techniques are developed. They are powerful and yield a simple procedure to compute the vacuum expectation value of an arbitrary product of Ising spin variables. From a field theorist's point of view, this is the simplest most logical derivation of the Ising model partition function and correlation functions. This work promises to open a new area of physics research when the methods are used to approximate unsolved problems. By the above methods a new model named the 128 pseudo-free vertex model is solved. Statistical mechanics intuition is applied to field theories. It is shown that certain relativistic field theories are equivalent to classical interacting gases. Using this analogy many results are obtained, particularly for the Sine-Gordon field theory. Quark confinement is considered. Although not a proof of confinement, a logical, esthetic, and simple picture is presented of how confinement works. A key ingredient is the insight gained by using an analog statistical system consisting of a gas of macromolecules. This analogy allows the computation of Wilson loops in the presence of topological vortices and when symmetry breakdown occurs in the topological quantum number. Topological symmetry breakdown calculations are placed on approximately the same level of rigor as instanton calculations. The picture of confinement that emerges is similar to the dual Meissner type advocated by Mandelstam. Before topological symmetry breakdown, QCD has monopoles bound linearly together by three topological strings. Topological symmetry breakdown corresponds to a new phase where these monopoles are liberated. It is these liberated monopoles that confine quarks. 64 references

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.

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.

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...

Non-Abelian vortex lattices

Science.gov (United States)

Tallarita, Gianni; Peterson, Adam

2018-04-01

We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.

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.

Hot B violation, the lattice, and hard thermal loops

International Nuclear Information System (INIS)

Arnold, P.

1997-01-01

It has recently been argued that the rate per unit volume of baryon number violation (topological transitions) in the hot, symmetric phase of electroweak theory is of the form ηα w 5 T 4 in the weak-coupling limit, where η is a nonperturbative numerical coefficient. Over the past several years, there have been attempts to extract the rate of baryon number violation from real-time simulations of classical thermal field theory on a spatial lattice. Unfortunately, the coefficient η will not be the same for classical lattice theories and the real quantum theory. However, by analyzing the appropriate effective theory on the lattice using the method of hard thermal loops, I show that the only obstruction to precisely relating the rates in the real and lattice theories is the fact that the long-distance physics on the lattice is not rotationally invariant. (This is unlike Euclidean-time measurements, where rotational invariance is always recovered in the continuum limit.) I then propose how this violation of rotational invariance can be eliminated emdash and the real B violation rate measured emdash by choosing an appropriate lattice Hamiltonian. I also propose a rough measure of the systematic error to be expected from using simpler, unimproved Hamiltonians. As a byproduct of my investigation, the plasma frequency and Debye mass are computed for classical thermal field theory on the lattice. copyright 1997 The American Physical Society

The ergodic theory of lattice subgroups

CERN Document Server

Gorodnik, Alexander

2010-01-01

The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean

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

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.

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.

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.)

K theoretical approach to the fusion rules of conformal quantum field theories

International Nuclear Information System (INIS)

Recknagel, A.

1993-09-01

Conformally invariant quantum field theories are investigated using concepts of the algebraic approach to quantum field theory as well as techniques from the theory of operator algebras. Arguments from the study of statistical lattice models in one and two dimensions, from recent developments in algebraic quantum field theory, and from other sources suggest that there exists and intimate connection between conformal field theories and a special class of C*-algebras, the so-called AF-algebras. For a series of Virasoro minimal models, this correspondence is made explicit by constructing path representations of the irreducible highest weight modules. We then focus on the K 0 -invariant of these path AF-algebras and show how its functorial properties allow to exploit the abstract theory of superselection sectors in order to derive the fusion rules of the W-algebras hidden in the Virasoro minimal models. (orig.)

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.

Ghost circles in lattice Aubry-Mather theory

Science.gov (United States)

Mramor, Blaz; Rink, Bob

Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics, as models for ferromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multi-dimensional counterpart of monotone twist maps. Such recurrence relations often admit a variational structure, so that the solutions x:Z→R are the stationary points of a formal action function W(x). Given any rotation vector ω∈R, classical Aubry-Mather theory establishes the existence of a large collection of solutions of ∇W(x)=0 of rotation vector ω. For irrational ω, this is the well-known Aubry-Mather set. It consists of global minimizers and it may have gaps. In this paper, we study the parabolic gradient flow {dx}/{dt}=-∇W(x) and we will prove that every Aubry-Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called 'ghost circle'. The existence of these ghost circles is known in dimension d=1, for rational rotation vectors and Morse action functions. The main technical result of this paper is therefore a compactness theorem for lattice ghost circles, based on a parabolic Harnack inequality for the gradient flow. This implies the existence of lattice ghost circles of arbitrary rotation vectors and for arbitrary actions. As a consequence, we can give a simple proof of the fact that when an Aubry-Mather set has a gap, then this gap must be filled with minimizers, or contain a non-minimizing solution.

Does one see gluon condensation after subtraction of mean field perturbation theory from Monte Carlo data

International Nuclear Information System (INIS)

Schlichting, H.

1985-01-01

We do a linearised mean field calculation in axial gauge for the four dimensional mixed fundamental adjoint SU(2) lattice gauge theory and extract the gluon condensate parameter from the expectation values of the plaquette and the action by subtracting mean field perturbation theory from Monte Carlo data. (orig.)

Vector fields and gravity on the lattice

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

1988-01-01

The problem of discretization of vector field on Regge lattice is considered. Our approach is based on geometrical interpretation of the vector field as the field of infinitesimal coordinate transformation. A discrete version of the vector field action is obtained as a particular case of the continuum action, and it is shown to have the true continuum limit

Lattice simulations of QCD-like theories at finite baryon density

Energy Technology Data Exchange (ETDEWEB)

Scior, Philipp Friedrich

2016-07-13

The exploration of the phase diagram of quantum chromodynamics (QCD) is of great importance to describe e.g. the properties of neutron stars or heavy-ion collisions. Due to the sign problem of lattice QCD at finite chemical potential we need effective theories to study QCD at finite density. Here, we use a three-dimensional Polyakov-loop theory to study the phase diagrams of QCD-like theories. In particular, we investigate the heavy quark limit of the QCD-like theories where the effective theory can be derived from the full theory by a combined strong coupling and hopping expansion. This expansion can be systematically improved order by order. Since there is no sign problem for the QCD-like theories we consider, we can compare our results to data from lattice calculations of the full theories to make qualitative and quantitative statements of the effective theory's validity. We start by deriving the effective theory up to next-to-next-to leading-order, in particular for two-color and G{sub 2}-QCD where replace the three colors in QCD with only two colors or respectively replace the gauge group SU(3) of QCD with G{sub 2}. We will then apply the effective theory at finite temperature mainly to test the theory and the implementation but also to make some predictions for the deconfinement phase transition in G{sub 2} Yang-Mills theory. Finally, we turn our attention to the cold and dense regime of the phase diagram where we observe a sharp increase of the baryon density with the quark chemical potential μ, when μ reaches half the diquark mass. At vanishing temperature this is expected to happen in a quantum phase transition with Bose-Einstein-condensation of diquarks. In contrast to the liquid-gas transition in QCD, the phase transition to the Bose-Einstein condensate is continuous. We find evidence that the effective theories for heavy quarks are able to describe the qualitative difference between first and second order phase transitions. For even higher μ we

Lattice simulations of QCD-like theories at finite baryon density

International Nuclear Information System (INIS)

Scior, Philipp Friedrich

2016-01-01

The exploration of the phase diagram of quantum chromodynamics (QCD) is of great importance to describe e.g. the properties of neutron stars or heavy-ion collisions. Due to the sign problem of lattice QCD at finite chemical potential we need effective theories to study QCD at finite density. Here, we use a three-dimensional Polyakov-loop theory to study the phase diagrams of QCD-like theories. In particular, we investigate the heavy quark limit of the QCD-like theories where the effective theory can be derived from the full theory by a combined strong coupling and hopping expansion. This expansion can be systematically improved order by order. Since there is no sign problem for the QCD-like theories we consider, we can compare our results to data from lattice calculations of the full theories to make qualitative and quantitative statements of the effective theory's validity. We start by deriving the effective theory up to next-to-next-to leading-order, in particular for two-color and G_2-QCD where replace the three colors in QCD with only two colors or respectively replace the gauge group SU(3) of QCD with G_2. We will then apply the effective theory at finite temperature mainly to test the theory and the implementation but also to make some predictions for the deconfinement phase transition in G_2 Yang-Mills theory. Finally, we turn our attention to the cold and dense regime of the phase diagram where we observe a sharp increase of the baryon density with the quark chemical potential μ, when μ reaches half the diquark mass. At vanishing temperature this is expected to happen in a quantum phase transition with Bose-Einstein-condensation of diquarks. In contrast to the liquid-gas transition in QCD, the phase transition to the Bose-Einstein condensate is continuous. We find evidence that the effective theories for heavy quarks are able to describe the qualitative difference between first and second order phase transitions. For even higher μ we find the rise of the

Dimers and the Critical Ising Model on lattices of genus >1

International Nuclear Information System (INIS)

Costa-Santos, Ruben; McCoy, B.M.

2002-01-01

We study the partition function of both Close-Packed Dimers and the Critical Ising Model on a square lattice embedded on a genus two surface. Using numerical and analytical methods we show that the determinants of the Kasteleyn adjacency matrices have a dependence on the boundary conditions that, for large lattice size, can be expressed in terms of genus two theta functions. The period matrix characterizing the continuum limit of the lattice is computed using a discrete holomorphic structure. These results relate in a direct way the lattice combinatorics with conformal field theory, providing new insight to the lattice regularization of conformal field theories on higher genus Riemann surfaces

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.

Cutoff dependence in lattice phi44 theory

International Nuclear Information System (INIS)

Symanzik, K.

1979-11-01

The author discusses corrections to the high temperature expansion of the lattice phi 4 4 theory in 4 + epsilon dimensions using the renormalization group. He works with vertex functions, whose expansion is derived from an effective Lagrangian for large-cutoff behaviour. He concludes that the numerical phi 4 4 results offer a test of the idea of asymptotic freedom. (HSI)

Dual field theories of quantum computation

International Nuclear Information System (INIS)

Vanchurin, Vitaly

2016-01-01

Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N+1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N

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.)

Integrable structures in quantum field theory

International Nuclear Information System (INIS)

Negro, Stefano

2016-01-01

This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q -operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only. (topical review)

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.)

Lattice Yang-Mills theory at finite densities of heavy quarks

International Nuclear Information System (INIS)

Langfeld, Kurt; Shin, Gwansoo

2000-01-01

SU(N c ) Yang-Mills theory is investigated at finite densities of N f heavy quark flavors. The calculation of the (continuum) quark determinant in the large-mass limit is performed by analytic methods and results in an effective gluonic action. This action is then subject to a lattice representation of the gluon fields and computer simulations. The approach maintains the same number of quark degrees of freedom as in the continuum formulation and a physical heavy quark limit (to be contrasted with the quenched approximation N f →0). The proper scaling towards the continuum limit is manifest. We study the partition function for given values of the chemical potential as well as the partition function which is projected onto a definite baryon number. First numerical results for an SU(2) gauge theory are presented. We briefly discuss the breaking of the color-electric string at finite densities and shed light onto the origin of the overlap problem inherent in the Glasgow approach

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.

The 'silent' phase transition in mesonic bags and lattice theory

International Nuclear Information System (INIS)

Dey, J.; Dey, M.; Araujo Junior, C.F. de; Tomio, L.

1993-10-01

It is shown that even the simple bag model is able to reproduce the lattice result for the masses and the sound velocity, at finite temperature, T, suggests that the transition point depends on the nature of the meson. It would be interesting to check the last conclusion in present day finite temperature lattice theory, since different transition points seem to be indicated by particle emission T in heavy ion reactions. (author)

Logarithmic conformal field theory

Science.gov (United States)

Gainutdinov, Azat; Ridout, David; Runkel, Ingo

2013-12-01

Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more

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

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.

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.)

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

Reggeon field theory for alpha (0)>1

CERN Document Server

Amati, Daniele; Le Bellac, M; Marchesini, G

1976-01-01

The asymptotic behaviour of the scattering amplitude is obtained when the pomeron has intercept alpha (0) larger than one. The reggeon field theory is studied by introducing a lattice in impact parameter space. Use is made of a previous result showing that asymptotically the dynamics is controlled at each lattice site ( alpha '=0 case) by a two-level structure. This leads to a non-Hermitean Hamiltonian expressed in terms of spin operators in which the intersite interaction term is proportional to the pomeron slope alpha '. The spectrum of such a system shows a degenerate ground state for alpha (0)> alpha /sub c/>or approximately=1 and a continuum with vanishing excitation gap at alpha (0)= alpha /sub c/. The vacuum does not change structure at the critical value. The criticality is shown by an order parameter which is given by the matrix element of a field operator between the vacuum and its degenerate companion. The nature of this critical phenomenon is better understood by continuously transforming the Hami...

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.

Effective field theories for correlated electrons

International Nuclear Information System (INIS)

Wallington, J.P.

1999-10-01

In this thesis, techniques of functional integration are applied to the construction of effective field theories for models of strongly correlated electrons. This is accomplished by means of the Hubbard-Stratonovic transformation which maps a system of interacting fermions onto one of free fermions interacting, not with each other, but with bosonic fields representing the collective modes of the system. Different choices of transformation are investigated throughout the thesis. It is shown that there exists a new group of discrete symmetries and transformations of the Hubbard model. Using this new group, the problem of choosing a Hubbard-Stratonovic decomposition of the Hubbard interaction term is solved. In the context of the exotic doped barium bismuthates, an extended Hubbard model with on-site attraction and nearest neighbour repulsion is studied. Mean field and renormalisation group analyses show a 'pseudospin-flop' from charge density wave to superconductivity as a function of filling. The nearest neighbour attractive Hubbard model on a quasi-2D lattice is studied as a simple phenomenological model for the high-T c cuprates. Mean field theory shows a transition from pure d-wave to pure s-wave superconductivity, via a mixed symmetry s + id state. Using Gaussian fluctuations, the BCS-Bose crossover is examined and suggestions are made about the origin of the angle dependence of the pseudogap. The continuum delta-shell potential model is introduced for anisotropic superconductors. Its mean field phases are studied and found to have some unusual properties. The BCS-Bose crossover is examined and the results are compared with those of the lattice model. Quasi-2D (highly anisotropic 3D) systems are considered. The critical properties of a Bose gas are investigated as the degree of anisotropy is varied. A new 2D Bose condensate state is found. A renormalisation group analysis is used to investigate the crossover from 2D to 3D. (author)

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

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

Convolution equations on lattices: periodic solutions with values in a prime characteristic field

OpenAIRE

Zaidenberg, Mikhail

2006-01-01

These notes are inspired by the theory of cellular automata. A linear cellular automaton on a lattice of finite rank or on a toric grid is a discrete dinamical system generated by a convolution operator with kernel concentrated in the nearest neighborhood of the origin. In the present paper we deal with general convolution operators. We propose an approach via harmonic analysis which works over a field of positive characteristic. It occurs that a standard spectral problem for a convolution op...

Thermodynamics of lattice QCD with 2 sextet quarks on Nt=8 lattices

International Nuclear Information System (INIS)

Kogut, J. B.; Sinclair, D. K.

2011-01-01

We continue our lattice simulations of QCD with 2 flavors of color-sextet quarks as a model for conformal or walking technicolor. A 2-loop perturbative calculation of the β function which describes the evolution of this theory's running coupling constant predicts that it has a second zero at a finite coupling. This nontrivial zero would be an infrared stable fixed point, in which case the theory with massless quarks would be a conformal field theory. However, if the interaction between quarks and antiquarks becomes strong enough that a chiral condensate forms before this IR fixed point is reached, the theory is QCD-like with spontaneously broken chiral symmetry and confinement. However, the presence of the nearby IR fixed point means that there is a range of couplings for which the running coupling evolves very slowly, i.e. it ''walks.'' We are simulating the lattice version of this theory with staggered quarks at finite temperature, studying the changes in couplings at the deconfinement and chiral-symmetry restoring transitions as the temporal extent (N t ) of the lattice, measured in lattice units, is increased. Our earlier results on lattices with N t =4, 6 show both transitions move to weaker couplings as N t increases consistent with walking behavior. In this paper we extend these calculations to N t =8. Although both transitions again move to weaker couplings, the change in the coupling at the chiral transition from N t =6 to N t =8 is appreciably smaller than that from N t =4 to N t =6. This indicates that at N t =4, 6 we are seeing strong-coupling effects and that we will need results from N t >8 to determine if the chiral-transition coupling approaches zero as N t →∞, as needed for the theory to walk.

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

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.)

Asymmetric Invisibility Cloaking Theory Based on the Concept of Effective Electromagnetic Fields for Photons

Science.gov (United States)

Amemiya, Tomo; Taki, Masato; Kanazawa, Toru; Arai, Shigehisa

2014-03-01

The asymmetric invisibility cloak is a special cloak with unidirectional transparency; that is, a person in the cloak should not be seen from the outside but should be able to see the outside. Existing theories of designing invisibility cloaks cannot be used for asymmetric cloaking because they are based on the transformation optics that uses Riemannian metric tensor independent of direction. To overcome this problem, we propose introducing directionality into invisibility cloaking. Our theory is based on ``the theory of effective magnetic field for photons'' proposed by Stanford University.[2] To realize asymmetric cloaking, we have extended the Stanford's theory to add the concept of ``effective electric field for photons.'' The effective electric and the magnetic field can be generated using a photonc resonator lattice, which is a kind of metamaterial. The Hamiltonian for photons in these fields has a similar form to that of the Hamiltonian for a charged particle in an electromagnetic field. An incident photon therefore experiences a ``Lorentz-like'' and a ``Coulomb-like'' force and shows asymmetric movement depending of its travelling direction.We show the procedure of designing actual invisibility cloaks using the photonc resonator lattice and confirm their operation with the aid of computer simulation. This work was supported in part by the MEXT; JSPS KAKENHI Grant Numbers #24246061, #24656046, #25420321, #25420322.

Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field

KAUST Repository

Zhang, Senfu; Zhang, Junwei; Zhang, Qiang; Barton, Craig; Neu, Volker; Zhao, Yuelei; Hou, Zhipeng; Wen, Yan; Gong, Chen; Kazakova, Olga; Wang, Wenhong; Peng, Yong; Garanin, Dmitry A.; Chudnovsky, Eugene M.; Zhang, Xixiang

2018-01-01

Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature skyrmions in sputtered multilayer films are an important step towards their use in ultra-low power devices. Such practical applications prefer skyrmions to be stable at zero magnetic fields and room temperature. Here, we report the creation of skyrmion lattices in Pt/Co/Ta multilayers by a scanning local field using magnetic force microscopy tips. We also show that those newly created skyrmion lattices are stable at both room temperature and zero fields. Lorentz transmission electron microscopy measurements reveal that the skyrmions in our films are of Néel-type. To gain a deeper understanding of the mechanism behind the creation of a skyrmion lattice by the scanning of local fields, we perform micromagnetic simulations and find the experimental results to be in agreement with our simulation data. This study opens another avenue for the creation of skyrmion lattices in thin films.

Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field

KAUST Repository

Zhang, Senfu

2018-03-29

Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature skyrmions in sputtered multilayer films are an important step towards their use in ultra-low power devices. Such practical applications prefer skyrmions to be stable at zero magnetic fields and room temperature. Here, we report the creation of skyrmion lattices in Pt/Co/Ta multilayers by a scanning local field using magnetic force microscopy tips. We also show that those newly created skyrmion lattices are stable at both room temperature and zero fields. Lorentz transmission electron microscopy measurements reveal that the skyrmions in our films are of Néel-type. To gain a deeper understanding of the mechanism behind the creation of a skyrmion lattice by the scanning of local fields, we perform micromagnetic simulations and find the experimental results to be in agreement with our simulation data. This study opens another avenue for the creation of skyrmion lattices in thin films.

Direct writing of room temperature and zero field skyrmion lattices by a scanning local magnetic field

Science.gov (United States)

Zhang, Senfu; Zhang, Junwei; Zhang, Qiang; Barton, Craig; Neu, Volker; Zhao, Yuelei; Hou, Zhipeng; Wen, Yan; Gong, Chen; Kazakova, Olga; Wang, Wenhong; Peng, Yong; Garanin, Dmitry A.; Chudnovsky, Eugene M.; Zhang, Xixiang

2018-03-01

Magnetic skyrmions are topologically protected nanoscale spin textures exhibiting fascinating physical behaviors. Recent observations of room temperature skyrmions in sputtered multilayer films are an important step towards their use in ultra-low power devices. Such practical applications prefer skyrmions to be stable at zero magnetic fields and room temperature. Here, we report the creation of skyrmion lattices in Pt/Co/Ta multilayers by a scanning local field using magnetic force microscopy tips. We also show that those newly created skyrmion lattices are stable at both room temperature and zero fields. Lorentz transmission electron microscopy measurements reveal that the skyrmions in our films are of Néel-type. To gain a deeper understanding of the mechanism behind the creation of a skyrmion lattice by the scanning of local fields, we perform micromagnetic simulations and find the experimental results to be in agreement with our simulation data. This study opens another avenue for the creation of skyrmion lattices in thin films.

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 ...

A new approach to spectrum calculations in lattice Hamiltonian field theories. 1. Introduction and application to lambda phi4 in (1+1) dimensions

International Nuclear Information System (INIS)

Barnes, T.; Daniell, G.J.

1982-09-01

A finite lattice technique is introduced for calculating the spectrum of fluctuating Bose theories in the continuum limit. The method gives the continuum spectrum to an estimated approximately 1% accuracy in (1+1) dimensions using available computer memory. The spectrum of lambda phi 4 theory in (1+1) dimensions is studied as a trial application; results are found consistent with a free theory spectrum. (author)

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

Lattice guage theories on a hypercube computer

International Nuclear Information System (INIS)

Otto, S.W.

1984-01-01

A report on the parallel computer effort underway at Caltech and the use of these machines for lattice gauge theories is given. The computational requirements of the Monte Carlos are, of course, enormous, so high Mflops (Million floating point operations per second) and large memories are required. Various calculations on the machines in regards to their programmability (a non-trivial issue on a parallel computer) and their efficiency in usage of the machine are discussed

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.

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

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

Integrability of a family of quantum field theories related to sigma models

Energy Technology Data Exchange (ETDEWEB)

Ridout, David [Australian National Univ., Canberra, ACT (Australia). Dept. of Theoretical Physics; DESY, Hamburg (Germany). Theory Group; Teschner, Joerg [DESY, Hamburg (Germany). Theory Group

2011-03-15

A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2 vertical stroke 1) Toda theory, and the N=2 supersymmetric Sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric Sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS{sub 2} x S{sup 2}, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space. (orig.)

Singular-perturbation--strong-coupling field theory and the moments problem

International Nuclear Information System (INIS)

Handy, C.R.

1981-01-01

Motivated by recent work of Bender, Cooper, Guralnik, Mjolsness, Rose, and Sharp, a new technique is presented for solving field equations in terms of singular-perturbation--strong-coupling expansions. Two traditional mathematical tools are combined into one effective procedure. Firstly, high-temperature lattice expansions are obtained for the corresponding power moments of the field solution. The approximate continuum-limit power moments are subsequently obtained through the application of Pade techniques. Secondly, in order to reconstruct the corresponding approximate global field solution, one must use function-moments reconstruction techniques. The latter involves reconsidering the traditional ''moments problem'' of interest to pure and applied mathematicians. The above marriage between lattice methods and moments reconstruction procedures for functions yields good results for the phi 4 field-theory kink, and the sine-Gordon kink solutions. It is argued that the power moments are the most efficient dynamical variables for the generation of strong-coupling expansions. Indeed, a momentum-space formulation is being advocated in which the long-range behavior of the space-dependent fields are determined by the small-momentum, infrared, domain

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.

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)

Diagrammatic Monte Carlo for the weak-coupling expansion of non-Abelian lattice field theories: Large-N U (N ) ×U (N ) principal chiral model

Science.gov (United States)

Buividovich, P. V.; Davody, A.

2017-12-01

We develop numerical tools for diagrammatic Monte Carlo simulations of non-Abelian lattice field theories in the t'Hooft large-N limit based on the weak-coupling expansion. First, we note that the path integral measure of such theories contributes a bare mass term in the effective action which is proportional to the bare coupling constant. This mass term renders the perturbative expansion infrared-finite and allows us to study it directly in the large-N and infinite-volume limits using the diagrammatic Monte Carlo approach. On the exactly solvable example of a large-N O (N ) sigma model in D =2 dimensions we show that this infrared-finite weak-coupling expansion contains, in addition to powers of bare coupling, also powers of its logarithm, reminiscent of resummed perturbation theory in thermal field theory and resurgent trans-series without exponential terms. We numerically demonstrate the convergence of these double series to the manifestly nonperturbative dynamical mass gap. We then develop a diagrammatic Monte Carlo algorithm for sampling planar diagrams in the large-N matrix field theory, and apply it to study this infrared-finite weak-coupling expansion for large-N U (N ) ×U (N ) nonlinear sigma model (principal chiral model) in D =2 . We sample up to 12 leading orders of the weak-coupling expansion, which is the practical limit set by the increasingly strong sign problem at high orders. Comparing diagrammatic Monte Carlo with conventional Monte Carlo simulations extrapolated to infinite N , we find a good agreement for the energy density as well as for the critical temperature of the "deconfinement" transition. Finally, we comment on the applicability of our approach to planar QCD at zero and finite density.

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

Numerical studies of fermionic field theories at large-N

International Nuclear Information System (INIS)

Dickens, T.A.

1987-01-01

A description of an algorithm, which may be used to study large-N theories with or without fermions, is presented. As an initial test of the method, the spectrum of continuum QCD in 1 + 1 dimensions is determined and compared to previously obtained results. Exact solutions of 1 + 1 dimensional lattice versions of the free fermion theory, the Gross-Neveu model, and QCD are obtained. Comparison of these exact results with results from the numerical algorithm is used to test the algorithms, and more importantly, to determine the errors incurred from the approximations used in the numerical technique. Numerical studies of the above three lattice theories in higher dimensions are also presented. The results are again compared to exact solutions for free fermions and the Gross-Neveu model; perturbation theory is used to derive expansions with which the numerical results for QCD may be compared. The numerical algorithm may also be used to study the euclidean formulation of lattice gauge theories. Results for 1 + 1 dimensional euclidean lattice QCD are compared to the exact solution of this model

Representations of classical groups on the lattice and its application to the field theory on discrete space-time

OpenAIRE

Lorente, M.

2003-01-01

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of any dimension invariant and apply these transformations to field equations.

O (a) improvement of 2D N = (2 , 2) lattice SYM theory

Science.gov (United States)

Hanada, Masanori; Kadoh, Daisuke; Matsuura, So; Sugino, Fumihiko

2018-04-01

We perform a tree-level O (a) improvement of two-dimensional N = (2 , 2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is needed for obtaining the correct continuum limit without a parameter fine tuning. The improved lattice action is given within a milder locality condition in which the interactions are decaying as the exponential of the distance on the lattice. We also prove that the path-integral measure is invariant under the improved Q-transformation.

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

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.

Spin-lattice dynamics simulation of external field effect on magnetic order of ferromagnetic iron

Directory of Open Access Journals (Sweden)

C. P. Chui

2014-03-01

Full Text Available Modeling of field-induced magnetization in ferromagnetic materials has been an active topic in the last dozen years, yet a dynamic treatment of distance-dependent exchange integral has been lacking. In view of that, we employ spin-lattice dynamics (SLD simulations to study the external field effect on magnetic order of ferromagnetic iron. Our results show that an external field can increase the inflection point of the temperature. Also the model provides a better description of the effect of spin correlation in response to an external field than the mean-field theory. An external field has a more prominent effect on the long range magnetic order than on the short range counterpart. Furthermore, an external field allows the magnon dispersion curves and the uniform precession modes to exhibit magnetic order variation from their temperature dependence.

Conformal field theories, Coulomb gas picture and integrable models

International Nuclear Information System (INIS)

Zuber, J.B.

1988-01-01

The aim of the study is to present the links between some results of conformal field theory, the conventional Coulomb gas picture in statistical mechanics and the approach of integrable models. It is shown that families of conformal theories, related by the coset construction to the SU(2) Kac-Moody algebra, may be regarded as obtained from some free field, and modified by the coupling of its winding numbers to floating charges. This representation reflects the procedure of restriction of the corresponding integrable lattice models. The work may be generalized to models based on the coset construction with higher rank algebras. The corresponding integrable models are identified. In the conformal field description, generalized parafermions appear, and are coupled to free fields living on a higher-dimensional torus. The analysis is not as exhaustive as in the SU(2) case: all the various restrictions have not been identified, nor the modular invariants completely classified

The Dirac-Kaehler equation and fermions on the lattice

International Nuclear Information System (INIS)

Becher, P.

1982-05-01

The geometrical description of spinor fields by E. Kaehler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice. (orig.)

Recursive integral equations with positive kernel for lattice calculations

International Nuclear Information System (INIS)

Illuminati, F.; Isopi, M.

1990-11-01

A Kirkwood-Salzburg integral equation, with positive defined kernel, for the states of lattice models of statistical mechanics and quantum field theory is derived. The equation is defined in the thermodynamic limit, and its iterative solution is convergent. Moreover, positivity leads to an exact a priori bound on the iteration. The equation's relevance as a reliable algorithm for lattice calculations is therefore suggested, and it is illustrated with a simple application. It should provide a viable alternative to Monte Carlo methods for models of statistical mechanics and lattice gauge theories. 10 refs

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.)

Lattice quantum chromodynamics

International Nuclear Information System (INIS)

Hassenfratz, P.

1983-01-01

It is generally accepted that relativistic field theory is relevant in high energy physics. It is also recognized that even in QCD, which is asymptotically free, the scope of perturbation theory is very limited. Despite the tremendous theoretical and experimental effort to study scaling, scaling violations, e + e - , lepton pair creation, jets, etc., the answer to the question whether and to what extent is QCD the theory of strong interactions is vague. At present-day energies it is difficult to disentangle perturbative and non-perturbative effects. The author states that QCD must be understood and that quantitative non-perturbative methods are needed. He states that the lattice formulation of field theories is a promising approach to meeting this need and discusses the formulation in detail in this paper

Non-perturbative analysis of some simple field theories on a momentum space lattice

International Nuclear Information System (INIS)

Brooks, E.D. III.

1984-01-01

In this work, a new technique is developed for the numerical study of quantum field theory. The procedure, borrowed from nonrelativistic quantum mechanics, is that of finding the eigenvalues of a finite Hamiltonian matrix. The matrix is created by evaluating the matrix elements of the Hamiltonian operator on a finite basis of states. The eigenvalues and eigenvectors of the finite dimensional matrix become an accurate approximation to those of the physical system as the finite basis of states is extended to become more complete. A model of scalars coupled to fermions in 0 + 1 dimensions as a simple field theory is studied to consider in the course of developing the technique. Having developed the numerical and analytical techniques, a Fermi field coupled to a Bose field in 1 + 1 dimensions with the Yukawa coupling lambda anti-psi phi psi is considered. The large coupling limit basis of the 0 + 1 dimensional model is extended to this case using a Bogoliubov transformation on the fermions. It provides a handle on the behavior of the system in the large coupling limit. The effects of renormalization and the generation of bound states are considered

A note on completeness of bounded lattices postulated in some axiomatics of the mathematical foundations of quantum theory

International Nuclear Information System (INIS)

Mukherjee, M.K.

1981-01-01

In an axiomatic study of quantum theory Jauch postulated the completeness of the lattice underlying a quantum logic. The theory of Baer semigroup is utilized to specify quite generally the completeness of the lattice. (author)

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

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

Chiral and continuum extrapolation of partially quenched lattice results

Energy Technology Data Exchange (ETDEWEB)

C.R. Allton; W. Armour; D.B. Leinweber; A.W. Thomas; R.D. Young

2005-04-01

The vector meson mass is extracted from a large sample of partially quenched, two-flavor lattice QCD simulations. For the first time, discretization, finite-volume and partial quenching artifacts are treated in a unified chiral effective field theory analysis of the lattice simulation results.

Self-interacting, boson, quantum field theory, and the thermodynamic limit in d dimensions

International Nuclear Information System (INIS)

Baker, G.A. Jr.

1975-01-01

By use of a finite volume, lattice approximation, an approximation to the analytic continuation of a polynomial, self-interacting boson quantum field theory from Minkowski space to Euclidean space was set up. The infinite volume limit for various boundary conditions is shown to exist and to be asymptotic to the perturbation expansion in the coupling constant g at g = 0. For g: phi 4 : d theory mass renormalizability is proved and it is shown how, by use of Nelson's reconstruction theorem, the corresponding Minkowski space quantum field theory can be obtained. It is discussed, at least for d greater than or equal to 4, how statistical mechanical techniques, used to analyze the Ising model in the critical region just above the critical temperature, can be used to compute the properties of quantum field theory. (U.S.)

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.

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

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

Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills

International Nuclear Information System (INIS)

Smith, Dominik

2010-01-01

We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)

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.)

Kink dynamics in a topological φ4 lattice

Science.gov (United States)

Adib, A. B.; Almeida, C. A. S.

2001-09-01

Recently proposed was a discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro barrier even for large spatial discretizations (h~1.0). It was then suggested that these ``topological discrete systems'' are a natural choice for the numerical study of continuum kink dynamics. Giving particular emphasis to the φ4 theory, we numerically investigate kink-antikink scattering and breather formation in these topological lattices. Our results indicate that, even though these systems are quite accurate for studying free kinks in coarse lattices, for legitimate dynamical kink problems the accuracy is rather restricted to fine lattices (h~0.1). We suggest that this fact is related to the breaking of the Bogomol'nyi bound during the kink-antikink interaction, where the field profile loses its static property as required by the Bogomol'nyi argument. We conclude, therefore, that these lattices are not suitable for the study of more general kink dynamics, since a standard discretization is simpler and has effectively the same accuracy for such resolutions.

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...

Italian Physical Society A journey with Roberto in lattice QCD

CERN Document Server

Lüscher, M

2017-01-01

Lattice field theory and lattice QCD, in particular, are areas of research in which Roberto was strongly interested practically since the beginning of his scientific career. He contributed to the development of lattice QCD through his ideas and publications, but also through his engagement in the APE project and in many other ways as well. Some of the work we did together is recalled in this talk and put in the context of the situation in the field at the time.

Automated generation of lattice QCD Feynman rules

Energy Technology Data Exchange (ETDEWEB)

Hart, A.; Mueller, E.H. [Edinburgh Univ. (United Kingdom). SUPA School of Physics and Astronomy; von Hippel, G.M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Horgan, R.R. [Cambridge Univ. (United Kingdom). DAMTP, CMS

2009-04-15

The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)

Two Dimensional Super QCD on a Lattice

Energy Technology Data Exchange (ETDEWEB)

Catterall, Simon [Syracuse U.; Veernala, Aarti [Fermilab

2017-10-04

We construct a lattice theory with one exact supersymmetry which consists of fields transforming in both the adjoint and fundamental representations of a U(Nc) gauge group. In addition to gluons and gluinos, the theory contains Nf flavors of fermion in the fundamental representation along with their scalar partners and is invariant under a global U(Nf) flavor symmetry. The lattice action contains an additional Fayet-Iliopoulos term which can be used to generate a scalar potential. We perform numerical simulations that corroborate the theoretical expectation that supersymmetry is spontaneously broken for Nf

Automated generation of lattice QCD Feynman rules

International Nuclear Information System (INIS)

Hart, A.; Mueller, E.H.; Horgan, R.R.

2009-04-01

The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)

Mixtures of bosonic and fermionic atoms in optical lattices

International Nuclear Information System (INIS)

Albus, Alexander; Illuminati, Fabrizio; Eisert, Jens

2003-01-01

We discuss the theory of mixtures of bosonic and fermionic atoms in periodic potentials at zero temperature. We derive a general Bose-Fermi Hubbard Hamiltonian in a one-dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean-field criterion for the onset of a bosonic superfluid transition. We investigate the ground-state properties of the mixture in the Gutzwiller formulation of mean-field theory, and present numerical studies of finite systems. The bosonic and fermionic density distributions and the onset of quantum phase transitions to demixing and to a bosonic Mott-insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasidegenerate ground states is related to a breaking of the mirror symmetry in the lattice

Freedom and confinement in lattice Yang-Mills theories: a case for divorce

International Nuclear Information System (INIS)

Colangelo, P.; Cosmai, L.; Pellicoro, M.; Preparata, G.

1986-01-01

It is presented evidence that nonperturbative effects in lattice gauge theories do not obey at small coupling constant (large β) asymptotic scaling, but they rather behave as suggested by a recent result in continuum Yang-Mills theories. It is also discussed the possible impact of these results on our understanding of QCD

The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit

International Nuclear Information System (INIS)

Becher, Thomas G

2002-01-01

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (''master integrals''). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions

Optimised Dirac operators on the lattice. Construction, properties and applications

Energy Technology Data Exchange (ETDEWEB)

Bietenholz, W. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik]|[Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2006-11-15

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (orig.)

Optimised Dirac operators on the lattice: construction, properties and applications

International Nuclear Information System (INIS)

Bietenholz, Wolfgang

2006-12-01

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the e-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (author)

Optimised Dirac operators on the lattice. Construction, properties and applications

International Nuclear Information System (INIS)

Bietenholz, W.; Deutsches Elektronen-Synchrotron

2006-11-01

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the epsilon-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (orig.)

Optimised Dirac operators on the lattice: construction, properties and applications

Energy Technology Data Exchange (ETDEWEB)

Bietenholz, Wolfgang [Humbolt-Universitaet zu Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing (NIC)

2006-12-15

We review a number of topics related to block variable renormalisation group transformations of quantum fields on the lattice, and to the emerging perfect lattice actions. We first illustrate this procedure by considering scalar fields. Then we proceed to lattice fermions, where we discuss perfect actions for free fields, for the Gross-Neveu model and for a supersymmetric spin model. We also consider the extension to perfect lattice perturbation theory, in particular regarding the axial anomaly and the quark gluon vertex function. Next we deal with properties and applications of truncated perfect fermions, and their chiral correction by means of the overlap formula. This yields a formulation of lattice fermions, which combines exact chiral symmetry with an optimisation of further essential properties. We summarise simulation results for these so-called overlap-hypercube fermions in the two-flavour Schwinger model and in quenched QCD. In the latter framework we establish a link to Chiral Perturbation Theory, both, in the p-regime and in the e-regime. In particular we present an evaluation of the leading Low Energy Constants of the chiral Lagrangian - the chiral condensate and the pion decay constant - from QCD simulations with extremely light quarks. (author)

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)

A Monte Carlo simulation for the field theory with quartic interaction

Energy Technology Data Exchange (ETDEWEB)

Santos, Sergio Mittmann dos [Instituto Federal de Educacao, Ciencia e Tecnologia do Rio Grande do Sul (IFRS), Porto Alegre, RS (Brazil)

2011-07-01

Full text: In the work [1-S. M. Santos, B. E. J. Bodmann and A. T. Gomez, Um novo metodo computacional para a teoria de campos na rede: resultados preliminares, IV Escola do Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, 2002; and 2-S. M. Santos and B. E. J. Bodmann, Simulacao na rede de teorias de campos quanticos, XXVIII Congresso Nacional de Matematica Aplicada e Computacional (CNMAC), Sao Paulo, 2005], a computational method on the lattice was elaborated for the problem known as scalar field theory with quartic interaction (for instance, see: J. R. Klauder, Beyound conventional quantization, Cambridge: Cambridge University Press, 2000). This one introduced an algorithm, which allows the simulation of a given field theory and is independent of the lattice spacing, by redefining the fields and the parameters (the mass m and the coupling constant g). This kind of approach permits varying the dimension of the lattice without changing the computational complexity of the algorithm. A simulation was made using the Monte Carlo method, where the renormalized mass m{sub R}, the renormalized coupling constant g{sub R} and the two point correlation function were determined with success. In the present work, the genuine computational method is used for new simulations. Now, the Monte Carlo method is not used just for the simulation of the algorithm, like in [1, 2], but also for defining the adjust parameters (the mass and the coupling constant), introduced ad hoc in [1, 2]. This work presents the first simulations' outcomes, where best results that [1, 2] were determined, for the renormalized mass and the renormalized coupling constant. (author)

Integrable systems and quantum field theory. Works in progress Nr 75

International Nuclear Information System (INIS)

Baird, Paul; Helein, Frederic; Kouneiher, Joseph; Roubtsov, Volodya; Antunes, Paulo; Banos, Bertrand; Barbachoux, Cecile; Desideri, Laura; Kahouadji, Nabil; Gerding, Aaron; Heller, Sebastian; Schmitt, Nicholas; Harrivel, Dikanaina; Hoevenaars, Luuk K.; Iftime, Mihaela; Levy, Thierry; Lisovyy, Oleg; Masson, Thierry; Skrypnyk, Taras; Pedit, Franz; Egeileh, Michel

2009-01-01

The contributions of this collective book address the quantum field theory (integrable systems and quantum field theory, introduction to supermanifolds and supersymmetry, beyond geometric quantification, Gaussian measurements and Fock spaces), differential geometry and physics (gravitation and geometry, physical events and the superspace about the hole argument, the Cartan-Kaehler theory and applications to local isometric and conformal embedding, calibrations, Cabal-Yau structures and Monge-Ampere structures, Hamiltonian multi-symplectic formalism and Monge-Ampere equations, big bracket, derivations and derivative multi-brackets), integrable system, geometry and physics (finite-volume correlation functions of monodromy fields on the lattice with the Toeplitz representation, Frobenius manifolds and algebraic integrability, an introduction to twistors, Hamiltonian systems on the 'coupled' curves, Nambu-Poisson mechanics and Fairlie-type integrable systems, minimal surfaces with polygonal boundary and Fuchsian equations, global aspects of integrable surface geometry), and non commutative geometry (an informal introduction to the ideas and concepts of non commutative geometry)

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.)

Unitary field theories

International Nuclear Information System (INIS)

Bergmann, P.G.

1980-01-01

A problem of construction of the unitary field theory is discussed. The preconditions of the theory are briefly described. The main attention is paid to the geometrical interpretation of physical fields. The meaning of the conceptions of diversity and exfoliation is elucidated. Two unitary field theories are described: the Weyl conformic geometry and Calitzy five-dimensioned theory. It is proposed to consider supersymmetrical theories as a new approach to the problem of a unitary field theory. It is noted that the supergravitational theories are really unitary theories, since the fields figuring there do not assume invariant expansion

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

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.)

Lattices applied to coding for reliable and secure communications

CERN Document Server

Costa, Sueli I R; Campello, Antonio; Belfiore, Jean-Claude; Viterbo, Emanuele

2017-01-01

This book provides a first course on lattices – mathematical objects pertaining to the realm of discrete geometry, which are of interest to mathematicians for their structure and, at the same time, are used by electrical and computer engineers working on coding theory and cryptography. The book presents both fundamental concepts and a wealth of applications, including coding and transmission over Gaussian channels, techniques for obtaining lattices from finite prime fields and quadratic fields, constructions of spherical codes, and hard lattice problems used in cryptography. The topics selected are covered in a level of detail not usually found in reference books. As the range of applications of lattices continues to grow, this work will appeal to mathematicians, electrical and computer engineers, and graduate or advanced undergraduate in these fields.

Structure functions at small xBj in a Euclidean field theory approach

International Nuclear Information System (INIS)

Hebecker, A.; Meggiolaro, E.; Nachtmann, O.

2000-01-01

The small-x Bj limit of deep inelastic scattering is related to the high-energy limit of the forward Compton amplitude in a familiar way. We show that the analytic continuation of this amplitude in the energy variable is calculable from a matrix element in Euclidean field theory. This matrix element can be written as a Euclidean functional integral in an effective field theory. Its effective Lagrangian has a simple expression in terms of the original Lagrangian. The functional integral expression obtained can, at least in principle, be evaluated using genuinely non-perturbative methods, e.g., on the lattice. Thus, a fundamentally new approach to the long-standing problem of structure functions at very small x Bj seems possible. We give arguments that the limit x Bj →0 corresponds to a critical point of the effective field theory where the correlation length becomes infinite in one direction

New numerical method for iterative or perturbative solution of quantum field theory

International Nuclear Information System (INIS)

Hahn, S.C.; Guralnik, G.S.

1999-01-01

A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills

Energy Technology Data Exchange (ETDEWEB)

Smith, Dominik

2010-11-17

We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)

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.)

Polyacetylene: a real material linking condensed matter and field theory

International Nuclear Information System (INIS)

Campbell, D.K.

1983-01-01

A subject at the interface between field theory and statistical mechanics is polyacetylene ((CH) /SUB x/ ), a quasi-one-dimensional organic polymer. Recent theoretical studies are reviewed in this paper. Background chemistry determines the schematic for trans (CH) /SUB x/ . A trans (CH) /SUB x/ chain is modelled microscopically by describing the coupled motions of the lattice backbone of C-H units and the single pi-orbital electron per carbon that determines where the double bond goes. Continuum theory is focused on here. Kink and polaron nonlinear excitations, fractionally charged solitons, and confinement of kinklike solutions in cis (CH) /SUB x/ are then studied. Finally, it is shown that the continuum electron-phonon equations for trans-(CH) /SUB x/ are identical to the static, semi-classical equations of the N=2 Gross-Neveu model. Another such field theory connection involves an alternate description of kink solutons in trans (CH) /SUB x/ . The possible existence of fractionally charged solutons is touched upon in conclusion

Zero-mode effects in the lattice thermodynamics of massless bose field

International Nuclear Information System (INIS)

Gorenstein, M.I.; Lipskikh, S.I.; Sorin, A.S.

1985-01-01

The thermodynamics of free massless Bose field on a lattice is discussed. The coefficients characterizing the finite size effects are obtained. The use of these coefficients in the Yang-Mills thermodynamics allows one to make Monte-Carlo calculations, carried out on the different size lattices, self-consistent

Lattice distortion under an electric field in BaTiO3 piezoelectric single crystal

International Nuclear Information System (INIS)

Tazaki, Ryoko; Fu Desheng; Daimon, Masahiro; Koshihara, Shin-ya; Itoh, Mitsuru

2009-01-01

Lattice distortions under an electric field in a mono-domain of BaTiO 3 ferroelectric crystal have been detected with synchrotron x-ray radiation. The variation of the lattice constant with an electric field observed with high angle diffraction shows a linear response nature of the piezoelectric effect. When an electric field is applied along the spontaneous polarization direction, the c-axis of the lattice elongates and the a-axis of the lattice shrinks at a rate of d 33 = 149 ± 54 pm V -1 and d 31 = -82 ± 61 pm V -1 ; these represent the longitudinal and transverse piezoelectric coefficients of BaTiO 3 crystal, respectively. These results give an insight into the intrinsic piezoelectric response on the lattice scale in BaTiO 3 that has been widely used to explore high performance lead-free piezoelectric alloys.

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 \

T-expansion and its application to SU(2) lattice gauge theory

International Nuclear Information System (INIS)

Karliner, M.

1984-01-01

A scheme allowing systematic improvement of variational calculations has been developed at SLAC. This paper contains an outline of the method, as well as some preliminary results of its application to two dimensional spin systems and four dimensional SU(2) lattice guage theory

Ward identities and mass spectrum of N=1 Super Yang-Mills theory on the lattice