Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Emergent Abelian Gauge Fields from Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Allen Stern
2010-02-01
Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.
Localization of abelian gauge fields on thick branes
Energy Technology Data Exchange (ETDEWEB)
Vaquera-Araujo, Carlos A. [Universidad de Colima, Facultad de Ciencias, CUICBAS, Colima (Mexico); Corradini, Olindo [Universidad Autonoma de Chiapas, Ciudad Universitaria, Facultad de Ciencias en Fisica y Matematicas, Tuxtla Gutierrez (Mexico); Universita di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Modena (Italy)
2015-02-01
In this work, we explore a mechanism for abelian gauge field localization on thick branes based on a five-dimensional Stueckelberg-like action. A normalizable zero mode is found through the identification of a suitable coupling function between the brane and the gauge field. The same mechanism is studied for the localization of the abelian Kalb-Ramond field. (orig.)
Non-Abelian gauge fields in two spatial dimensions
International Nuclear Information System (INIS)
Hagen, C.R.
1987-01-01
Generalizing an earlier work on the Abelian case the most general non-Abelian gauge theory in two spatial dimensions is derived. It is shown that local gauge invariance leads to a new term in the action which in turn requires that the gauge current operator have a part which is bilinear in the non-Abelian gauge field-strength tensor. Although a radiation (or axial) gauge quantization is possible, this approach is found not to yield the maximal set of commutation relations among the basic fields. The latter goal can be accomplished only by a rather unusual gauge choice which has not previously been studied. Quantization conditions on the coupling constant implied by invariance under large gauge transformations are also derived
Non-Abelian gauge theory of fields associated with dyons
International Nuclear Information System (INIS)
Rajput, B.S.; Kumar, S.R.
1983-01-01
A suitable Lorentz invariant non-Abelian gauge theory of the fields associated with dyons has been constructed to describe the dual dynamics between colour isocharges and topological charges. It has been shown that the generalized particle current is gauge covariant and not conserved in non-Abelian theory. It has also been shown that in this theory the unphysical string variables and unphysical charged fields are not needed and that any extra constraint to maintain the dual symmetry of field equation and Lagrangian is also not needed. (author)
Massive Abelian gauge fields coupled with nonconserved currents
International Nuclear Information System (INIS)
Nakazato, Hiromichi; Namiki, Mikio; Yamanaka, Yoshiya; Yokoyama, Kan-ichi.
1985-04-01
A massive Abelian gauge field coupled with a nonconserved mass-changing current is described within the framework of canonical quantum theory with indefinite metric. In addition to the conventional Lagrange multiplier fields, another ghost field is introduced to preserve gauge invariance and unitarity of a physical S-matrix in the case of the nonconserved current. The renormalizability of the theory is explicitly shown in the sense of superpropagator approach for nonpolynomial Lagrangian theories. (author)
Non-Abelian gauge field theory in scale relativity
International Nuclear Information System (INIS)
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-01-01
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description
Classical and quantum mechanics of non-abelian gauge fields
International Nuclear Information System (INIS)
Savvidy, G.K.
1984-01-01
Classical and quantum mechanics of non-abelian gauge fields are investigated both with and without spontaneous symmetry breaking. The fundamental subsystem (FS) of Yang-Mills classical mechanics (YMCM) is considered. It is shown to be a Kolmogorov K-system, and hence to have strong statistical properties. Integrable systems are also found, to which in terms of KAM theory Yang-Mills-Higgs classical mechanics (YMHCM) is close. Quantum-mechanical properties of the YM system and their relation to the problem of confinement are discussed. (orig.)
The Weyl non-Abelian gauge field and the Thomas precession
International Nuclear Information System (INIS)
Barbashov, B.M.; Pestov, A.B.
1998-01-01
The connection between the Fermi-Walker transport and the Weyl non-Abelian gauge field is established. A theoretical possibility of detecting the Weyl gauge field caused by the Thomas precession of a gyroscope is discussed
Constant self-dual Abelian gauge fields and fermions in SU(2) gauge theory
International Nuclear Information System (INIS)
Kay, D.; Parthasarathy, R.; Viswanathan, K.S.
1983-01-01
Fermion one-loop corrections to the effective action in a self-dual Abelian background field are calculated for an SU(2) gauge theory. It is found that these corrections for massless fermions tend to destabilize the vacuum. The quantitative and qualitative features of such corrections for the case of massive fermions are discussed
Possible physical manifestation of the Weyl non-Abelian gauge field
International Nuclear Information System (INIS)
Barbashov, B.M.; Pestov, A.B.
1998-01-01
On the basis of the Weyl equations of congruent transference, we consider a possible influence of the Weyl non-Abelian gauge field defining the transference on the precession of a gyroscope. Plane-wave solutions to the equations of the Abelian gauge field are derived
Hidden singularities in non-abelian gauge fields
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.
1978-01-01
It is shown that the potential (and field) of a non-abelian gauge theory is not well determined when it has a singular point. When this is the cause, it is important to specify the regularization procedure used to give a precise definition of physical quantities at the singularity at any stage of the computation. The fact that a certain A sub(μ) (associated with the given regularization) represents the vacuum when F sub(μν) is a zero distribution not only on the global space but also in all its projections to arbitrary subspaces is discussed. The example used as a base for the discussion is A vetor = i (sigma vetor Λ r vetor / r 2 ). For this example it is shown that different regularizations give the same field in the global space but they give different distributions when projected to subspaces containing the singular point [pt
Unveiling a spinor field classification with non-Abelian gauge symmetries
Fabbri, Luca; da Rocha, Roldão
2018-05-01
A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses spinor multiplets, corresponding to non-Abelian gauge fields. The particular case of SU(2) gauge symmetry, encompassing electroweak and electromagnetic conserved charges, is then implemented by a non-Abelian spinor classification, now involving 14 mixed classes of spinor doublets. A richer flagpole, dipole, and flag-dipole structure naturally descends from this general classification. The Lounesto's classification of spinors is shown to arise as a Pauli's singlet, into this more general classification.
Non-Abelian tensor gauge fields and higher-spin extension of standard model
International Nuclear Information System (INIS)
Savvidy, G.
2006-01-01
We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Construction of quantized gauge fields: continuum limit of the Abelian Higgs model in two dimensions
International Nuclear Information System (INIS)
Seiler, E.
1981-01-01
The author proves the existence of the continuum limit of the two-dimensional Higgs model for two cases: External gauge fields that are Hoelder continuous and may be non-Abelian, and the fully quantized Abelian model. In the latter case all Wightman axioms are verified except clustering. Important ingredients are a universal diamagnetic bound and correlation inequalities. (Auth.)
Quantum field theory I foundations and Abelian and non-Abelian gauge theories
Manoukian, Edouard B
2016-01-01
This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman’s well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Pa...
Gravitational waves from non-Abelian gauge fields at a tachyonic transition
Tranberg, Anders; Tähtinen, Sara; Weir, David J.
2018-04-01
We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.
Energy Technology Data Exchange (ETDEWEB)
Yokoyama, Kan-ichi; Kubo, Reijiro
1974-12-01
The framework of the Nakanishi-Lautrup formalism should be enlarged by introducing a scalar dipole ghost field B(x), which is called gauge on field, together with its pair field. By taking free Lagrangian density, Free-field equations can be described. The vacuum is defined by using a neutral vector field U..mu..(x). The state-vector space is generated by the adjoining conjugates of U..mu..sup((+))(x), and auxiliary fields B(x), B/sub 1/(x) and B/sub 2/(x), which were introduced in the form of the Lagrangian density. The physical states can be defined by the supplementary conditions of the form B/sub 1/sup((+))(x) 1 phys>=B/sub 2/sup((+))(x) 1 phys>=0. It is seen that all the field equations and all the commutators are kept form-invariant, and that the gauge parameter ..cap alpha.. is transformed into ..cap alpha..' given by ..cap alpha..'=..cap alpha..+lambda, with epsilon unchanged. The Lagrangian density is specified only by the gauge invariant parameter epsilon. The gauge structure of theory has universal meaning over whole Abelian-gauge field. C-number gauge transformation and the gauge structure in the presence of interaction are also discussed.
Dynamical chaos of non-Abelian gauge fields
International Nuclear Information System (INIS)
Matinyan, S.G.
1985-01-01
The review studies a special class of Yang--Mills fields: spatially homogeneous fields (classical Yang--Mills mechanics), which have no analog in linear Abelian electrodynamics. Computer and analytic approaches show that such fields possess dynamical stochasticity, on the basis of which it may be asserted that the classical Yang--Mills equations without external sources constitute a nonintegrable system. The Higgs mechanism eliminates this stochasticity, and at a certain value of the vacuum expectation of the scalar field there is a phase transition of the disorder-order (confinement-deconfinement) type. The system with external sources apparently behaves similarly. The connection between this stochasticity and the mechanism of dimensional reduction in macroscopic systems and with the color-confinement phenomenon is considered. It is shown that the presence in the vacuum of random (Gaussian) currents leads to confinement of the fields generated by these currents. Attention is drawn to the possible manifestation of the stochasticity of the classical fields in multiparticle hadron-production processes. Such manifestation reflects universal stochastic features characteristic of systems of very different natures (statistics of the counting of thermoelectrons from random sources and photoelectrons from laser radiation that passes through a liquid in the critical state, developed turbulence in hydrodynamics, stellar systems, and KNO scaling in multiparticle production)
'Symmetry dictates interaction'. For the jubilee of the non-abelian gauge fields
International Nuclear Information System (INIS)
Li Huazhong
2004-01-01
The article is written for the Jubilee, 50 years after the birth of non-abelian gauge field theory which was proposed by C.N. yang and R. Mills in 1954. The main ideas initiated in the paper and great influences are briefly outlined
On a stochastic process associated to non-abelian gauge fields
International Nuclear Information System (INIS)
Vilela Mendes, R.
1989-01-01
A stochastic process is constructed from a ground state measure that generalizes to non-abelian fields the ground state of abelian (free) gauge fields without fermions. Using a latticized version one shows how the process leads to a well-defined quantum theory in the Schroedinger representation. An analysis of the qualitative behaviour of the theory seems to imply a quasi-free behaviour at short distances and a maximally disordered field strength configuration for the low-momentum component of the ground state. Scaling relations for the mass gap are inferred from the theory of small random perturbations of dynamical systems. (orig.)
New results in topological field theory and Abelian gauge theory
International Nuclear Information System (INIS)
Thompson, G.
1995-10-01
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs
New results in topological field theory and Abelian gauge theory
Energy Technology Data Exchange (ETDEWEB)
Thompson, G
1995-10-01
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs.
Problems of an external field in non-Abelian gauge theory
International Nuclear Information System (INIS)
Gavrilov, S.P.; Gitman, D.M.
1992-01-01
In the Abelian gauge field theory QED the principal problems connected with an external field are the problems of exact keeping of an external field in a perturbation theory and appearing in this case the peculiarities of the theory such as the instability of the vacuum and so on. There is the problem of an external field introduction or its interpretation side by side with this problem in Non-Abelian gauge theory. The solution of both these problems in Non-Abelian theory can be considered by analogy with QED. In the present paper, the authors discuss on the example of the spontaneously broken SU(2) x U(1) electroweak theory both the problems of an external field introduction and the problem of exact keeping of this field in the perturbation theory. The Langrangian of this theory in covariant gauge is chosen in the BRST invariant form. In spite of concrete character of the theory studied, the method can be extended to any gauge theory
Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report
International Nuclear Information System (INIS)
Wadia, Spenta R.
2009-01-01
We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)
Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field
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.
Field-strength formulation of gauge theories. The Hamiltonian approach in the Abelian theory
International Nuclear Information System (INIS)
Mendel, E.; Durand, L.
1984-01-01
We develop a Hamiltonian approach to the field-strength or dual formation of the Abelian gauge theory in which the potential A/sup μ/ is eliminated as a dynamical variable. Our work is based on the covariant gauge x/sup μ/A/sub μ/(x) = 0 which allows a simple elimination of A/sup μ/ in terms of the field strengths F/sup munu/. We obtain complete results for the generating functional for the Green's functions of the theory, Z = Z[f,g], where f and g are nonlocal currents coupled to E and B, and illustrate some unfamiliar aspects of the new formalism
International Nuclear Information System (INIS)
Jing Sicong; Ruan Jie; AH. Dept. of Modern Physics)
1990-01-01
The perturbation theory in coset pure gauge field theory is studied for the first time. By using the Bjorken-johnson-Low technique and calculating the Schwinger term in related commutators, the anomalous Ward identity in Abelian coset pure gauge field theory is derived, which is consistent with the non-perutrbative calculation
Abelian 2-form gauge theory: special features
International Nuclear Information System (INIS)
Malik, R P
2003-01-01
It is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two (1 + 1)-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is not an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the topological 2D free Abelian (and self-interacting non-Abelian) gauge theories
Localizing gauge fields on a topological Abelian string and the Coulomb law
International Nuclear Information System (INIS)
Torrealba S, Rafael S.
2010-01-01
The confinement of electromagnetic field is studied in axial symmetrical, warped, six-dimensional brane world, using a recently proposed topological Abelian string-vortex solution as background. It was found, that the massless gauge field fluctuations follow four-dimensional Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string vortex is less than 5β/4πe 2 v 2 and there are no other localized massless modes. There is also an infinite of nonlocalized massive Fourier modes, that follow four-dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As a main result, a (R o /βR 2 ) correction was found for the four-dimensional effective Coulomb law; the result is in correspondence with the observed behavior of the Coulomb potential at today's measurable distances.
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Classical field theory on electrodynamics, non-abelian gauge theories and gravitation
Scheck, Florian
2018-01-01
Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...
Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime
International Nuclear Information System (INIS)
Leen, T.K.
1983-01-01
In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space
q q ¯ Pair production in non-Abelian gauge fields
Indian Academy of Sciences (India)
Non-Abelian interactions in the colour field are time-dependent and hence should oscillate with a characteristic frequency 0 , which depends on the amplitude of the field strength. Using the WKB approximation in complex time, we calculated the pair production probability. When the strength of the field is comparable to the ...
A new gauge for supersymmetric abelian gauge theories
International Nuclear Information System (INIS)
Smith, A.W.; Barcelos Neto, J.
1984-01-01
A new gauge for supersymmetric abelian gauge theories is presented. It is shown that this new gauge allows us to obtain terms which usually come as radiative corrections to the supersymmetric abelian gauge theories when one uses the Wess-Zumino gauge. (Author) [pt
Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.
Energy Technology Data Exchange (ETDEWEB)
Scheck, Florian
2018-04-01
Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.
SU(2) gauge theory in the maximally Abelian gauge without monopoles
International Nuclear Information System (INIS)
Shmakov, S.Yu.; Zadorozhnyj, A.M.
1995-01-01
We present an algorithm for simulation of SU(2) lattice gauge theory under the maximally Abelian (MA) gauge and first numerical results for the theory without Abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual Abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected. 12 refs., 1 tab
International Nuclear Information System (INIS)
Snyderman, N.J.
1976-01-01
The Schwinger-Dyson equation for the Nambu-Jona Lasinio model is solved systematically subject to the constraint of spontaneously broken chiral symmetry. The solution to this equation generates interactions not explicitly present in the original Lagrangian, and the original 4-fermion interaction is not present in the solution. The theory creates bound-states with respect to which a perturbation theory consistent with the chiral symmetry is set up. The analysis suggests that this theory is renormalizable in the sense that all divergences can be grouped into a few arbitrary parameters. The renormalized propagators of this model are shown to be identical to those of a new solution to the sigma-model in which the bare 4-field coupling lambda 0 is chosen to be twice the π-fermion coupling g 0 . Also considered is spontaneously broken abelian gauge model without fundamental scalar fields by coupling an axial vector gauge field to the N ambu-Jona Lasinio model. It is shown how the Goldstone consequence of spontaneous symmetry breaking is avoided in the radiation gauge, and verify the Guralnik, Hagen, and Kibble theorem that under these conditions the global charge conservation is lost even though there is still local current conservation. This is contrasted with the Lorentz gauge situation. This also demonstrated the way the various noncovariant components of the massive gauge field combine in a gauge invariant scattering amplitude to propagate covariantly as a massive spin-1 particle, and this is compared with the Lorentz gauge calculation. F inally, a new model of interacting massless fermions is introduced, based on the models of Nambu and Jona Lasinio, and the Bjorken, which spontaneously breaks both chiral symmetry and Lorentz invariance. The content of this model is the same as that of the gauge model without fundamental scalar fields, but without fundamental gauge fields as well
International Nuclear Information System (INIS)
Phillips, S.
1985-01-01
The mathematical problem of inverting the operator Δ x μν ≡ g μν g αβ δ x α δ x β -δ x μ δ x ν , as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article. Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, Δ x μν L ν (x) J μ (x), can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one. Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action
Effective monopole potential for SU(2) lattice gluodynamics in spatial maximal Abelian gauge
International Nuclear Information System (INIS)
Chernodub, M.N.; Polikarpov, M.I.; Veselov, A.I.
1999-01-01
We investigate the dual superconductor hypothesis in finite-temperature SU(2) lattice gluodynamics in the Spatial Maximal Abelian gauge. This gauge is more physical than the ordinary Maximal Abelian gauge due to absence of non-localities in temporal direction. We shown numerically that in the Spatial Maximal Abelian gauge the probability distribution of the abelian monopole field is consistent with the dual superconductor mechanism of confinement [ru
Nonperturbative dynamics of hot non-Abelian gauge fields: Beyond the leading log approximation
International Nuclear Information System (INIS)
Arnold, Peter; Yaffe, Laurence G.
2000-01-01
Many aspects of high-temperature gauge theories, such as the electroweak baryon number violation rate, color conductivity, and the hard gluon damping rate, have previously been understood only at leading logarithmic order (that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling). We discuss how to systematically go beyond leading logarithmic order in the analysis of physical quantities. Specifically, we extend to next-to-leading-log order (NLLO) the simple leading-log effective theory due to Bo''deker that describes non-perturbative color physics in hot non-Abelian plasmas. A suitable scaling analysis is used to show that no new operators enter the effective theory at next-to-leading-log order. However, a NLLO calculation of the color conductivity is required, and we report the resulting value. Our NLLO result for the color conductivity can be trivially combined with previous numerical work by Moore to yield a NLLO result for the hot electroweak baryon number violation rate
On the relation between fields and potentials in non abelian Gauge Theories
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1979-01-01
Some examples have been given in the literature of ambiguous gauge fields, i.e. those not having a unique potential (up to a gauge transformation). An example given by Deser and Wilczek is examined and found the condition (for any gauge group) that the group element generating the potentials must satisfy in order for the potentials not to be related by any gauge transformation. In three dimensions (for Su 2 ) there are other families of ambiguous fields characterized by arbitrary unit vector fields n vector (n vector) (n 2 vector =1). The example given by Wu and Yang belongs to a particular family with n vector = n vector. r vector / r vector. The sources of these fields and some interesting relations between them are also found [pt
Blockspin and multigrid for staggered fermions in non-abelian gauge fields
International Nuclear Information System (INIS)
Kalkreuter, T.; Mack, G.; Speh, M.
1991-07-01
We discuss blockspins for staggered fermions, i.e. averaging and interpolation procedures which are needed in a real space renormalization group approach to gauge theories with staggered fermions and in a multigrid approach to the computation of gauge covariant propagators. The discussion starts from the requirement that the symmetries of the free action should be preserved by the blocking procedure in the limit of a pure gauge. A definition of an averaging kernel as a solution of a gauge covariant eigenvalue equation is proposed, and the properties of a corresponding interpolation kernel are examined in the light of general criteria for good choices of blockspins. Some results of multigrid computation of bosonic propagation in an SU(2) gauge field in 4 dimensions are also presented. (orig.)
Spontaneously broken abelian gauge invariant supersymmetric model
International Nuclear Information System (INIS)
Mainland, G.B.; Tanaka, K.
A model is presented that is invariant under an Abelian gauge transformation and a modified supersymmetry transformation. This model is broken spontaneously, and the interplay between symmetry breaking, Goldstone particles, and mass breaking is studied. In the present model, spontaneously breaking the Abelian symmetry of the vacuum restores the invariance of the vacuum under a modified supersymmetry transformation. (U.S.)
The chiral bosonization in non-Abelian gauge theories
International Nuclear Information System (INIS)
Andrianov, A.A.; Novozhilov, Y.
1985-01-01
The chiral bosonization in non-Abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, the QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour Skyrmion-boson with the baryon number 2/3. (author)
Maximal Abelian gauge and a generalized BRST transformation
Directory of Open Access Journals (Sweden)
Shinichi Deguchi
2016-05-01
Full Text Available We apply a generalized Becchi–Rouet–Stora–Tyutin (BRST formulation to establish a connection between the gauge-fixed SU(2 Yang–Mills (YM theories formulated in the Lorenz gauge and in the Maximal Abelian (MA gauge. It is shown that the generating functional corresponding to the Faddeev–Popov (FP effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.
Gravitational waves from Abelian gauge fields and cosmic strings at preheating
International Nuclear Information System (INIS)
Dufaux, Jean-Francois; Figueroa, Daniel G.; Garcia-Bellido, Juan
2010-01-01
Primordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in the polarization anisotropies of the cosmic microwave background. The detection of these waves will open a new window into the early Universe, and therefore it is important to characterize in detail all possible sources of primordial gravitational waves. In this paper we develop theoretical and numerical methods to study the production of gravitational waves from out-of-equilibrium gauge fields at preheating. We then consider models of preheating after hybrid inflation, where the symmetry breaking field is charged under a local U(1) symmetry. We analyze in detail the dynamics of the system in both momentum and configuration space. We show that gauge fields leave specific imprints in the resulting gravitational wave spectra, mainly through the appearance of new peaks at characteristic frequencies that are related to the mass scales in the problem. We also show how these new features in the spectra correlate with stringlike spatial configurations in both the Higgs and gauge fields that arise due to the appearance of topological winding numbers of the Higgs around Nielsen-Olesen strings. We study in detail the time evolution of the spectrum of gauge fields and gravitational waves as these strings evolve and decay before entering a turbulent regime where the gravitational wave energy density saturates.
Local observables in non-Abelian gauge theories
International Nuclear Information System (INIS)
Sharatchandra, H.S.
1981-09-01
Labelling of the physical states of a non-Abelian gauge theory on a lattice in terms of local observables in considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter field is also included. The non-local variables required when space is multiply-connected, are specified. Non-Abelian version of the Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail. (orig.)
Construction of non-Abelian gauge theories on noncommutative spaces
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin
2001-01-01
We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)
Construction of non-Abelian gauge theories on noncommutative spaces
Energy Technology Data Exchange (ETDEWEB)
Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)
2001-06-01
We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)
Topological insulators in cold-atom gases with non-Abelian gauge fields: the role of interactions
Energy Technology Data Exchange (ETDEWEB)
Orth, Peter Philipp [Institut fuer Theorie der Kondensierten Materie, Karlsruher Institut fuer Technologie, 76128 Karlsruhe (Germany); Cocks, Daniel; Buchhold, Michael; Hofstetter, Walter [Institut fuer Theoretische Physik, Goethe Universitaet, 60438 Frankfurt am Main (Germany); Rachel, Stephan [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Le Hur, Karyn [Department of Physics, Yale University, New Haven, Connecticut 06520 (United States); Center for Theoretical Physics, Ecole Polytechnique, 91128 Palaiseau Cedex (France)
2012-07-01
With the recent technological advance of creating (non)-Abelian gauge fields for ultracold atoms in optical lattices, it becomes possible to study the interplay of topological phases and interactions in these systems. Specifically, we consider a spinful and time-reversal invariant version of the Hofstadter problem. In addition, we allow for a hopping term which does not preserve S{sub z} spin symmetry and a staggered sublattice potential. Without interactions, the parameters can be tuned such that the system is a topological insulator. Using a combination of analytical techniques and the powerful real-space dynamical mean-field (R-DMFT) method, we discuss the effect of interactions and determine the interacting phase diagram.
Abelian gauge theories on homogeneous spaces
International Nuclear Information System (INIS)
Vassilevich, D.V.
1992-07-01
An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S 3 is calculated. A generalization of the Chern-Simons action is suggested and analysed with the example of SU(3)/U(1) x U(1). (author). 11 refs
International Nuclear Information System (INIS)
Huang Yongchang; Huo Qiuhong
2008-01-01
Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-Abelian Chern-Simons topological term in 2+1 dimensions. We use consistency of Coulomb gauge condition to naturally deduce a new gauge condition. Furthermore, we obtain the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum is the sum of the orbital angular momentum and spin angular momentum of the non-Abelian gauge field. Finally, we obtain the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and A 0 s (x) charge
Noncommuting fields and non-Abelian fluids
International Nuclear Information System (INIS)
Jackiw, R.
2004-01-01
The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described
Instantons and Gribov copies in the maximally Abelian gauge
International Nuclear Information System (INIS)
Bruckmann, F.; Heinzl, T.; Wipf, A.; Tok, T.
2000-01-01
We calculate the Faddeev-Popov operator corresponding to the maximally Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit zero modes of this operator. Within an illuminating toy model (Yang-Mills mechanics) the problem can be completely solved and understood. In the field theory case we are able to find an analytic expression for a normalizable zero mode in the background of a single 't Hooft instanton. Accordingly, such an instanton corresponds to a horizon configuration in the maximally Abelian gauge. Possible physical implications are discussed
Fermion-dyon dynamics in non-Abelian gauge theory
International Nuclear Information System (INIS)
Pant, P.C.; Pandey, V.P.; Rajput, B.S.
1999-01-01
The study of behaviour of a fermion in the field of non-Abelian dyon has been undertaken in Lagrangian and Hamiltonian formulation. Solving Dirac equation, expression for energy Eigen value has been obtained and the Hamiltonian of this system has been shown to involve spin as well as contribution of massive fields associated with these particles. By introducing suitable spinors, the Pauli equation for a dyon moving in the field of fermion has been solved in non-Abelian gauge gauge theory and it is shown that introduction of massive fields perceptibly modifies the energy Eigen value and Eigen function of bound states of the system. (author)
The Hawking effect in abelian gauge theories
International Nuclear Information System (INIS)
Stephens, C.R.
1989-01-01
In an effort to compare and contrast gravity with other field theories an investigation is made into whether the Hawking effect is a peculiarly gravitational phenomenon. It is found that the effect exists for a particular background abelian gauge field configuration, as well as certain background gravitational field configurations. Specifically, pair production in a uniform electric field is shown to admit a thermal interpretation. In an effort to find out just what is singular about gravity it is found that the Hawking temperature characteristic of a particular gravitational field configuration is independent of the properties of the quantum fields propagating theorem, in direct contrast to the gauge field case. This implies that if the one loop approximation is to be valid the electric field must be ''cold'' relative to the energy scales set by the quantum fields. In gravity, however, because of the existence of a fundamental scale, the Planck length, the gravitational field can be ''hot'' or ''cold'' and a one loop approximation still remain valid. copyright 1989 Academic Press, Inc
International Nuclear Information System (INIS)
Scheck, Florian
2010-01-01
Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [de
Some aspects of non-Abelian gauge theories
International Nuclear Information System (INIS)
Tyburski, L.J.
1976-01-01
Two aspects of the theory of non-Abelian gauge fields are considered. In the first part, the fermion-fermion scattering amplitude is calculated for a non-Abelian gauge theory with SU(N) gauge symmetry in the limit of high energy with fixed momentum transfer through sixth order in the coupling constant. Only the leading logarithmic terms in each order of perturbation theory are kept. To avoid the infrared problem, the Higgs mechanism is invoked to give masses to the vector bosons of the theory. It is found that the scattering amplitude exponentiates to a Regge form. This result is qualitatively different from an earlier published calculation. In the second part of the thesis, we consider fermion-fermion scattering in a non-Abelian gauge theory with massless vector bosons, and demonstrate that for physically measurable cross sections the infrared divergences of the theory cancel out to lowest nontrivial order
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)
Colored, spinning classical particle in an external non-Abelian gauge field
International Nuclear Information System (INIS)
Arodz, H.
1982-04-01
Classical non-relativistic equations of motion are derived for a colored, spinning point-like particle in an external SU(2) gauge field from Dirac equation. It is found that in addition to the classical spin and color spin vectors, S, I, it is necessary to introduce a new classical dynamical variable [Jsup(ab)], a,b = 1,2,3, describing a mixing of the spin and color. The constraint relations between [Jsup(ab)], S, I are also found. (Auth.)
Self-dual configurations in Abelian Higgs models with k-generalized gauge field dynamics
Energy Technology Data Exchange (ETDEWEB)
Casana, R.; Cavalcante, A. [Departamento de Física, Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil); Hora, E. da [Departamento de Física, Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil); Coordenadoria Interdisciplinar de Ciência e Tecnologia, Universidade Federal do Maranhão,65080-805, São Luís, Maranhão (Brazil)
2016-12-14
We have shown the existence of self-dual solutions in new Maxwell-Higgs scenarios where the gauge field possesses a k-generalized dynamic, i.e., the kinetic term of gauge field is a highly nonlinear function of F{sub μν}F{sup μν}. We have implemented our proposal by means of a k-generalized model displaying the spontaneous symmetry breaking phenomenon. We implement consistently the Bogomol’nyi-Prasad-Sommerfield formalism providing highly nonlinear self-dual equations whose solutions are electrically neutral possessing total energy proportional to the magnetic flux. Among the infinite set of possible configurations, we have found families of k-generalized models whose self-dual equations have a form mathematically similar to the ones arising in the Maxwell-Higgs or Chern-Simons-Higgs models. Furthermore, we have verified that our proposal also supports infinite twinlike models with |ϕ|{sup 4}-potential or |ϕ|{sup 6}-potential. With the aim to show explicitly that the BPS equations are able to provide well-behaved configurations, we have considered a test model in order to study axially symmetric vortices. By depending of the self-dual potential, we have shown that the k-generalized model is able to produce solutions that for long distances have a exponential decay (as Abrikosov-Nielsen-Olesen vortices) or have a power-law decay (characterizing delocalized vortices). In all cases, we observe that the generalization modifies the vortex core size, the magnetic field amplitude and the bosonic masses but the total energy remains proportional to the quantized magnetic flux.
Non Abelian T-duality in Gauged Linear Sigma Models
Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto
2018-04-01
Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.
Renormalization of an abelian gauge theory in stochastic quantization
International Nuclear Information System (INIS)
Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.
1987-01-01
The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)
International Nuclear Information System (INIS)
Mills, R.
1989-01-01
This article is a survey of the history and ideas of gauge theory. Described here are the gradual emergence of symmetry as a driving force in the shaping of physical theory; the elevation of Noether's theorem, relating symmetries to conservation laws, to a fundamental principle of nature; and the force of the idea (''the gauge principle'') that the symmetries of nature, like the interactions themselves, should be local in character. The fundamental role of gauge fields in mediating the interactions of physics springs from Noether's theorem and the gauge principle in a remarkably clean and elegant way, leaving, however, some tantalizing loose ends that might prove to be the clue to a future deeper level of understanding. The example of the electromagnetic field as the prototype gauge theory is discussed in some detail and serves as the basis for examining the similarities and differences that emerge in generalizing to non-Abelian gauge theories. The article concludes with a brief examination of the dream of total unification: all the forces of nature in a single unified gauge theory, with the differences among the forces due to the specific way in which the fundamental symmetries are broken in the local environment
High-energy behavior of non-Abelian gauge theories
International Nuclear Information System (INIS)
Nieh, H.T.; Yao, Y.
1976-01-01
This paper is a detailed account of a study in perturbation theory of the high-energy behavior of non-Abelian gauge theories. The fermion-fermion scattering amplitude is calculated up to sixth order in the coupling constant in the high-energy limit s → infinity with fixed t, in the approximation of keeping only the leading logarithmic terms. Results indicate that the high-energy behavior of non-Abelian gauge theories are complicated, and quite different from the known behaviors of other field theories studied so far
Problem of colour confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Gribov, V.N.
1978-01-01
The problem of the colour confinement in the non-abelian gauge theories is studied. A more rigorous treatment of the Fadeev-Popov procedure for the quantization of the non-abelian gauge theories is presented. In the improved procedure one has to introduce additional bounds on the region of integration in the functional space of non-abelian fields. The integration is to be performed over the fields with positive-definite Faddeev-Popov determinant. This limitation has little influence on oscillations with high frequencies, but reduces drastically the amplitudes of low-frequency oscillations. This implies, that interaction of two colour charges does not go into infinity at finite distances, rather it is linearly rising with distance
Non-Abelian formulation of a vector-tensor gauge theory with topological coupling
International Nuclear Information System (INIS)
Barcelos Neto, J.; Cabo, A.; Silva, M.B.D.
1995-08-01
We obtain a non-Abelian version of a theory involving vector and tensor and tensor gauge fields interacting via a massive topological coupling, besides the nonminimum one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to compatibilize gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case. (author). 9 refs
Scattering theory of space-time non-commutative abelian gauge field theory
International Nuclear Information System (INIS)
Rim, Chaiho; Yee, Jaehyung
2005-01-01
The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.
The static quark potential from the gauge independent Abelian decomposition
Energy Technology Data Exchange (ETDEWEB)
Cundy, Nigel, E-mail: ndcundy@gmail.com [Lattice Gauge Theory Research Center, FPRD, and CTP, Department of Physics & Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of); Cho, Y.M. [Administration Building 310-4, Konkuk University, Seoul 143-701 (Korea, Republic of); Department of Physics & Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of); Lee, Weonjong; Leem, Jaehoon [Lattice Gauge Theory Research Center, FPRD, and CTP, Department of Physics & Astronomy, Seoul National University, Seoul 151-747 (Korea, Republic of)
2015-06-15
We investigate the relationship between colour confinement and the gauge independent Cho–Duan–Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are
The static quark potential from the gauge independent Abelian decomposition
Cundy, Nigel; Cho, Y. M.; Lee, Weonjong; Leem, Jaehoon
2015-06-01
We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for
Abelian projection on the torus for general gauge groups
International Nuclear Information System (INIS)
Ford, C.; Tok, T.; Wipf, A.
1999-01-01
We consider Yang-Mills theories with general gauge groups G and twists of the four-torus. We find consistent boundary conditions for gauge fields in all instanton sectors. An extended abelian projection with respect to the Polyakov loop operator is presented, where A 0 is independent of time and in the Cartan subalgebra. Fundamental domains for the gauge fixed A 0 are constructed for arbitrary gauge groups. In the sectors with non-vanishing instanton number such gauge fixings are necessarily singular. The singularities can be restricted to Dirac strings joining magnetically charged defects. The magnetic charges of these monopoles take their values in the co-root lattice of the gauge group. We relate the magnetic charges of the defects and the windings of suitable Higgs fields about these defects to the instanton number
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.)
Non-Abelian Gauge Theory in the Lorentz Violating Background
Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais
2018-03-01
In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.
Higgs phase in non-Abelian gauge theories
International Nuclear Information System (INIS)
Kaymakcalan, O.S.
1981-06-01
A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed, it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase
Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles
International Nuclear Information System (INIS)
Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru
2009-01-01
The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix E-mail: felix.finster@mis.mpg.de; Smoller, Joel E-mail: smoller@umich.edu; Yau, S.-T. E-mail: yau@math.harvard.edu
2000-09-18
We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
Finster, Felix; Smoller, Joel; Yau, Shing-Tung
2000-09-01
We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.
The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states
International Nuclear Information System (INIS)
Finster, Felix; Smoller, Joel; Yau, S.-T.
2000-01-01
We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling
Role of Lie algebra for confinement in non-abelian gauge field scheme
International Nuclear Information System (INIS)
Fukushima, K.; Sato, H.
2014-01-01
This article reports an explicit function form for confining classical Yang-Mills vector potentials and quantum fluctuations around the classical field. The classical vector potential, which is composed of a confining localized function and an unlocalized function, satisfies the classical Yang-Mills equation. The confining localized function contributes to the Wilson loop, while the unlocalized function makes no contribution to this loop. The confining linear potential between a heavy fermion and antifermion is due to (1) the Lie algebra and (2) the form of the confining localized function which has opposite signs at the positions of the particle and antiparticle along the Wilson loop in the time direction. Some classical confining parts of vector potentials also change sign on inversion of the coordinates of the axis perpendicular to the axis joining the two particles. The localized parts of the vector potentials are squeezed around the axis connecting the two particles, and the string tension of the confining linear potential is derived. Quantum fluctuations are formulated using a field expression in terms of local basis functions in real spacetime. The quantum path integral gives the Coulomb potential between the two particles in addition to the linear potential due to the classical fields
Dilatonic dyon-like black hole solutions in the model with two Abelian gauge fields
Energy Technology Data Exchange (ETDEWEB)
Abishev, M.E. [Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty (Kazakhstan); Institute of Gravitation and Cosmology, RUDN University, Moscow (Russian Federation); Boshkayev, K.A. [Institute of Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Almaty (Kazakhstan); Ivashchuk, V.D. [Center for Gravitation and Fundamental Metrology, VNIIMS, Moscow (Russian Federation); Institute of Gravitation and Cosmology, RUDN University, Moscow (Russian Federation)
2017-03-15
Dilatonic black hole dyon-like solutions in the gravitational 4d model with a scalar field, two 2-forms, two dilatonic coupling constants λ{sub i} ≠ 0, i = 1,2, obeying λ{sub 1} ≠ -λ{sub 2} and the sign parameter ε = ±1 for scalar field kinetic term are considered. Here ε = -1 corresponds to a ghost scalar field. These solutions are defined up to solutions of two master equations for two moduli functions, when λ{sup 2}{sub i} ≠ 1/2 for ε = -1. Some physical parameters of the solutions are obtained: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters β and γ. The PPN parameters do not depend on the couplings λ{sub i} and ε. A set of bounds on the gravitational mass and scalar charge are found by using a certain conjecture on the parameters of solutions, when 1 + 2λ{sub i}{sup 2} ε > 0, i = 1,2. (orig.)
Non-Abelian duality in N = 4 supersymmetric gauge theories
International Nuclear Information System (INIS)
Dorey, Nicholas; Fraser, Christophe; Hollowood, Timithy J.; Kneipp, Marco A.C.
1996-03-01
A semi-classical check of the Goddard-Nuyts-Olive (GNO) generalized duality conjecture for gauge theories with adjoint Higgs fields is performed for the case where the unbroken gauge group is non-Abelian. The monopole solutions of the theory transform under the non-Abelian part of the unbroken global symmetry and the associated component of the moduli space is a Lie group coset space. The well-known problems in introducing collective coordinates for these degrees-of-freedom are solved by considering suitable multi monopole configurations in which the long-range non-Abelian fields cancel. In the context of an N = 4 supersymmetric gauge theory, the multiplicity of BPS saturated states is given by the number of ground-states of a supersymmetric quantum mechanics on the compact internal moduli space. The resulting degeneracy is expressed as the Euler character of the coset space. In all cases the number of states is consistent with the dimensions of the multiplets of the unbroken dual gauge group, and hence the results provide strong support for the GNO conjecture. (author). 39 refs
Abelian gauge potentials on cubic lattices
DEFF Research Database (Denmark)
Burrello, M.; Lepori, L.; Paganelli, S.
2017-01-01
The study of the properties of quantum particles in a periodic potential subjected to a magnetic field is an active area of research both in physics and mathematics, and it has been and is yet deeply investigated. In this chapter we discuss how to implement and describe tunable Abelian magnetic...... potentials in one-dimensional rings....
Nonequilibrium formulation of abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Zoeller, Thorsten
2013-09-01
This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at
Central extensions of some Abelian finite gauge groups
International Nuclear Information System (INIS)
Combe, Ph.; Rodriguez, R.; Sirugue, M.; Sirugue-Collin, M.
1981-01-01
The authors describe central extensions of Abelian finite gauge groups on lattices which are permutation invariant. Moreover some remarks are made on the gauge models on lattice associated with these non-commutative central extensions. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Gattringer, Christof, E-mail: christof.gattringer@uni-graz.at; Marchis, Carlotta, E-mail: carla.marchis@uni-graz.at
2017-03-15
We propose a new approach to strong coupling series and dual representations for non-abelian lattice gauge theories using the SU(2) case as an example. The Wilson gauge action is written as a sum over “abelian color cycles” (ACC) which correspond to loops in color space around plaquettes. The ACCs are complex numbers which can be commuted freely such that the strong coupling series and the dual representation can be obtained as in the abelian case. Using a suitable representation of the SU(2) gauge variables we integrate out all original gauge links and identify the constraints for the dual variables in the SU(2) case. We show that the construction can be generalized to the case of SU(2) gauge fields with staggered fermions. The result is a strong coupling series where all gauge integrals are known in closed form and we discuss its applicability for possible dual simulations. The abelian color cycle concept can be generalized to other non-abelian gauge groups such as SU(3).
The static quark potential from the gauge independent Abelian decomposition
Directory of Open Access Journals (Sweden)
Nigel Cundy
2015-06-01
Full Text Available We investigate the relationship between colour confinement and the gauge independent Cho–Duan–Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential.We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that
Vortices and quark confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Mandelstam, S.
1976-01-01
Non-Abelian vortices of the type proposed by Nielsen and Olesen are discussed. It is shown that the vortices must contain a single unit of quantized flux absorbed by a Dirac monopole at each end. The monopoles satisfy a confinement condition; if quark numbers are assigned to the monopoles, is is found that the model contains a natural explanation of quark confinement. The I-spin variables associated with the non-Abelian gauge field correspond to the colour degree freedom. An alternative model in which (colour) charges and monopoles are interchanged is also suggested. The Higgs field which breaks the degeneracy of the vacuum is replaced by an operator which creates monopoles of the type suggested by 't Hooft. In such a model colour might be confined. The investigations are at a very preliminary stage, but the model appears to offer a natural explanation of confinement without the explicit introduction of monopole fields. (Auth.)
Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials
International Nuclear Information System (INIS)
Satija, Indubala I.; Dakin, Daniel C.; Clark, Charles W.
2006-01-01
We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta
Gauge invariance and the effective potential: the Abelian Higgs model
International Nuclear Information System (INIS)
Ramaswamy, S.
1995-01-01
The gauge invariance of the effective potential in the Abelian Higgs model is examined. The Nielsen identities, which ensure gauge independence of the effective potential and other physical quantities, are shown to hold at finite temperature and in the presence of the chemical potential. It is also shown that, as a consequence of the Nielsen identities, the standard order parameter for symmetry breaking, namely the scalar field vacuum expectation value, has a non-zero parametric dependence on the gauge choice employed. These are then verified to one loop at finite temperature. High-temperature symmetry breaking is considered. In the leading high-temperature limit, the potential agrees with the previous calculations. (orig.)
Renormalizable Abelian-projected effective gauge theory derived from quantum chromodynamics
International Nuclear Information System (INIS)
Kondo, Kei-ichi; Shinohara, Toru
2001-01-01
We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the β-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory. (author)
Energy Technology Data Exchange (ETDEWEB)
Capri, M.A.L.; Fiorentini, D.; Sorella, S.P. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Pereira, A.D. [UERJ - Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); UFF - Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)
2017-08-15
In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hepth]), Pereira et al. (arXiv:1605.09747 [hep-th]), the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement. (orig.)
Capri, M. A. L.; Fiorentini, D.; Pereira, A. D.; Sorella, S. P.
2017-08-01
In this work, we study the propagators of matter fields within the framework of the refined Gribov-Zwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the Faddeev-Popov operator is added in the matter sector. Making use of the recent BRST-invariant formulation of the Gribov-Zwanziger framework achieved in Capri et al. (Phys Rev D 92(4):045039, 2015), (Phys Rev D 94(2):025035, 2016), (Phys Rev D 93(6):065019, 2016), (arXiv:1611.10077 [hep-th]), Pereira et al. (arXiv:1605.09747 [hep-th]),the propagators of scalar and quark fields in the adjoint and fundamental representations of the gauge group are worked out explicitly in the linear covariant, Curci-Ferrari and maximal Abelian gauges. Whenever lattice data are available, our results exhibit good qualitative agreement.
Non-abelian gauge invariant classical Lagrangian formalism for point electric and magnetic charge
International Nuclear Information System (INIS)
Brandt, R.A.; Neri, F.
1978-01-01
The classical electrodynamics of electrically charged point particles has been generalized to include non-Abelian gauge groups and to include magnetically charged point particles. In this paper these two distinct generalizations are unified into a non-Abelian gauge theory of electric and magnetic charge. Just as the electrically charged particles constitute the generalized source of the gauge fields, the magnetically charged particles constitute the generalized source of the dual fields. The resultant equations of motion are invariant to the original 'electric' non-Abelian gauge group, but, because of the absence of a corresponding 'magnetic' gauge group, there is no 'duality' symmetry between electric and magnetic quantities. However, for a class of solutions to these equations, which includes all known point electric and magnetic monopole constructions, there is shown to exist an equivalent description based on a magnetic, rather than electric, gauge group. The gauge potentials in general are singular on strings extending from the particle position to infinity, but it is shown that the observables are without string singularities, and that the theory is Lorentz invariant, provided a charge quantization condition is satisfied. This condition, deduced from a stability analysis, is necessary for the consistency of the classical non-Abelian theory, in contrast to the Abelian case, where such a condition is necessary only for the consistency of the quantum theory. It is also shown that in the classical theory the strings cannot be removed by gauge transformations, as they sometimes can be in the quantum theory. (Auth.)
Flavored gauge mediation with discrete non-Abelian symmetries
Everett, Lisa L.; Garon, Todd S.
2018-05-01
We explore the model building and phenomenology of flavored gauge-mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the S U (2 ) messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S3 Higgs-messenger symmetry, we demonstrate that, while the minimal implementation of this scenario suffers from a severe μ /Bμ problem that is well known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that μ and Bμ can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry-breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.
Scalar formalism for non-Abelian gauge theory
International Nuclear Information System (INIS)
Hostler, L.C.
1986-01-01
The gauge field theory of an N-dimensional multiplet of spin- 1/2 particles is investigated using the Klein--Gordon-type wave equation ]Pi x (1+isigma) x Pi+m 2 ]Phi = 0, Pi/sub μ/equivalentpartial/partialix/sub μ/-eA/sub μ/, investigated before by a number of authors, to describe the fermions. Here Phi is a 2 x 1 Pauli spinor, and sigma repesents a Lorentz spin tensor whose components sigma/sub μ//sub ν/ are ordinary 2 x 2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. The equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum tau-functions, tau(2,1, xxx 3 xxx)equivalent , where Psi/sub in/ is a Heisenberg operator belonging to a 4N x 1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics
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.
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.
Dual potentials in non-Abelian gauge theories
International Nuclear Information System (INIS)
Caticha, A.
1988-01-01
Motivated by the possibility that confinement and superconductivity are similar phenomena, dual potentials are introduced into Yang-Mills theory in two different ways. Both are extensions of Zwanziger's two-potential formalism for Abelian charges and monopoles to the non-Abelian case. In the first approach the dual potentials carry a color index and there is a rather simple, although nonlocal, dual-variable formulation. In the second approach dual variables are introduced into the so-called Abelian projection of the SU(2) Yang-Mills theory. An interesting feature is that the quartic contact interactions are absent and there is a special gauge choice for which the theory takes on a ''purely electromagnetic'' form. More important, however, is the appearance of an additional Abelian magnetic gauge symmetry the dynamical breaking of which may be associated with confinement
Non-Abelian vortices in N=1* gauge theory
International Nuclear Information System (INIS)
Markov, V.; Marshakov, A.; Yung, A.
2005-01-01
We consider the N=1* supersymmetric SU(2) gauge theory and demonstrate that the Z2 vortices in this theory acquire orientational zero modes, associated with the rotation of magnetic flux inside SU(2) group, and turn into the non-Abelian strings, when the masses of all chiral fields become equal. These non-Abelian strings are not BPS-saturated. We study the effective theory on the string world sheet and show that it is given by two-dimensional non-supersymmetric O(3) sigma model. The confined 't Hooft-Polyakov monopole is seen as a junction of the Z2-string and anti-string, and as a kink in the effective world sheet sigma model. We calculate its mass and show that besides the four-dimensional confinement of monopoles, they are also confined in the two-dimensional theory: the monopoles stick to anti-monopoles to form the meson-like configurations on the strings they are attached to
Restoration of the local gauge symmetry and color confinement in non-Abelian gauge theories
International Nuclear Information System (INIS)
Hata, Hiroyuki
1982-01-01
Restoration of the local gauge symmetry and its connection to color confinement is investigated in non-Abelian gauge theories with covariant gauge fixing. We consider the Noether current J sub(μ,#betta#)sup(a) of the local gauge transformation with transformation functions #betta#sup(b)(x) linear in x sub(μ); #betta#sup(b)(x) = delta sup(ab)x sub(#betta#). This current is conserved only in the physical subspace of the state vector space and in perturbation theory contains a massless pole communicating to the gauge field. We define the local gauge symmetry restoration as the disappearance of this massless ''Goldstone'' pole from J sub(μ,#betta#)sup(a). The restoration condition is obtained and it coincides exactly with the color confinement criterion proposed earlier by Kugo and Ojima. Quarks and other colored particles are shown to be confined in the local gauge symmetry restored phase by using the Ward identities of J sub(μ,#betta#)sup(a). (author)
Abelian gauge symmetries in F-theory and dual theories
Song, Peng
In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by
Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge
International Nuclear Information System (INIS)
Capri, M.A.L.; Guimaraes, M.S.; Lemes, V.E.R.; Sorella, S.P.; Tedesco, D.G.
2014-01-01
A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2) and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm. -- Highlights: •We study the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge. •For d=2 we obtain solutions with finite action but not finite Hilbert norm. •For d=3,4 we obtain solutions with finite action and finite Hilbert norm. •These results can be compared with those previously obtained in the Landau gauge
Plasma instabilities and turbulence in non-Abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Scheffler, Sebastian Herwig Juergen
2010-02-17
Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (
Plasma instabilities and turbulence in non-Abelian gauge theories
International Nuclear Information System (INIS)
Scheffler, Sebastian Herwig Juergen
2010-01-01
Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the ''colour glass condensate'' is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (< or similar 1 GeV). Essential results can be translated from the gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the quasi
International Nuclear Information System (INIS)
Itzykson, C.
1978-01-01
In these notes the author provides some background on the theory of gauge fields, a subject of increasing popularity among particle physicists (and others). Detailed motivations and applications which are covered in the other lectures of this school are not presented. In particular the application to weak interactions is omitted by referring to the introduction given by J. Ilipoulos a year ago (CERN Report 76-11). The aim is rather to stress those aspects which suggest that gauge fields may play some role in a future theory of strong interactions. (Auth.)
Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.
2016-12-01
We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.
On the loop-loop scattering amplitudes in Abelian and non-Abelian gauge theories
International Nuclear Information System (INIS)
Meggiolaro, Enrico
2005-01-01
The high-energy elastic scattering amplitude of two colour-singlet qq-bar pairs is governed by the correlation function of two Wilson loops, which follow the classical straight lines for quark (antiquark) trajectories. This quantity is expected to be free of IR divergences, differently from what happens for the parton-parton elastic scattering amplitude, described, in the high-energy limit, by the expectation value of two Wilson lines. We shall explicitly test this IR finiteness by a direct non-perturbative computation of the loop-loop scattering amplitudes in the (pedagogic, but surely physically interesting) case of quenched QED. The results obtained for the Abelian case will be generalized to the case of a non-Abelian gauge theory with Nc colours, but stopping to the order O(g4) in perturbation theory. In connection with the above-mentioned IR finiteness, we shall also discuss some analytic properties of the loop-loop scattering amplitudes in both Abelian and non-Abelian gauge theories, when going from Minkowskian to Euclidean theory, which can be relevant to the still unsolved problem of the s-dependence of hadron-hadron total cross-sections
Phase structure and critical properties of an abelian gauge theory
Energy Technology Data Exchange (ETDEWEB)
Mo, Sjur
2001-12-01
The main new results are presented in the form of three papers at the end of this thesis. The main topic is Monte-Carlo studies of the phase structure and critical properties of the phenomenological Ginzburg-Landau model, i.e. an abelian gauge theory. However, the first paper is totally different and deals with microscopic theory for lattice-fermions in a magnetic field. Paper I is about ''Fermion-pairing on a square lattice in extreme magnetic fields''. We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to ''k-space'', or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C{sub 4{nu}} of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down. Paper II is about the ''Hausdorff dimension of critical fluctuations in abelian gauge theories''. Here we analyze the geometric properties of the line-like critical fluctuations (vortex loops) in the Ginzburg-Landau model in zero magnetic background field. By using a dual description, we obtain scaling relations between exponents of geometric arid thermodynamic nature. In particular we connect the anomalous scaling dimension {eta} of the dual matter field to the Hausdorff or fractal dimension D{sub H} of the critical fluctuations, in the original model
Free Abelian 2-form gauge theory: BRST approach
International Nuclear Information System (INIS)
Malik, R.P.
2008-01-01
We discuss various symmetry properties of the Lagrangian density of a four- (3+1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition, which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of our present theory are found to be absolutely anticommuting in nature. For the present 2-form theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of physicality criteria, where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of the BRST formalism, from the constraint analysis. (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
New topological invariants for non-abelian antisymmetric tensor fields from extended BRS algebra
International Nuclear Information System (INIS)
Boukraa, S.; Maillet, J.M.; Nijhoff, F.
1988-09-01
Extended non-linear BRS and Gauge transformations containing Lie algebra cocycles, and acting on non-abelian antisymmetric tensor fields are constructed in the context of free differential algebras. New topological invariants are given in this framework. 6 refs
The geometry and physics of Abelian gauge groups in F-theory
Energy Technology Data Exchange (ETDEWEB)
Keitel, Jan
2015-07-14
In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.
The geometry and physics of Abelian gauge groups in F-theory
International Nuclear Information System (INIS)
Keitel, Jan
2015-01-01
In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.
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.
Renormalization of gauge fields models
International Nuclear Information System (INIS)
Becchi, C.; Rouet, A.; Stora, R.
1974-01-01
A new approach to gauge field models is described. It is based on the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme making extensive use of the quantum action principle, and the Slavnov invariance. The quantum action principle being first summarized in the framework of the BPHZ is then applied to a global symmetry problem. The symmetry property of the gauge field Lagrangians in the tree approximation is exhibited, and the preservation of this property at the quantum level is discussed. The main results relative to the Abelian and SU(2) Higgs-Kibble models are briefly reviewed [fr
On the elimination of infinitesimal Gribov ambiguities in non-Abelian gauge theories
International Nuclear Information System (INIS)
Pereira, Antonio D.; Sobreiro, Rodrigo F.
2013-01-01
An alternative method to account for the Gribov ambiguities in gauge theories is presented. It is shown that, to eliminate Gribov ambiguities, at infinitesimal level, it is required to break the BRST symmetry in a soft manner. This can be done by introducing a suitable extra constraint that eliminates the infinitesimal Gribov copies. It is shown that the present approach is consistent with the well established known cases in the literature, i.e., the Landau and maximal Abelian gauges. The method is valid for gauges depending exclusively on the gauge field and is restricted to classical level. However, occasionally, we deal with quantum aspects of the technique, which are used to improve the results. (orig.)
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
Energy Technology Data Exchange (ETDEWEB)
Zohar, Erez, E-mail: erez.zohar@mpq.mpg.de [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany); Wahl, Thorsten B. [Rudolf Peierls Centre for Theoretical Physics, Oxford, 1 Keble Road, OX1 3NP (United Kingdom); Burrello, Michele, E-mail: michele.burrello@mpq.mpg.de [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany); Cirac, J. Ignacio [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching (Germany)
2016-11-15
Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.
Constrained Gauge Fields from Spontaneous Lorentz Violation
Chkareuli, J L; Jejelava, J G; Nielsen, H B
2008-01-01
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type $A_{\\mu}^{2}=M^{2}$ ($M$ is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory proves to be QED with a massless vector Goldstone boson naturally associated with the photon, while the non-Abelian symmetry case results in a conventional Yang-Mills theory. These theories, both Abelian and non-Abelian, look essentially nonlinear and contain particular Lorentz (and $CPT$) violating couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical ...
Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio
2010-08-01
It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.
Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism
International Nuclear Information System (INIS)
Lima, Gabriel Di Lemos Santiago
2014-01-01
Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism. -- Highlights: • A gauge restoration technique from Abelian anomalous models is discussed. • It is shown that there is another way that leads to gauge symmetry restoration from such technique. • It is shown that the first gauge restoration preserves the anomaly, while the proposed second one is free from anomalies. • It is shown that the proposed gauge symmetry restoration can be identified with the Stueckelberg mechanism
Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism
Energy Technology Data Exchange (ETDEWEB)
Lima, Gabriel Di Lemos Santiago, E-mail: gabriellemos3@hotmail.com
2014-02-15
Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism. -- Highlights: • A gauge restoration technique from Abelian anomalous models is discussed. • It is shown that there is another way that leads to gauge symmetry restoration from such technique. • It is shown that the first gauge restoration preserves the anomaly, while the proposed second one is free from anomalies. • It is shown that the proposed gauge symmetry restoration can be identified with the Stueckelberg mechanism.
International Nuclear Information System (INIS)
Kazama, Y.; Yao, Y.
1982-01-01
In spontaneously broken non-Abelian gauge theories which admit gauge hierarchy at the tree level, we show, to all orders in perturbation theory, that (i) the superheavy particles decouple from the light sector at low energies, (ii) an effective low-energy renormalizable theory emerges together with appropriate counterterms, and (iii) the gauge hierarchy can be consistently maintained in the presence of radiative corrections. These assertions are explicitly demonstrated for O(3) gauge theory with two triplets of Higgs particles in a manner easily applicable to more realistic grand unified theories. Furthermore, as a by-product of our analysis, we obtain a systematic method of computing the parameters of the effective low-energy theory via renormalization-group equations to any desired accuracy
Non-Abelian black holes in D=5 maximal gauged supergravity
International Nuclear Information System (INIS)
Cvetic, M.; Lue, H.; Pope, C. N.
2010-01-01
We investigate static non-Abelian black hole solutions of anti-de Sitter (AdS) Einstein-Yang-Mills-dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-Abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS 2 xS 3 . If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-Abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalized to dimensions other than five.
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.)
Black string first order flow in N=2, d=5 abelian gauged supergravity
Energy Technology Data Exchange (ETDEWEB)
Klemm, Dietmar; Petri, Nicolò; Rabbiosi, Marco [Dipartimento di Fisica, Università di Milano andINFN, Sezione di Milano, Via Celoria 16, I-20133 Milano (Italy)
2017-01-25
We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N=2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.
Extended pure Yang-Mills gauge theories with scalar and tensor gauge fields
International Nuclear Information System (INIS)
Gabrielli, E.
1991-01-01
The usual abelian gauge theory is extended to an interacting Yang-Mills-like theory containing vector, scalar and tensor gauge fields. These gauge fields are seen as components along the Clifford algebra basis of a gauge vector-spinorial field. Scalar fields φ naturally coupled to vector and tensor fields have been found, leading to a natural φ 4 coupling in the lagrangian. The full expression of the lagrangian for the euclidean version of the theory is given. (orig.)
Comment on the Adler-Bardeen theorem in non-Abelian gauge theories
International Nuclear Information System (INIS)
Fujikawa, Kazuo.
1981-09-01
It is pointed out that the constructive proof of the Adler-Bardeen theorem for the chiral and scale (counting identity) anomalies in non-Abelian gauge theories proceeds just as in the spinor electrodynamics, although several interesting features characteristic of non-Abelian theories appear. (author)
Properties of Gribov region and horizon function in the SU(N) Maximal Abelian Gauge
International Nuclear Information System (INIS)
Capri, Marcio Andre Lopes; Gomez, A.J.; Guimaraes, M.S.; Lemes, Vitor Emanuel Rodino; Sorella, Silvio Paolo
2011-01-01
Full text: The problem of the Gribov copies deals with the impossibility of to choose a unique gauge condition in the quantization process in the Yang Mills theories. In the Landau gauge, several properties of the Gribov region are established, the implementation of the Gribov copies in the path integral is taking account by the introduction of the horizon function directly in the action giving rise to modifications in the ghost and gluon propagator in the infrared regime. However, is interesting to looking at other gauge choices for obtain additional information of the phenomena, and compare our results in the landau gauge. In this work we address the issue of the Gribov copies in SU(N),N ¿ 2, Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similarly to the case of SU(2), the Gribov region turns out to be convex, bounded along the off-diagonals directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension two condensates. (author)
Concerning Gribov vacuum copies in non-abelian gauge theory
International Nuclear Information System (INIS)
Frampton, P.H.; Palmer, W.F.; Pinsky, S.S.
1978-01-01
Construction of gauge field configurations A/sub μ//sup a/(x) in an SU(2) Yang-Mills theory satisfying everywhere F/sub μν//sup a/(x) = 0 is discussed. Using the method of sections, a field related to the zero-size limit of an instanton is presented. The corresponding limit for a multi-instanton solution requires a generalization of the Landau gauge condition. Finally, an alternative method and explicit solution is given for the case of delta/sub μ/A/sub μ//sup a/ = 0
Dark matter model with non-Abelian gauge symmetry
International Nuclear Information System (INIS)
Zhang Hao; Li Chongsheng; Cao Qinghong; Li Zhao
2010-01-01
We propose a dark-matter model in which the dark sector is gauged under a new SU(2) group. The dark sector consists of SU(2) dark gauge fields, two triplet dark Higgs fields, and two dark fermion doublets (dark-matter candidates in this model). The dark sector interacts with the standard model sector through kinetic and mass mixing operators. The model explains both PAMELA and Fermi LAT data very well and also satisfies constraints from both the dark-matter relic density and standard model precision observables. The phenomenology of the model at the LHC is also explored.
Dual transformations of the non-abelian fields in Minkowsky, Euclid, and Galilei-Newton spaces
International Nuclear Information System (INIS)
Tolkaehev, E.A.; Kurochkin, Y.A.; Trequbovich, A.Y.
1991-01-01
In this paper it is shown that the generalization of the Yang-Mills equations in Minkowsky space to the case of the biquaternions over dual and double numbers enables one to define the corresponding representations of the Galilei and SO(4) groups in a rather natural way. it makes construction of the non-Abelian field equations in Euclidean and Galilei-Newton spaces possible and proves their invariance under generalized dual transformations by use of the analogy with the Abelian gauge
Twisted boundary conditions: a non-perturbative probe for pure non-abelian gauge theories
International Nuclear Information System (INIS)
Baal, P. van.
1984-01-01
In this thesis the author describes a pure non-abelian gauge theory on the hypertorus with gauge group SU(N). To test the flux tube picture he has studied the large distance limit of this theory, leading to a large coupling constant. To tackle this problem, he describes two approaches, in both of which twisted boundary conditions play an important role. (Auth.)
Zero-modes of non-Abelian solitons in three-dimensional gauge theories
International Nuclear Information System (INIS)
Eto, Minoru; Gudnason, Sven Bjarke
2011-01-01
We study non-Abelian solitons of the Bogomol'nyi type in N=2 (d = 2 + 1) supersymmetric Chern-Simons (CS) and Yang-Mills (YM) theory with a generic gauge group. In CS theory, we find topological, non-topological and semi-local (non-)topological vortices of non-Abelian kinds in unbroken, broken and partially broken vacua. We calculate the number of zero-modes using an index theorem and then we apply the moduli matrix formalism to realize the moduli parameters. For the topological solitons we exhaust all the moduli while we study several examples of the non-topological and semi-local solitons. We find that the zero-modes of the topological solitons are governed by the moduli matrix H 0 only and those of the non-topological solitons are governed by both H 0 and the gauge invariant field Ω. We prove local uniqueness of the master equation in the YM case and finally compare all results between the CS and YM theories.
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
A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold S4 via the connection, with the general- ized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
International Nuclear Information System (INIS)
Giavarini, G.; Martin, C.P.; Ruiz Ruiz, F.
1993-01-01
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in bbfR 3 can be defined so that its large-mass limit be the renormalized vaccum expectation value of the Wilson loop for abelian Chern-Simons theory also in bbfR 3 . (orig.)
Maximal Abelian and Curci-Ferrari gauges in momentum subtraction at three loops
Bell, J. M.; Gracey, J. A.
2015-12-01
The vertex structure of QCD fixed in the maximal Abelian gauge (MAG) and Curci-Ferrari gauge is analyzed at two loops at the fully symmetric point for the 3-point functions corresponding to the three momentum subtraction (MOM) renormalization schemes. Consequently, the three-loop renormalization group functions are determined for each of these three schemes in each gauge using properties of the renormalization group equation.
International Nuclear Information System (INIS)
Tanimura, Shogo
1992-01-01
R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs
Chauhan, B.; Kumar, S.; Malik, R. P.
2018-02-01
We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the (D,1)-dimensional (anti-) chiral super-submanifolds (of the general (D,2)-dimensional supermanifold) where only the (anti-)chiral super expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism.
Electric-magnetic duality in non-Abelian gauge theories
International Nuclear Information System (INIS)
Mizrachi, L.
1982-03-01
The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase) is performed in the radial gauge (xsub(μ)Asub(μ)sup(a)(x)=0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is 1/g. The theory is self dual in this region, and the effective coupling of the dual Lagrangian is 1/g. Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operator transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self duality holds only for this subset of fields. In the strong coupling region a strong coupling expansion in powers of 1/g is suggested. (author)
Abelian Toda field theories on the noncommutative plane
Cabrera-Carnero, Iraida
2005-10-01
Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.
Superfield approach to topological features of non-Abelian gauge theory
International Nuclear Information System (INIS)
Malik, R.P.
2002-01-01
We discuss some of the key topological aspects of a (1+1)-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of chiral superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy-momentum tensor, topological invariants, etc, by exploiting the on-shell nilpotent BRST and co-BRST symmetries that emerge after the application of (dual) horizontality conditions. We show that the above physically interesting quantities geometrically correspond to the translation of some local (but composite) chiral superfields along one of the two independent Grassmannian directions of a (2+2)-dimensional supermanifold. This translation is generated by the conserved and on-shell nilpotent (co-)BRST charges that are present in the theory. (author)
Quaternionic non abelian relativistic quantum fields in four dimensions
International Nuclear Information System (INIS)
Albeverio, S.; Hoeegh-Krohn, R.
1986-01-01
We give a simple construction of certain Lie-group valued Euclidean Markov random fields and quantum fields in four dimensions. These fields can be looked upon as non abelian extensions of electromagnetic fields. (orig.)
Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
International Nuclear Information System (INIS)
Dudal, D.; Verschelde, H.; Sarandy, M.S.
2007-01-01
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension two condensate discussed here, with the non-trivial vacuum energy originating from the condensate 2 μ >, which has attracted much attention in the Landau gauge. (author)
Anomalous commutator of gauge group generators in a non-Abelian chiral theory
International Nuclear Information System (INIS)
Jo, S.
1985-01-01
This paper discusses commutators among non-Abelian fermion currents that are calculated using the BJL limit. It is observed that the gauge dependence of the fermion current with fixed canonical variables should be different from the covariant seagull in order to have correct anomalous commutators
Phase structure of lattice gauge theories for non-abelian subgroups of SU(3)
International Nuclear Information System (INIS)
Grosse, H.; Kuehnelt, H.
1981-01-01
The authors study the phase structure of Euclidean lattice gauge theories in four dimensions for certain non-abelian subgroups of SU(3) by using Monte-Carlo simulations and strong coupling expansions. As the order of the group increases a splitting of one phase transition into two is observed. (Auth.)
Recursion rules for scattering amplitudes in non-Abelian gauge theories
International Nuclear Information System (INIS)
Kim, C.; Nair, V.P.
1997-01-01
We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Wadia, S.R.
1979-01-01
A detailed formulation of the quantum theory of non-abelian gauge fields is presented in the Schroedinger picture. It is applied to the semiclassical quantization of the t'Hoft-Polyakov monopole, with special attention paid to the treatment of boundary conditions and local and global gauge symmetry. The perturbation expansion is then discussed with the aid of standard collective co-ordinates. In the Prasad-Sommerfield limit, all the eigenfunctions of the fluctuation equation are presented, the ground-state wave function is constructed in terms of gauge and translation invariant co-ordinates, and its total angular momentum is computed to be zero. Aspects of instanton phenomena are then examined in the Schroedinger picture; the role of euclidean time is elucidated. The precise relation between boundary conditions, choice of gauge, and the corresponding picture of the semiclassical vacuum is demonstrated
Fermions and vortex solutions in Abelian and non-Abelian gauge theories
International Nuclear Information System (INIS)
de Vega, H.J.
1978-01-01
The interaction of fermions with an extended vortex solution of the Higgs model is investigated. It is found that this interaction has long-range inverse-square tail. It is caused by the coupling of the fermion angular momentum with the vortex gauge field itself. The fermion-vortex bound states present at the threshold and the fermion-vortex scattering are studied. The scattering phase shifts and the Jost functions are obtained for large and small fermion momenta as well as the low-energy cross section which diverges at zero momentum. The quantum field theory in the one-vortex sectors is developed. It is found that, in the presence of fermions, a vortex with an even (odd) number of flux quanta has a half-integer (integer) fermionic number. It follows that a two-quantum vortex is stable. Finally, the stable vortex solution of an SU(2) Higgs model is investigated. The appropriate ansatz for the field is given and radial equations are discussed. It is shown that the interaction of a vortex with any nonsinglet particle has a long-range inverse-square tail
Light-induced gauge fields for ultracold atoms
Goldman, N.; Juzeliūnas, G.; Öhberg, P.; Spielman, I. B.
2014-12-01
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms.
Light-induced gauge fields for ultracold atoms
International Nuclear Information System (INIS)
Goldman, N; Juzeliūnas, G; Öhberg, P; Spielman, I B
2014-01-01
Gauge fields are central in our modern understanding of physics at all scales. At the highest energy scales known, the microscopic universe is governed by particles interacting with each other through the exchange of gauge bosons. At the largest length scales, our Universe is ruled by gravity, whose gauge structure suggests the existence of a particle—the graviton—that mediates the gravitational force. At the mesoscopic scale, solid-state systems are subjected to gauge fields of different nature: materials can be immersed in external electromagnetic fields, but they can also feature emerging gauge fields in their low-energy description. In this review, we focus on another kind of gauge field: those engineered in systems of ultracold neutral atoms. In these setups, atoms are suitably coupled to laser fields that generate effective gauge potentials in their description. Neutral atoms ‘feeling’ laser-induced gauge potentials can potentially mimic the behavior of an electron gas subjected to a magnetic field, but also, the interaction of elementary particles with non-Abelian gauge fields. Here, we review different realized and proposed techniques for creating gauge potentials—both Abelian and non-Abelian—in atomic systems and discuss their implication in the context of quantum simulation. While most of these setups concern the realization of background and classical gauge potentials, we conclude with more exotic proposals where these synthetic fields might be made dynamical, in view of simulating interacting gauge theories with cold atoms. (review article)
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.
1979-01-01
The construction of field strength copies without any gauge constraint is discussed. Several examples are given, one of which is not only a field strength copy but also (at the same time) a 'current copy'. (author) [pt
The non-Abelian gauge theory of matrix big bangs
O'Loughlin, Martin; Seri, Lorenzo
2010-07-01
We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.
Infrared problem in non-Abelian gauge theory
International Nuclear Information System (INIS)
Yao, Y.
1976-01-01
I extend the Bloch--Nordsieck idea to show that in the lowest nontrivial order of radiative correction the fermion--fermion and gauge-meson--fermion scattering rates are finite, provided that they are averaged over the initial and summed over the final internal spin states. Questions of the physical gauge coupling and infrared slavery are discussed
International Nuclear Information System (INIS)
Becchi, C.; Rouet, A.; Stora, R.
1975-10-01
Stora's analysis is continued in discussing the nonabelian (Yang-Mills) gauge field models (G.F.M.). The gauge independence of the physical scattering operator is discussed in some details and the connection between its unitary and the Slavnov symmetry outlined. Only the models involving semisimple gauge groups are considered. This greatly simplifies the analysis of the possible quantum corrections to the Quantum Action Principle which is reduced to the study of the cohomology group of the Lie algebra characterizing the gauge theory. The discussion is at the classical level for the algebraic properties of the SU(2) Higgs-Kibble-Englert-Brout-Faddeev-Popov lagrangian and its invariance under Slavnov identity transformations is exhibited. The renormalization of the Slavnov identity in the G.M.F. involving semisimple gauge groups is studied. The unitary and gauge independence of the physical S operator in the SU(2) H.K. model is dealt with [fr
International Nuclear Information System (INIS)
Hart, C.F.
1981-01-01
A gauge invariant effective action which generalizes the usual background field method is applied to quantum non-Abelian gauge theories. The gauge properties of the theory as well as its equivalence to the conventional theory are presented. Solutions to the new effective field equations are found to be physical and it is shown how S-matrix elements may be computed in terms of this new effective action. Feynman rules are given and the renormalization theory is discussed using minimal subtraction and dimensional regularization. The resulting computation of counterterms is found to be simpler than that of the usual method. A complete two-loop calculation of the β function for pure Yang-Mills theory is given as a specific example of this approach
Renormalization of non-abelian gauge theories in curved space-time
International Nuclear Information System (INIS)
Freeman, M.D.
1984-01-01
We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe
Srinivas, N.; Malik, R. P.
2017-11-01
We derive the off-shell nilpotent symmetries of the two (1 + 1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parametrized by the superspace coordinates ZM = (xμ,𝜃,𝜃¯) where xμ (with μ = 0, 1) are the bosonic coordinates and a pair of Grassmannian variables (𝜃,𝜃¯) obey the relationships: 𝜃2 = 𝜃¯2 = 0, 𝜃𝜃¯ + 𝜃¯𝜃 = 0. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.
Monte Carlo studies of non-Abelian gauge theories
International Nuclear Information System (INIS)
Creutz, M.
1980-05-01
After some general remarks on the efficiency of various Monte Carlo algorithms for gauge theories, the calculation of the asymptotic freedom scales of SU(2) and SU(3) gauge theories in the absence of quarks was discussed. There are large numerical factors between these scales when defined in terms of the bare coupling of the lattice theory or when defined in terms of the physical force between external sources
International Nuclear Information System (INIS)
Leite Lopes, J.
1981-01-01
The book is intended to explain, in an elementary way, the basic notions and principles of gauge theories. Attention is centred on the Salem-Weinberg model of electro-weak interactions, as well as neutrino-lepton scattering and the parton model. Classical field theory, electromagnetic, Yang-Mills and gravitational gauge fields, weak interactions, Higgs mechanism and the SU(5) model of grand unification are also discussed. (U.K.)
International Nuclear Information System (INIS)
Dudal, David; Verschelde, Henri; Rodino Lemes, Vitor Emanuel; Sarandy, Marcelo S.; Sorella, Silvio Paolo; Picariello, Marco
2002-01-01
The existence of a SL(2;R) symmetry is discussed in SU(N) Yang-Mills in the maximal abelian gauge. This symmetry, also present in the Landau and Curci-Ferrari gauge, ensures the absence of tachyons in the maximal abelian gauge. In all these gauges, SL(2;R) turns out to be dynamically broken by ghost condensates. (author)
Representations of l-p-i functionals in gauge field theories
International Nuclear Information System (INIS)
Bordag, M.; Kaschluhn, L.; Matveev, V.A.; Robaschik, D.
1981-01-01
A representation of the functions which solve by construction the Slavnov-Taylor identities and contain independent coefficient functions is given. These solutions show the different role of the gauge field which acts in some respect as an ordinary field. The Slavnov-Taylor identities are solved for axial gauge conditions in non-Abelian gauge field theory and in quantum electrodynamics
Atomic Quantum Simulations of Abelian and non-Abelian Gauge Theories
CERN. Geneva
2014-01-01
Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, in a collaboration of atomic and particle physicists, we have constructed a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum link models which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows investigations of string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods. Similarly, using ultracold alkaline-earth atoms in optical lattices, we have constructed a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum ...
International Nuclear Information System (INIS)
Capri, M. A. L.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.; Thibes, R.
2006-01-01
We pursue the study of SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge by taking into account the effects of the Gribov horizon. The Gribov approximation, previously introduced in [M. A. L. Capri, V. E. R. Lemes, R. F. Sobreiro, S. P. Sorella, and R. Thibes, Phys. Rev. D 72, 085021 (2005).], is improved through the introduction of the horizon function, which is constructed under the requirements of localizability and renormalizability. By following Zwanziger's treatment of the horizon function in the Landau gauge, we prove that, when cast in local form, the horizon term of the maximal Abelian gauge leads to a quantized theory which enjoys multiplicative renormalizability, a feature which is established to all orders by means of the algebraic renormalization. Furthermore, it turns out that the horizon term is compatible with the local residual U(1) Ward identity, typical of the maximal Abelian gauge, which is easily derived. As a consequence, the nonrenormalization theorem, Z g Z A 1/2 =1, relating the renormalization factors of the gauge coupling constant Z g and of the diagonal gluon field Z A , still holds in the presence of the Gribov horizon. Finally, we notice that a generalized dimension two gluon operator can be also introduced. It is BRST invariant on-shell, a property which ensures its multiplicative renormalizability. Its anomalous dimension is not an independent parameter of the theory, being obtained from the renormalization factors of the gauge coupling constant and of the diagonal antighost field
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
International Nuclear Information System (INIS)
Khoze, V.V.
1991-06-01
The semiclassical evaluation of the functional integral on non-Abelian gauge theories is generalized by means of the so-called valley method. The physically very important example of the valley, the instanton-anti-instanton field configuration, is discussed in details and its contributions to the physical quantities for zero-temperature and for thermal field theories are investigated. The high-energy behaviour of the total cross-section σ Δ F for electroweak fermion number violating two particles collisions is studied using the optical theorem approach. The calculation is done at energies below the sphaleron mass (E<10TeV) where it leads to the most complete result for σ Δ F known to date. Some estimations and a qualitative physical picture are discussed for energies above the sphaleron mass for the confinement and Higgs phases of the gauge theory. The effects of instanton-anti-instanton interactions are also studied in thermal QCD. (au)
Supersymmetric gauge field theories
International Nuclear Information System (INIS)
Slavnov, A.A.
1976-01-01
The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models
Constrained gauge fields from spontaneous Lorentz violation
DEFF Research Database (Denmark)
Chkareuli, J. L.; Froggatt, C. D.; Jejelava, J. G.
2008-01-01
Spontaneous Lorentz violation realized through a nonlinear vector field constraint of the type AµAµ=M2 (M is the proposed scale for Lorentz violation) is shown to generate massless vector Goldstone bosons, gauging the starting global internal symmetries in arbitrary relativistically invariant...... theories. The gauge invariance appears in essence as a necessary condition for these bosons not to be superfluously restricted in degrees of freedom, apart from the constraint due to which the true vacuum in a theory is chosen by the Lorentz violation. In the Abelian symmetry case the only possible theory...... couplings when expressed in terms of the pure Goldstone vector modes. However, they do not lead to physical Lorentz violation due to the simultaneously generated gauge invariance. Udgivelsesdato: June 11...
Jurco, B.; Schraml, S.; Schupp, P.; Wess, J.
2000-11-01
An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
International Nuclear Information System (INIS)
Jurco, B.; Schraml, S.; Wess, J.; Schupp, P.
2000-01-01
An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schraml, S.; Wess, J. [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)
2000-11-01
An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. (orig.)
International Nuclear Information System (INIS)
Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.
2010-01-01
Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.
Gauge field copies and Higgs mechanism
International Nuclear Information System (INIS)
Gleiser, M.
1982-07-01
From the algebric classification of the possible solutions of the necessary and sufficient condition for the existence of gauge field copies in two possible classes the Higgs mechanism for the potential obtained from the difference between two copied potentials is applied. It is shown that for class I 'electric type' it is possible to construct a vector field that satisfies an electromagnetic wave equation. For class I 'magnetic type', a vector field that satisfies a non-linear equation as a consequence of the non-abelianity of the theory, is obtained. It is shown that for class II it's not possible to apply the Higgs mechanism. A possible physical interpretation for the 'gauge field copies' phenomenon, is obtained. (author) [pt
International Nuclear Information System (INIS)
Aquino, V.M. de.
1987-01-01
We have analysed, within a semi classical approach, the influence of external electromagnetic field on phase transitions in gauge theories. The critical temperature was calculated for an Abelian case, scalar electrodynamics, and for an non Abelian case, the Weinberg Salam model. (author)
International Nuclear Information System (INIS)
Ward, B.F.L.
2006-01-01
We present the elements of three applications of resummation methods in non-Abelian gauge theories: (1), QED-QCD exponentiation and shower/ME matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed quantum gravity and the final state of Hawking radiation. In all cases, the extension of the YFS approach, originally introduced for Abelian gauge theory, to non-Abelian gauge theories, QCD and quantum general relativity, leads to new results and solutions which we briefly summarize
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Magnetic monopole solution in non-Abelian gauge theory
International Nuclear Information System (INIS)
Hietarinta, J.; Takasugi, E.; Tanaka, K.
1976-01-01
An approximate analytic solution of the equations of motion of the 't Hooft magnetic monopole model is proposed. Virial type global tests are carried out for the solution. Then, the monopole mass, energies of the vector field A/sub mu/sup a/, Higgs field phi/sup a/ and interaction are computed in closed form. The form factors of A/sub i/sup a/ and phi/sup a/ in a quantized version are also calculated
Energy Technology Data Exchange (ETDEWEB)
Scheck, Florian [Mainz Univ. (Germany). Inst. fuer Physik
2017-09-01
The following topics are dealt with: Maxwell's equations together with their symmetry and covariance, the Maxwell theory as classical field theory, simple applications of Maxwell's theory, local gauge theories, classical field theory of gravitation. (HSI)
Point-splitting analysis of commutator anomalies in non-abelian chiral gauge theories
International Nuclear Information System (INIS)
Ghosh, S.; Banerjee, R.
1988-01-01
A gauge covariant point-splitting regularisation is employed to calculate different anomalous commutators in four dimensional chiral gauge theories. For an external gauge field the fixed time anomalous commutator of the gauge group generators is seen to violate the Jacobi identity. The cohomological prediction can be confirmed provided the electric fields do not commute. Other commutators like the current-current and current-electric field are consistent with the Bjorken-Johnson-Low (BJL) derivation. (orig.)
Dynamical generation of non-abelian gauge group via the improved perturbation theory
International Nuclear Information System (INIS)
Kuroki, Tsunehide
2008-01-01
It was suggested that the massive Yang-Mills-Chern-Simons matrix model has three phases and that in one of them a non-Abelian gauge symmetry is dynamically generated. The analysis was at the one-loop level around a classical solution of fuzzy sphere type. We obtain evidences that three phases are indeed realized as nonperturbative vacua by using the improved perturbation theory. It gives a good example that even if we start from a trivial vacuum, the improved perturbation theory around it enables us to observe nontrivial vacua. (author)
Group quantization on configuration space: Gauge symmetries and linear fields
International Nuclear Information System (INIS)
Navarro, M.; Aldaya, V.; Calixto, M.
1997-01-01
A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyze, in a systematic manner and with complete generality, the case of linear fields (Abelian current groups). To illustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the Abelian Chern endash Simons models over an arbitrary closed surface in detail. copyright 1997 American Institute of Physics
International Nuclear Information System (INIS)
Arodz, H.
1987-01-01
The two formulations of quantum theory of the free electromagnetic field are presented. In the Coulomb gauge approach the independent dynamical variables have been identified and then, in order to quantize the theory, it has been sufficient to apply the straightforward canonical quantization. In the Gupta-Bleuler approach the auxilliary theory is first considered. The straightforward canonical quantization of it leads to the quantum theory defined in the space G with indefinite norm. 15 refs. (author)
Abelian Chern endash Simons theory. I. A topological quantum field theory
International Nuclear Information System (INIS)
Manoliu, M.
1998-01-01
We give a construction of the Abelian Chern endash Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern endash Simons theory [J. Diff. Geom. 33, 787 endash 902 (1991); Topology 32, 509 endash 529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175 endash 186 (1989)]. copyright 1998 American Institute of Physics
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Slavnov, A.A.
1981-01-01
This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks [ru
Hot gauge field properties from the thermal variational principle
International Nuclear Information System (INIS)
Schroeder, Y.; Schulz, H.
1995-10-01
A Feynman-Jensen version of the thermal variational principle is applied to hot gauge fields, abelian as well as nonabelian: scalar electrodynamics (without scalar self-coupling) and the gluon plasma. The perturbatively known self-energies are shown to derive by variation from a free quadratic (''gaussian'') trial Lagrangian. Independence of the covariant gauge fixing parameter is reached (within the order g 2 studies and for scalar ED) after a reformulation of the partition function such that it depends on only even powers of the gauge field. This way, however, the potential non-perturbative power of the calculus seems to be ruined. (orig.)
Relaxation methods for gauge field equilibrium equations
International Nuclear Information System (INIS)
Adler, S.L.; Piran, T.
1984-01-01
This article gives a pedagogical introduction to relaxation methods for the numerical solution of elliptic partial differential equations, with particular emphasis on treating nonlinear problems with delta-function source terms and axial symmetry, which arise in the context of effective Lagrangian approximations to the dynamics of quantized gauge fields. The authors present a detailed theoretical analysis of three models which are used as numerical examples: the classical Abelian Higgs model (illustrating charge screening), the semiclassical leading logarithm model (illustrating flux confinement within a free boundary or ''bag''), and the axially symmetric Bogomol'nyi-Prasad-Sommerfield monopoles (illustrating the occurrence of p topological quantum numbers in non-Abelian gauge fields). They then proceed to a self-contained introduction to the theory of relaxation methods and allied iterative numerical methods and to the practical aspects of their implementation, with attention to general issues which arise in the three examples. The authors conclude with a brief discussion of details of the numerical solution of the models, presenting sample numerical results
International Nuclear Information System (INIS)
Pokorski, S.
1987-01-01
Quantum field theory forms the present theoretical framework for the understanding of the fundamental interactions of particle physics. This book examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. The author discusses field-theoretical techniques and encourages the reader to perform many of the calculations presented. This book includes a brief introduction to perturbation theory, the renormalization programme, and the use of the renormalization group equation. Several topics of current research interest are covered, including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry
Adler's theorem in finite massless QED and possible extensions to non-Abelian gauge theories. II
International Nuclear Information System (INIS)
Bernstein, J.
1975-01-01
The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (Auth.)
Dynamical chaos of nonabelian gauge fields
International Nuclear Information System (INIS)
Matinyan, S.G.
1985-01-01
A special class of the Yang - Mills field-the spatially homogeneous fields (Yan - Mills classical mechanics)-having no analog in the linear abelian electrodynamics is studied. Both the computer and analytical approaches show that such fields possess dynamical stochasticity, this allowing one to claim that the Yang - Mills classical equations without external sources represent a non-integrable system. The Higgs mechanism eliminates this stochasticity: at some expectation value of scalar field, a phase transition of disorder-order (confinement-deconfinement) type takes plce. The system with external sources behaves apparently analogously. A relation of the discovered stochasticity with the dimensional reduction mechanism in the macroscopic systems as well as with colour confinement is considered. It is shown that the presence of the random (Gaussian) currents in vacuum leads to confinement of fields generated by those currents. Attention is paid to the possible manifestation of the revealed stochasticity of the classical non-abelian gauge fields in the multiple hadrnoproduction processes which apparently reflect the universal stochastic regularities typical of the systems of quite different nature
Dynamical chaos of nonabelian gauge fields
Energy Technology Data Exchange (ETDEWEB)
Matinyan, S G
1985-01-01
A special class of the Yang - Mills field-the spatially homogeneous fields (Yan - Mills classical mechanics)-having no analog in the linear abelian electrodynamics is studied. Both the computer and analytical approaches show that such fields possess dynamical stochasticity, this allowing one to claim that the Yang - Mills classical equations without external sources represent a non-integrable system. The Higgs mechanism eliminates this stochasticity: at some expectation value of scalar field, a phase transition of disorder-order (confinement-deconfinement) type takes plce. The system with external sources behaves apparently analogously. A relation of the discovered stochasticity with the dimensional reduction mechanism in the macroscopic systems as well as with colour confinement is considered. It is shown that the presence of the random (Gaussian) currents in vacuum leads to confinement of fields generated by those currents. Attention is paid to the possible manifestation of the revealed stochasticity of the classical non-abelian gauge fields in the multiple hadrnoproduction processes which apparently reflect the universal stochastic regularities typical of the systems of quite different nature.
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
Maleknejad, A.; Sheikh-Jabbari, M. M.; Soda, J.
2013-07-01
The isotropy and homogeneity of the cosmic microwave background (CMB) favors “scalar driven” early Universe inflationary models. However, gauge fields and other non-scalar fields are far more common at all energy scales, in particular at high energies seemingly relevant to inflation models. Hence, in this review we consider the role and consequences, theoretical and observational, that gauge fields can have during the inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the level of cosmic perturbations. There have been two main classes of models with gauge fields in the background, models which show violation of the cosmic no-hair theorem and those which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem. Models in which gauge fields are only turned on at the cosmic perturbation level, may source primordial magnetic fields. We also review specific observational features of these models on the CMB and/or the primordial cosmic magnetic fields. Our discussions will be mainly focused on the inflation period, with only a brief discussion on the post inflationary (p)reheating era. Large field models: The initial value of the inflaton field is large, generically super-Planckian, and it rolls slowly down toward the potential minimum at smaller φ values. For instance, chaotic inflation is one of the representative models of this class. The typical potential of large-field models has a monomial form as V(φ)=V0φn. A simple analysis using the dynamical equations reveals that for number of e-folds Ne larger than 60, we require super-Planckian initial field values,5φ0>3M. For these models typically ɛ˜η˜Ne-1. Small field models: Inflaton field is initially small and slowly evolves toward the potential minimum at larger φ values. The small field models are characterized by the following potential V(φ)=V0(1-(), which corresponds to a Taylor expansion about the origin, but more realistic
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
Axial-gauge formulation of a three-dimensional field theory
International Nuclear Information System (INIS)
Hagen, C.R.
1985-01-01
Since the non-Abelian version of a recently formulated gauge theory in two spatial dimensions gives rise to a nonlinear constraint upon the fields in the radiation-gauge approach, one is motivated to attempt a description in terms of the axial gauge. This is accomplished in the Abelian version of the model, with results similar to those encountered in the radiation gauge. The non-Abelian case is then formally solved in the same gauge, it being subsequently shown, however, that the theory is not covariant. It is argued on the basis of perturbation theory that such noncovariance is a real effect which is not readily circumvented by modification of the field transformation properties
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
International Nuclear Information System (INIS)
Dudal, D.; Verschelde, H.; Gracey, J.A.; Lemes, V.E.R.; Sobreiro, R.F.; Sorella, S.P.; Sarandy, M.S.
2004-01-01
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with the algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension-two condensate discussed here, with the nontrivial vacuum energy originating from the condensate μ 2 >, which has attracted much attention in the Landau gauge
Introduction to gauge field theory
International Nuclear Information System (INIS)
Bailin, David; Love, Alexander
1986-01-01
The book is intended as an introduction to gauge field theory for the postgraduate student of theoretical particle physics. The topics discussed in the book include: path integrals, classical and quantum field theory, scattering amplitudes, feynman rules, renormalisation, gauge field theories, spontaneous symmetry breaking, grand unified theory, and field theories at finite temperature. (UK)
Origin of Abelian Gauge Symmetries in Heterotic/F-theory Duality
Cvetic, Mirjam; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-01-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required ...
Questions of quark confinement and ambiguities in Coulomb gauge of Yang-Mills fields
International Nuclear Information System (INIS)
Abarbanel, H.D.I.; Bartels, J.
1978-01-01
The ambiguities considered by Gribov in the formulation of Coulomb gauge in non-Abelian gauge theories are discussed and the division of gauge field space into a sector with a unique transverse gauge, a sector with a two-fold ambiguity in transverse gauge, etc. is reviewed. The authors argue in a semi-classical fashion that transitions between these sectors readily occur and discuss the connection with ideas of quark confinement in Coulomb gauge. Because of these transitions it appears that the functional integral formulation of Coulomb gauge will be rather more complicated than expected in the past. (Auth.)
High-energy behaviour in a non-abelian gauge theory. Pt. 2
International Nuclear Information System (INIS)
Bartels, J.
1980-01-01
In this second part of our attempt to construct a unitary high-energy description of a spontaneously broken non-abelian gauge theory we calculate, for the n → m amplitude in the multi-Regge limit, the first corrections beyond the leading logarithmic approximation. The resulting amplitudes come in the form of the reggeon calculus where the number of reggeons in each t-channel is restricted to one or two. We then study the limit where the mass of the vector particle is taken to zero: for the 2 → 2 amplitude show that this limit exists, not only for the approximation of the present paper but also for higher-order corrections. (orig.)
Introduction to gauge theories
International Nuclear Information System (INIS)
Wit, B. de
1983-01-01
In these lectures we present the key ingredients of theories with local gauge invariance. We introduce gauge invariance as a starting point for the construction of a certain class of field theories, both for abelian and nonabelian gauge groups. General implications of gauge invariance are discussed, and we outline in detail how gauge fields can acquire masses in a spontaneous fashion. (orig./HSI)
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
Gauge anomaly with vector and axial-vector fields in 6D curved space
Yajima, Satoshi; Eguchi, Kohei; Fukuda, Makoto; Oka, Tomonori
2018-03-01
Imposing the conservation equation of the vector current for a fermion of spin 1/2 at the quantum level, a gauge anomaly for the fermion coupling with non-Abelian vector and axial-vector fields in 6D curved space is expressed in tensorial form. The anomaly consists of terms that resemble the chiral U(1) anomaly and the commutator terms that disappear if the axial-vector field is Abelian.
Adler's theorem in finite massless QED and possible extensions to non- Abelian gauge theories II
Bernstein, J
1975-01-01
For pt.I see ibid., vol.B95, p.461 (1975). The indefinite metric produced by the ghost fields in the Coulomb gauge in Yang-Mills theories is discussed. It is shown that the ghosts greatly complicate the job of proving, or disproving, an Adler theorem in this gauge. An old result of Schwinger (1962) for Coulomb gauge Yang-Mills theories is also found to be compromised by ghosts. (7 refs).
Abelian projection at the multi-instanton
International Nuclear Information System (INIS)
Fukushima, M.
2001-01-01
We study full non-Abelian, Abelian projected lattice field configurations built up from random instanton gas configurations in the continuum. We study the instanton contribution to the Q-barQ force with respect to whether various versions of Abelian dominance hold. We show that the lattice used to discretize the instanton gas configurations has to be sufficiently coarse (a ≅ 2ρ-bar compared with the instanton size ρ-bar) such that maximal Abelian gauge projection as well as the monopole gas contribution to the Q-barQ force reproduce the non-Abelian instanton-mediated force in the intermediate range of linear quasi-confinement. (author)
Pair creation by an external non-Abelian field
International Nuclear Information System (INIS)
Hamil, B; Chetouani, L
2014-01-01
The problem of the creation of particle pairs of spin 0 and 1/2 from the vacuum by an external field of a non-Abelian type plane wave on the light cone is considered following the approach of Schwinger. Using simple shifts and only by an algebraic calculation, it is shown that with this form of interaction, there is no creation of particles. (paper)
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A W; Kwek, Leong Chuan
2014-08-08
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan
2014-08-01
Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a ``hairline'' solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
Magnetic Monopoles, Center Vortices and Topology of Gauge Fields
Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schafke, A.
1999-01-01
The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed.
Magnetic monopoles, center vortices and topology of gauge fields
International Nuclear Information System (INIS)
Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schaefke, A.
2000-01-01
The topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills Theory. For this purpose the continuum analog of the maximum center gauge is constructed
International Nuclear Information System (INIS)
Tellis, D.R.
2000-01-01
Full text: Instantons in pure Yang-Mills gauge theory have been studied extensively by physicists and mathematicians alike. The surprisingly rich topological structure plays an important role in hadron structure. A crucial role is played by how the boundary conditions on the gauge fields are imposed. While the topology of gauge fields in pure Yang-Mills gauge theory is understood for the compact manifold of the 4-sphere, the manifold of the 4-torus remains an active area of study. The latter is particularly important in the study of Lattice QCD
Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory
International Nuclear Information System (INIS)
Chernicoff, Mariano; Garcia, J. Antonio; Gueijosa, Alberto
2011-01-01
We study the dynamics of a 'composite' or 'dressed' quark in strongly-coupled large-N c N=4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a Lorentz covariant formula for its rate of radiation.
Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory
Chernicoff, Mariano; Garcia, J. Antonio; Guijosa, Alberto
2010-01-01
We study a `dressed' or `composite' quark in strongly-coupled N=4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding quantum non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a...
Radiation Damping in a Non-Abelian Strongly-Coupled Gauge Theory
Chernicoff, Mariano; García, J. Antonio; Güijosa, Alberto
2011-09-01
We study the dynamics of a 'composite` or 'dressed` quark in strongly-coupled large-Nc N=4 super-Yang-Mills (SYM), making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a Lorentz covariant formula for its rate of radiation.
International Nuclear Information System (INIS)
Leite Lopes, J.
1998-04-01
In this work, we discuss the physical ideas which represents the basis for the unified gauge field model. Despite of the difficulties that we presently have for embodying in a natural manner muons and hadrons in that model, we have the feeling that we are on the way which seems to lead to the construction of a theory in which the Maxwell electromagnetic field and the Fermi weak interaction field are manifestations of a unique subjacent physical entity - the unified gauge fields. (author)
Origin of Abelian gauge symmetries in heterotic/F-theory duality
International Nuclear Information System (INIS)
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
2016-01-01
We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m)×U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m)×ℤ_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)’s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)’s is found by taking into account a Stückelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.
Gauge invariance of string fields
International Nuclear Information System (INIS)
Banks, T.; Peskin, M.E.
1985-10-01
Some work done to understand the appearance of gauge bosons and gravitons in string theories is reported. An action has been constructed for free (bosonic) string field theory which is invariant under an infinite set of gauge transformations which include Yang-Mills transformations and general coordinate transformations as special cases. 15 refs., 1 tab
'Baldin autumn' and gauge fields
International Nuclear Information System (INIS)
Konopleva, N.P.
2008-01-01
The paper is the reminiscences of the participant of the gauge field theory beginning and the first 'Baldin Autumn' conference in 1969. This conference was named 'Vector Mesons and Electromagnetic Interactions'. At that time, just the processes with vector mesons participation contained some experimental indications of new universal interactions existence. Vector dominance was the experimental evidence of physical reasons of the gauge field theory. In the course of time the gauge field theory form, which was under discussion thirty seven years ago, became generally recognized and experimentally corroborated. It led to construction of the well-known Standard Model of elementary particle interactions
On infrared problems of effective Lagrangians of massive spin 2 fields coupled to gauge fields
Energy Technology Data Exchange (ETDEWEB)
Canfora, Fabrizio, E-mail: canfora@cecs.cl [Centro de Estudios Científicos (CECs), Casilla 1469, Valdivia (Chile); Giacomini, Alex, E-mail: alexgiacomini@uach.cl [Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia (Chile); Zerwekh, Alfonso R., E-mail: alfonso.zerwekh@usm.cl [Departamento de Física and Centro Científico-Tecnológico de Valparaíso, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso (Chile)
2016-12-15
In this paper we analyze the interactions of massive spin-2 particles charged under both Abelian and non-Abelian group using the Porrati–Rahman Lagrangian. This theory is valid up to an intrinsic cutoff scale. Phenomenologically a theory valid up to a cutoff scale is sensible as all known higher spin particles are non-fundamental and it is shown that indeed this action can be used to estimate some relevant cross section. Such action necessarily includes Stückelberg field and therefore it is necessary to fix the corresponding gauge symmetry. We show that this theory, when the Stückelberg symmetry is gauge-fixed, possesses a non-trivial infrared problem. A gauge fixing ambiguity arises which is akin to the Gribov problem in QCD in the Abelian case as well. In some cases (such as when the space–time is the four-dimensional torus) the vacuum copies can be found analytically. A similar phenomenon also appears in the case of Proca fields. A very interesting feature of these copies is that they arise only for “large enough” gauge potentials. This opens the possibility to avoid the appearance of such gauge fixing ambiguities by using a Gribov–Zwanziger like approach.
Anatomy of isolated monopole in Abelian projection od SU(2) lattice gauge theory
Belavin, V A; Veselov, A I
2001-01-01
The structure of the isolated static monopolies in the maximum Abelian projection of the SU(2) gluodynamics on the lattice studied. The standard parametrization of the coupling matrix was used by determining the maximum Abelian projection of the R functional maximization relative to all scale transformations. The monopole radius R approx = 0.06 fm is evaluated
Directory of Open Access Journals (Sweden)
A. G. Sergeev
1986-01-01
Full Text Available We describe briefly the basic ideas and results of the twistor theory. The main points: twistor representation of Minkowsky space, Penrose correspondence and its geometrical properties, twistor interpretation of linear massless fields, Yang-Mills fields (including instantons and monopoles and Einstein-Hilbert equations.
Topics in gravitation and gauge fields
International Nuclear Information System (INIS)
Leen, T.K.
1982-01-01
The theoretical studies presented here address three distinct topics. The first deals with quantum-mechanical effects of classical gravitational radiation. Specifically, the use of the interstellar medium itself as a remote quantum-mechanical detector of gravitational waves is investigated. This study is motivated by the presumed existence of atomic hydrogen in the vicinity of astrophysical sources of gravitational radiation. Space-time curvature produces uniquely identifiable shifts in atomic hydrogen energy levels. The oscillating level shifts induced by a passing gravitational wave could conceivably be detected spectroscopically. Accordingly the level shifts for both low-lying and highly excited states of single electron atoms immersed in gravitational radiation have been studied. The second two topics deal with the theory of quantized fields on curved space-times. In the first of these studies, a naive model of cosmological baryon synthesis is examined. The model incorporates a hard CP violation as well as a baryon (and lepton) non-conserving interaction and is thus capable of generating an excess of matter over antimatter. The time dependent background geometry of the early universe drives the interaction producing net excess of baryon/lepton pairs. In the final topic, the question of renormalizability of non-Abelian gauge fields theories in a general curved space-time is addressed. All modern theories of elementary particle physics are gauge theories and one would like to know if their perturbative expansions continue to be well defined (i.e. renormalizable) on curved backgrounds. In general, one is interested in knowing if field theories renormalizable in Minkowski space remain so in a general curved space-time
A further pathology of the Coulomb gauge in non-Abelian Yang-Mills theories
International Nuclear Information System (INIS)
Ademollo, M.; Napolitano, E.; Sciuto, S.
1978-01-01
In the first part the vacuum structure of SU(2) Yang-Mills theories in the Coulomb gauge is discussed. It is proved that the only transverse pure gauge field Asub(μ)(x) = U -1 deltasub(μ)U with U(x) → (as r→infinity) const., is the trivial one Asub(μ)(x) equivalent to 0; the features of other possible vacua with U(x) → (as r→infinity) U(theta, pli) are studied. In the second part, regular Euclidean configurations that connect a vacuum state at x 4 = -infinity to another at x 4 = +infinity are discussed. It is proved, always working in the Coulomb gauge, that the perturbative vacuum Asub(μ)(x) equivalent to 0 cannot tunnel into any other one and that regular configurations with non-vanishing Pontryagin number q cannot affect such a vacuum. Moreover, strong arguments are given to show that many-instanton configurations (mod(q)>=2) cannot be expressed at all in the Coulomb gauge, that is by a regular field Asub(μ) satisfying the transversality condition deltasub(i)Asub(i) (x, x 4 ) = 0. (Auth.)
Introduction to gauge field theory
International Nuclear Information System (INIS)
Bailin, D.; Love, A.
1986-01-01
This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications
Gauge invariant fractional electromagnetic fields
International Nuclear Information System (INIS)
Lazo, Matheus Jatkoske
2011-01-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Gauge invariant fractional electromagnetic fields
Energy Technology Data Exchange (ETDEWEB)
Lazo, Matheus Jatkoske, E-mail: matheuslazo@furg.br [Instituto de Matematica, Estatistica e Fisica - FURG, Rio Grande, RS (Brazil)
2011-09-26
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators. -- Highlights: → We propose a fractional Lagrangian formulation for fractional Maxwell's fields. → We obtain gauge invariant fractional electromagnetic fields. → Our generalized fractional Maxwell's field is spatially symmetrical. → We discuss the non-causality of the theory.
Two-loop ghost-antighost condensation for SU(2) Yang-Mills theories in the maximal abelian gauge
International Nuclear Information System (INIS)
Fazio, A.R.
2004-01-01
In the framework of the formalism of Cornwall et.al. for composite operators I study the ghost-antighost condensation in SU(2) Yang-Mills theories quantized in the Maximal Abelian Gauge and derive analytically a condensating effective potential at two ghost loops. I find that in this approximation the one-loop pairing ghost-antighost is not destroyed and no mass is generated if the ansatz for the propagator suggested by the tree level Hubbard-Stratonovich transformations is used
High-energy behaviour in a non-abelian gauge theory. Pt. 3
International Nuclear Information System (INIS)
Bartels, J.
1991-07-01
The high energy limit (Regge limit) of a spontaneously broken SU(2) gauge theory is studied beyond the leading-lns approximation. Calculations are based upon the analytic structure of scattering amplitudes in generalized Regge limits, and the resulting amplitudes satisfy reggeon unitarity in the t-channel as well as unitarity in the s-channel. The calculations lead to a systematic construction of a reggeon field theory. (orig.)
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07000 Mexico, D. F., Mexico)
1987-01-01
It is shown that in an algebraically special space-time that admits a congruence of null strings, the Yang--Mills equations with sources reduce to a pair of nonlinear first-order differential equations for two matrices, provided that the gauge field is aligned with the congruence. In the case where the current is tangent to the null strings, the gauge field is determined by a matrix potential that has to satisfy a second-order differential equation with quadratic nonlinearities. As an example of this case, the Yang--Mills--Weyl equations are reduced, assuming that the multiplet of Weyl neutrino fields are also aligned with the congruence, and a reduced form of the Einstein--Yang--Mills--Weyl equations is also given
Canonical Yang-Mills field theory with invariant gauge-families
International Nuclear Information System (INIS)
Yokoyama, Kan-ichi
1978-01-01
A canonical Yang-Mills field theory with indefinite metric is presented on the basis of a covariant gauge formalism for quantum electrodynamics. As the first step of the formulation, a many-gauge-field problem, in which many massless Abelian-gauge fields coexist, is treated from a new standpoint. It is shown that only a single pair of a gaugeon field and its associated one can govern the gauge structure of the whole system. The result obtained is further extended to cases of non-Abelian gauge theories. Gauge parameters for respective components of the Yang-Mills fields are introduced as a group vector. There exists a q-number local gauge transformation which connects relevant fields belonging to the same invariant gauge family with one another in a manifestly covariant way. In canonical quantization, the Faddeev-Popov ghosts are introduced in order to guarantee the existence of a desirable physical subspace with positive semi-definite metric. As to treatment of the Faddeev-Popov ghosts, Kugo and Ojima's approach is adopted. Three supplementary conditions which are consistent with one another constrain the physical subspace. (author)
Vortex operators in gauge field theories
International Nuclear Information System (INIS)
Polchinski, J.G.
1980-01-01
We study several related aspects of the t Hooft vortex operator. The first chapter reviews the current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator. The second chapter deals with the Abelian vortex operator written in terms of elementary fields and with the calculation of its Green's functions. The Dirac veto problem appears in a new guise. We present a two dimensional solvable model of a Dirac string. This leads us to a new solution of the veto problem; we discuss its extension to four dimensions. We then show how the Green's functions can be expressed more neatly in terms of Wu and Yang's geometrical idea of sections. In the third chapter we discuss the dependence of the Green's functions of the Wilson and t Hooft operators on the nature of the vacuum. In the fourth chapter we consider systems which have fields in the fundamental representation, so that there are no vortex operators. When these fields enter only weakly into the dynamics, as is the case in QCD and in real superconductors, we would expect to be able to define a vortex-like operator. We show that any such operator can no longer be local looplike, but must have commutators at long range. We can still find an operator with useful properties, its cluster property, though more complicated than that of the usual vortex operator, still appears to distinguish Higgs, confining and perturbative phases. To test this, we consider a U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint)
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.)
Gauge invariant fractional electromagnetic fields
Lazo, Matheus Jatkoske
2011-09-01
Fractional derivatives and integrations of non-integers orders was introduced more than three centuries ago but only recently gained more attention due to its application on nonlocal phenomenas. In this context, several formulations of fractional electromagnetic fields was proposed, but all these theories suffer from the absence of an effective fractional vector calculus, and in general are non-causal or spatially asymmetric. In order to deal with these difficulties, we propose a spatially symmetric and causal gauge invariant fractional electromagnetic field from a Lagrangian formulation. From our fractional Maxwell's fields arose a definition for the fractional gradient, divergent and curl operators.
Systematics of higher-spin gauge fields
International Nuclear Information System (INIS)
de Wit, B.; Freedman, D.Z.
1980-01-01
Free-field theories for symmetric tensor and tensor-spinor gauge fields have recently been obtained which describe massless particles of arbitrary integer or half-integer spin. An independent discussion of these field theories is given here, based on a hierarchy of generalized Christoffel symbols with simple gauge transformation properties. The necessity of certain constraints on gauge fields and parameters is easily seen. Wave equations and Lagrangians are expressed in terms of the Christoffel symbols, and the independent modes of the system are counted in covariant gauges. Minimal-coupling inconsistency and a combined system of higher-spin boson gauge fields interacting with relativistic particles is discussed
Magnetoelasticity as a gauge field
International Nuclear Information System (INIS)
Zorawski, Marek
1987-01-01
The goal of the paper is to formulate such a system in such a metric space that the geodesics of the space give the movement equations with the influence of electromagnetic forces. Local fields (stress) should be, of course, also included in the movement equations. For the geometrical structure of energy-momentum tensor, the known Einstein equation is adopted. It is also supposed that the Bianchi identities hold. Then in Riemannian space a non-holonomic system of reference is introduced, and the anholonomity object is associated to the electromagnetic field, as a gauge field. The considered theory is the classical one, it is not difficult to extend it to quantum field theory. (Auth.)
Gauge fields in a torsion field
International Nuclear Information System (INIS)
Rosu, Ion
2004-01-01
In this paper we analyse the motion and the field equations in a non-null curvature and torsion space. In this 4-n dimensional space, the connection coefficients are γ bc a = 1/2S bc a + 1/2T bc a, where S bc a is the symmetrical part and T bc a are the components of the torsion tensor. We will consider that all the fields depend on x = x α , α = 1,2,3,4 and do not depend on y = y k , k=1,2,...,n. The factor S bc a depends on the components of the metric tensor g αβ (x) and on the gauge fields A ν s 0 (x) and the components of the torsion depend only on the gauge fields A ν s 0 (x). We take into consideration the particular case for which the geodesic equations coincide with the motion equations in the presence of the gravitational and the gauge fields. In this case the field equations are Einstein equations in a 4-n dimensional space. We show that both the geodesic equations and the field equations can be obtained from a variational principle. (author)
Tensor gauge condition and tensor field decomposition
Zhu, Ben-Chao; Chen, Xiang-Song
2015-10-01
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.
Contemporary status of gauge fields
International Nuclear Information System (INIS)
Slavnov, A.A.
1979-01-01
A successive and a self-consistent scheme of calculation is developed for the Yang-Mills theory. Boundary conditions related to the problem on the physical vacuum are predetermined for solving the field theory equations. It is noted that the principal problem for the Yang-Mills theory consists in finding the actual ground state. The role of instantons in constructing the gauge field ground state and of the dynamic mechanism of quark confinement are also discussed. An assumption has been made that the Yang-Mills theory can be solved exactly. This assumption is based on analogy between the Yang-Mills theory and the two-dimensional nonlinear σ-model. An exceptionality of the Yang-Mills theory is stressed which consists in the fact that it is a unique massless vector field theory in which no patologies are observed connected with nonpositive determination of energy
Gauge-field topology in two dimensions: θ-vacuum, topological phases and composite fields
International Nuclear Information System (INIS)
Ilieva, N.; Pervushin, V.N.
1990-06-01
In the framework of the minimal quantization method, the residual 'longitudinal' vacuum dynamics of the Abelian gauge field, that is described by a new pair of canonical variables, is revealed. This dynamics is shown to give origin to the θ-vacuum, thus providing a field analogy of the Josephson effect. The destructive interference of the topological phases - that the fermion fields are shown to acquire - is considered as a reason for the charge screening in the two-dimensional massless QED. (author). 11 refs
International Nuclear Information System (INIS)
Ogilvie, M.C.
1999-01-01
Analytic methods for Abelian projection are developed. A number of results are obtained related to string tension measurements. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The methods used emphasize that the projected theory is derived from the underlying non-Abelian theory rather than vice versa. In general, the choice of subgroup used for projection is not very important, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements. Two other issues, Casimir scaling and the conflict between projection and critical universality, are also discussed. copyright 1999 The American Physical Society
Conformal field theory construction for non-Abelian hierarchy wave functions
Tournois, Yoran; Hermanns, Maria
2017-12-01
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
Adding gauge fields to Kaplan's fermions
International Nuclear Information System (INIS)
Blum, T.; Kaerkkaeinen, L.
1994-01-01
We experiment with adding dynamical gauge field to Kaplan (defect) fermions. In the case of U(1) gauge theory we use an inhomogeneous Higgs mechanism to restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d theory produce the correct 2d gauge dynamics. We measure fermion propagators with dynamical gauge fields. They posses the correct chiral structure. The fermions at the boundary of the support of the gauge field (waveguide) are non-chiral, and have a mass two times heavier than the chiral modes. Moreover, these modes cannot be excited by a source at the defect; implying that they are dynamically decoupled. We have also checked that the anomaly relation is fullfilled for the case of a smooth external gauge field. (orig.)
Abelian dominance in Einstein’s theory
International Nuclear Information System (INIS)
Cho, Y M; Oh, S H; Kim, Sang-Woo
2012-01-01
We conjecture the Abelian dominance in Einstein’s theory, that is, the Abelian part of the theory plays the central role in the dynamics. Treating Einstein’s theory as a gauge theory of the Lorentz group, we show that Einstein’s theory can be decomposed into the restricted part made up of the restricted connection which has the full Lorentz gauge invariance and the valence part made up of the valence connection which plays the role of gravitational source of the restricted gravity. In this decomposition, the role of the metric g μν is replaced by a four-index metric tensor g μν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇ α g μν = 0 of the connection is replaced by the gauge and generally covariant condition D μ g μν = 0. We show that there are two different Abelian decompositions, the light-like (or null) decomposition and the non-light-like (or non-null) decomposition, because the Lorentz group has two maximal Abelian subgroups. The decomposition shows the existence of the restricted gravity which has the full general invariance but is much simpler than Einstein’s theory. Moreover, it tells us that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-1 field. This establishes the Abelian dominance in Einstein’s theory. (paper)
Moduli space of self-dual connections in dimension greater than four for abelian Gauge groups
Cappelle, Natacha
2018-01-01
In 1954, C. Yang and R. Mills created a Gauge Theory for strong interaction of Elementary Particles. More generally, they proved that it is possible to define a Gauge Theory with an arbitrary compact Lie group as Gauge group. Within this context, it is interesting to find critical values of a functional defined on the space of connections: the Yang-Mills functional. If the based manifold is four dimensional, there exists a natural notion of (anti-)self-dual 2-form, which gives a natural notio...
SUSY non-Abelian gauge models: exact beta function from one loop of perturbation theory
International Nuclear Information System (INIS)
Shifman, M.A.; Vajnshtejn, A.I.; Zakharov, V.I.
1985-01-01
The method for calculating the exact β function (to all orders in the coupling constant) proposed earlier in supersymmetric electrodynamics is extended. The starting point is the observation that the low-energy effective action is exhausted by one loop provided that the theory is regularized supersymmetrically both in the ultraviolet and infrared domains in four dimensions. The Pouli-Villars method of the ultraviolet regularization is used. Two methods for the infrared regularization are considered. The first one - quantization in a box with a finite volume L 3 - is universally applicable to anygauge theory. The second method is based on the effective Higgs mechanism for mass generation and requires the presence of certain matter superfields in the lagrangian. Within this method the necessary condition is the existence of flat directions, so called valeys, along which the vacuum energy vanishes. The theory is quantized near epsilon non-vanishing value of the scalar field from the bottom of the valley. After calculating the one-loop effective action one and the same exact expression is obtained for the β function within the both approaches, and it also coincides with our earlier result extracted from instanton calculus. A few remarks on the problem of anomalies in SUSY gauge theories are presented
Kinoshita-Lee-Nauenberg theorem and soft radiation in gauge theories: Abelian case
International Nuclear Information System (INIS)
Akhoury, R.; Sotiropoulos, M.G.; Zakharov, V.I.
1997-01-01
We present a covariant formulation of the Kinoshita-Lee-Nauenberg (KLN) theorem for processes involving the radiation of soft particles. The role of the disconnected diagrams is explored and a rearrangement of the perturbation theory is performed such that the purely disconnected diagrams are factored out. The remaining effect of the disconnected diagrams results in a simple modification of the usual Feynman rules for the S-matrix elements. As an application, we show that, when combined with the Low theorem, this leads to a proof of the absence of the 1/Q corrections to inclusive processes (such as the Drell-Yan process). In this paper the Abelian case is discussed to all orders in the coupling. copyright 1997 The American Physical Society
On behaviour of Weyl's gauge field
International Nuclear Information System (INIS)
Yuan Zhong Zhang.
1990-05-01
We consider a system, consisting of a metric tensor g μυ , a scalar field φ, a Weyl's gauge field A μ and a scalar matter field Φ, which is invariant under general coordinate transformation and Weyl's gauge transformation. Two kinds of identities and field equations are given and discussed. A special space-time with g μυ =φ -2 η μυ is considered in a gauge-independent manner. We point out that in a correct treatment where g μυ is not regarded as an independent variable, an auxiliary condition for Weyl's gauge field cannot be obtained. Therefore Weyl's gauge field can be treated as a usual field of positive norm. (author). 11 refs
Nilpotent BRST charge without auxillary B fields in quantum gauge theories
International Nuclear Information System (INIS)
Tsai, E.C.
1991-01-01
This paper introduces a modified BRST transformation for non-Abelian gauge theories. In this transformation, there is no need to introduce auxiliary B fields, yet the generatior Q for the modified transformation is nilpotent and commutes with the Hamiltonian. The Lagrangian is no longer invariant under Q, but the quantum theory which is defined by the Hamiltonian is still symmetric with respect to the transformation generated by Q
Gauge field condensation in geometric quantum chromodynamics
International Nuclear Information System (INIS)
Guendelman, E.I.
1991-09-01
In odd number of dimensions, it is possible to construct general covariant gauge theories, where the metric is not an independent variable, but local function of the gauge fields. Starting from standardly defined gauge theory, upon functional integration of some variables, we could end up with such moodels. For models with SU(2) and SU(3) symmetry in three dimensions, gauge field condensation take place in the vacuum, which is nevertheless homogeneous and isotropic up to a gauge transformation, provided the space is flat. Introducing Higgs fields that spontaneously break the gauge symmetry, we get a breakdown of the homogenity and isotropy of the vacuum. Finally, we discuss how some of this ideas can be generalized to four and other even dimensions. (author)
Measurability of non-abelium gauge fields
Energy Technology Data Exchange (ETDEWEB)
Ivanenko, D.D.; Obukhov, Yu.N.
New estimations of the accuracy of measurement of non-abeliar gauge field components are obtained on the base of qualitative analysis of the test body equations of motion. They generalize the Bohr and Rosenfeld results on the measurability of an electomagnetic field for the case of an arbitrary gauge group.
Renormalization of gauge theories in the background-field approach arXiv
Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.
Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.
Antisymmetric tensor Zp gauge symmetries in field theory and string theory
International Nuclear Information System (INIS)
Berasaluce-González, Mikel; Ramírez, Guillermo; Uranga, Angel M.
2014-01-01
We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general Z p gauge theory can be described in terms of a r-form gauge field made massive by a (r−1)-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality
Temperature dependence of critical magnetic fields for the Abelian Higgs model
International Nuclear Information System (INIS)
Magpantay, J.; Mukku, C.; Sayed, W.A.
1981-05-01
One loop temperature and external electromagnetic field effects on the Abelian Higgs model are studied using the momentum space heat kernel. We obtain expressions for the critical fields necessary for symmetry restoration at some finite temperature and display the critical B vs. T curve separating the broken and restored phases in the B-T plane. (author)
Quantum gauge freedom in very special relativity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com [Centre for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur-721302, West Bengal (India); Panigrahi, Prasanta K., E-mail: pprasanta@iiserkol.ac.in [Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal (India)
2017-02-15
We demonstrate Yokoyama gaugeon formalism for the Abelian one-form gauge (Maxwell) as well as for Abelian two-form gauge theory in the very special relativity (VSR) framework. In VSR scenario, the extended action due to introduction of gaugeon fields also possesses form invariance under quantum gauge transformations. It is observed that the gaugeon field together with gauge field naturally acquire mass, which is different from the conventional Higgs mechanism. The quantum gauge transformation implements a shift in gauge parameter. Further, we analyze the BRST symmetric gaugeon formalism in VSR which embeds only one subsidiary condition rather than two.
Discrete finite nilpotent Lie analogs: New models for unified gauge field theory
International Nuclear Information System (INIS)
Kornacker, K.
1978-01-01
To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors
Abelian Chern-Simons theory and contact torsion
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas in ...... in quantum field theory. We compare the shift reduced partition function with other formulations of the abelian Chern-Simons partition function. This study naturally motivates an Atiyah-Patodi-Singer type index problem in contact geometry.......Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas...
Magnetic monopoles, center vortices, confinement and topology of gauge fields
International Nuclear Information System (INIS)
Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Schaefke, A.
2000-01-01
The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed
Magnetic Monopoles, Center Vortices, Confinement and Topology of Gauge Fields
Reinhardt, H.; Engelhardt, M.; Langfeld, K.; Quandt, M.; Sch"afke, A.
1999-01-01
The vortex picture of confinement is studied. The deconfinement phase transition is explained as a transition from a phase in which vortices percolate to a phase of small vortices. Lattice results are presented in support of this scenario. Furthermore the topological properties of magnetic monopoles and center vortices arising, respectively, in Abelian and center gauges are studied in continuum Yang-Mills-theory. For this purpose the continuum analog of the maximum center gauge is constructed.
Anomalous coupling of scalars to gauge fields
Energy Technology Data Exchange (ETDEWEB)
Brax, Philippe [CEA, IPhT, CNRS, URA 2306, Gif-sur-Yvette (France). Inst. de Physique Theorique; Burrage, Clare [Geneve Univ. (Switzerland). Dept. de Physique Theorique; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Davis, Anne-Christine [Centre for Mathematical Sciences, Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics; Seery, David [Sussex Univ., Brighton (United Kingdom). Dept. of Physics and Astronomy; Weltman, Amanda [Cape Town Univ., Rondebosch (South Africa). Astronomy, Cosmology and Gravity Centre
2010-10-15
We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)
Anomalous coupling of scalars to gauge fields
International Nuclear Information System (INIS)
Brax, Philippe; Davis, Anne-Christine; Seery, David; Weltman, Amanda
2010-10-01
We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)
Constraints on Gauge Field Production during Inflation
DEFF Research Database (Denmark)
Nurmi, Sami; Sloth, Martin Snoager
2014-01-01
In order to gain new insights into the gauge field couplings in the early universe, we consider the constraints on gauge field production during inflation imposed by requiring that their effect on the CMB anisotropies are subdominant. In particular, we calculate systematically the bispectrum...... of the primordial curvature perturbation induced by the presence of vector gauge fields during inflation. Using a model independent parametrization in terms of magnetic non-linearity parameters, we calculate for the first time the contribution to the bispectrum from the cross correlation between the inflaton...
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1989-01-01
In this paper, we generalize our earlier discussion of renormalization of the energy-momentum tensor in scalar QED to that in non-Abelian gauge theories involving scalar fields. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be derived from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/)
Non-abelian gauge bosons in the compactified bosonic membrane theory
International Nuclear Information System (INIS)
Kubo, J.
1988-01-01
We consider the bosonic membrane compactified on a torus. The membrane motion is stabilized by a topologically non-trivial background. We find that, in the narrow membrane limit, the mass formula to O(ℎ) reduces to exactly the same form as that of the compactified closed bosonic string theory, and we obtain (almost) massless vector bosons in the adjoint representation of a simply laced Lie group in D=27. This is only dimension at which the graviton and gauge bosons may coexist in that background. (orig.)
Elastic Gauge Fields in Weyl Semimetals
Cortijo, Alberto; Ferreiros, Yago; Landsteiner, Karl; Hernandez Vozmediano, Maria Angeles
We show that, as it happens in graphene, elastic deformations couple to the electronic degrees of freedom as pseudo gauge fields in Weyl semimetals. We derive the form of the elastic gauge fields in a tight-binding model hosting Weyl nodes and see that this vector electron-phonon coupling is chiral, providing an example of axial gauge fields in three dimensions. As an example of the new response functions that arise associated to these elastic gauge fields, we derive a non-zero phonon Hall viscosity for the neutral system at zero temperature. The axial nature of the fields provides a test of the chiral anomaly in high energy with three axial vector couplings. European Union structural funds and the Comunidad de Madrid MAD2D-CM Program (S2013/MIT-3007).
Gravitating SO (3,1) gauge field
International Nuclear Information System (INIS)
Aragone, C.; Restuccia, A.
1978-01-01
In this article, we postulate SO (3,1) as a local symmetry of any relativistic theory. This is equivalent to assuming the existence of a gauge field associated with this noncompact group. This SO (3,1) gauge field is the spinorial affinity which usually appears when we deal with weighting spinors, which, as is well known, cannot be coupled to the metric tensor field. Furthermore, according to the integral approach to gauge fields proposed by Yang, it is also recognized that in order to obtain models of gravity we have to introduce ordinary affinities as the gauge field associated with GL (4) (the local symmetry determined by the parallel transport). Thus if we assume both GL (4) and SO (3,1) as local independent symmetries we are led to analyze the dynamical gauge system constituted by the Einstein field interacting with the SO (3,1) Weyl--Yang gauge field. We think this system is a possible model of strong gravity. Once we give the first-order action for this Einstein--Weyl--Yang system we study whether the SO (3,1) gauge field could have a tetrad associated with it. It is also shown that both fields propagate along a unique characteristic cone. Algebraic and differential constraints are solved when the system evolves along a null coordinate. The unconstrained expression for the action of the system is found working in the Bondi gauge. That allows us to exhibit an explicit expression of the dynamical generator of the system. Its signature turns out to be nondefinite, due to the nondefinite contribution of the Weyl--Yang field, which has the typical spinorial behavior. A conjecture is made that such an unpleasant feature could be overcome in the quantized version of this model
Toward a gauge field theory of gravity.
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Derivation of the Finslerian gauge field equations
International Nuclear Information System (INIS)
Asanov, G.S.
1984-01-01
As is well known the simplest way of formulating the equations for the Yang-Mills gauge fields consists in taking the Lagrangian to be quadratic in the gauge tensor, whereas the application of such an approach to the gravitational field yields equations which are of essentially more complicated structure than the Einstein equations. On the other hand, in the gravitational field theory the Lagrangian can be constructed to be of forms which may be both quadratic and linear in the curvature tensor, whereas the latter possibility is absent in the current gauge field theories. In previous work it has been shown that the Finslerian structure of the space-time gives rise to certain gauge fields provided that the internal symmetries may be regarded as symmetries of a three-dimensional Riemannian space. Continuing this work we show that appropriate equations for these gauge fields can be formulated in both ways, namely on the basis of the quadratic Lagrangian or, if a relevant generalization of the Palatini method is applied, on the basis of a Lagrangian linear in the gauge field strength tensor. The latter possibility proves to result in equations which are similar to the Einstein equations, a distinction being that the Finslerian Cartan curvature tensor rather then the Riemann curvature tensor enters the equations. (author)
World-sheet gauge fields in superstrings
International Nuclear Information System (INIS)
Porrati, M.; Tomboulis, E.T.
1989-01-01
We investigate the introduction of world-sheet 2-dimensional gauge fields in a manner consistent with world-sheet supersymmetry. We obtain the effective string action resulting from the exact integration over the world-sheet gauge fields to show that it generally describes string models with spontaneous breaking of gauge symmetries with continuous breaking parameters. We examine the question of spacetime supersymmetry spontaneous breaking, and show that breaking with continuous, in particular arbitrarily small breaking parameters does not occur; only breaking for discrete values of parameters is possible. (orig.)
Gauge bridges in classical field theory
International Nuclear Information System (INIS)
Jakobs, S.
2009-03-01
In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called ''gauge bridges''are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)
A Conclusive Test of Abelian Dominance Hypothesis for Topological Charge in the QCD Vacuum
Sasaki, Shoichi; Miyamura, Osamu
1998-01-01
We study the topological feature in the QCD vacuum based on the hypothesis of abelian dominance. The topological charge $Q_{\\rm SU(2)}$ can be explicitly represented in terms of the monopole current in the abelian dominated system. To appreciate its justification, we directly measure the corresponding topological charge $Q_{\\rm Mono}$, which is reconstructed only from the monopole current and the abelian component of gauge fields, by using the Monte Carlo simulation on SU(2) lattice. We find ...
Group theory and lattice gauge fields
International Nuclear Information System (INIS)
Creutz, M.
1988-09-01
Lattice gauge theory, formulated in terms of invariant integrals over group elements on lattice bonds, benefits from many group theoretical notions. Gauge invariance provides an enormous symmetry and powerful constraints on expectation values. Strong coupling expansions require invariant integrals over polynomials in group elements, all of which can be evaluated by symmetry considerations. Numerical simulations involve random walks over the group. These walks automatically generate the invariant group measure, avoiding explicit parameterization. A recently proposed overrelaxation algorithm is particularly efficient at exploring the group manifold. These and other applications of group theory to lattice gauge fields are reviewed in this talk. 17 refs
Emergent Gauge Fields in Holographic Superconductors
Domènech, Oriol; Pomarol, Alex; Salvio, Alberto; Silva, Pedro J
2010-01-01
Holographic superconductors have been studied so far in the absence of dynamical electromagnetic fields, namely in the limit in which they coincide with holographic superfluids. It is possible, however, to introduce dynamical gauge fields if a Neumann-type boundary condition is imposed on the AdS-boundary. In 3+1 dimensions, the dual theory is a 2+1 dimensional CFT whose spectrum contains a massless gauge field, signaling the emergence of a gauge symmetry. We study the impact of a dynamical gauge field in vortex configurations where it is known to significantly affect the energetics and phase transitions. We calculate the critical magnetic fields H_c1 and H_c2, obtaining that holographic superconductors are of Type II (H_c1 < H_c2). We extend the study to 4+1 dimensions where the gauge field does not appear as an emergent phenomena, but can be introduced, by a proper renormalization, as an external dynamical field. We also compare our predictions with those arising from a Ginzburg-Landau theory and identif...
Gauge field vacuum structure in geometrical aspect
International Nuclear Information System (INIS)
Konopleva, N.P.
2003-01-01
Vacuum conception is one of the main conceptions of quantum field theory. Its meaning in classical field theory is also very profound. In this case the vacuum conception is closely connected with ideas of the space-time geometry. The global and local geometrical space-time conceptions lead to different vacuum definitions and therefore to different ways of physical theory construction. Some aspects of the gauge field vacuum structure are analyzed. It is shown that in the gauge field theory the vacuum Einstein equation solutions describe the relativistic vacuum as common vacuum of all gauge fields and its sources. Instantons (both usual and hyperbolical) are regarded as nongravitating matter, because they have zero energy-momentum tensors and correspond to vacuum Einstein equations
Wang, Juven C.; Wen, Xiao-Gang
2015-01-01
String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.
Path integral quantization in the temporal gauge
International Nuclear Information System (INIS)
Scholz, B.; Steiner, F.
1983-06-01
The quantization of non-Abelian gauge theories in the temporal gauge is studied within Feynman's path integral approach. The standard asymptotic boundary conditions are only imposed on the transverse gauge fields. The fictituous longitudinal gauge quanta are eliminated asymptotically by modified boundary conditions. This abolishes the residual time-independent gauge transformations and leads to a unique fixing of the temporal gauge. The resulting path integral for the generating functional respects automatically Gauss's law. The correct gauge field propagator is derived. It does not suffer from gauge singularities at n x k = 0 present in the usual treatment of axial gauges. The standard principal value prescription does not work. As a check, the Wilson loop in temporal gauge is calculated with the new propagator. To second order (and to all orders in the Abelian case) the result agrees with the one obtained in the Feynman and Coulomb gauge. (orig.)
Gauge field theories an introduction with applications
Guidry, Mike
1991-01-01
Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises
International Nuclear Information System (INIS)
Nguyen Quoc Thang
2004-08-01
We show the validity of te Corestriction Principle for non-abelian cohomology of connected reductive groups over local ad global fields of characteristic p > 0 , by extending some results by Kneser and Douai. (author)
Vacuum in intensive gauge fields
International Nuclear Information System (INIS)
Matinian, S.G.
1977-12-01
The behaviour of vacuum in a covariantly constant Yang-Mills field is considered. The expressions for the effective Lagrangian in an intensive field representing the asymptotic freedom of the theory are found
Consistency of lattice definitions of U(1) flux in Abelian projected SU(2) gauge theory
International Nuclear Information System (INIS)
Matsuki, Takayuki; Haymaker, Richard W.
2004-01-01
We reexamine the dual Abrikosov vortex under the requirement that the lattice averages of the fields satisfy exact Maxwell equations [ME]. The electric ME accounts for the total flux and the magnetic ME determines the shape of the confining string. This leads to unique and consistent definitions of flux and electric and magnetic currents at finite lattice spacing. The resulting modification of the standard DeGrand-Toussaint construction gives a magnetic current comprised of smeared monopoles
International Nuclear Information System (INIS)
Izaurieta, F.; Rodriguez, E.; Salgado, P.
2008-01-01
A new Lagrangian realizing the symmetry of the M-algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian semigroup expansion, a link between the M-algebra and the orthosymplectic algebra osp(32 vertical stroke 1) is established, and an M-algebra-invariant symmetric tensor of rank six is computed. This symmetric invariant tensor is a key ingredient in the construction of the new Lagrangian. The gauge-invariant Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a subspace separation method based on the extended Cartan homotopy formula. (orig.)
On the topological vacuum degeneracy in gauge theories
International Nuclear Information System (INIS)
Pervushin, V.N.
1982-01-01
It is shown that the nontrivial topology of gauge fields leads to the Josephson effect in the field space, i. e., to nonvanishing vacuum fields. The same definition is proposed for the physical (infrared) vacuum for Abelian (QED) and nonAbelian (QCD) theories. The equations and the topological Josephson effect for the gluon vacuum are discussed
Analytical results for Abelian projection
International Nuclear Information System (INIS)
Ogilivie, Michael C.
1999-01-01
Analytic methods for Abelian projection are developed, and a number of results related to string tension measurements are obtained. It is proven that even without gauge fixing, Abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The subgroup used for projection need only contain the center of the gauge group, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements
Confinement through tensor gauge fields
International Nuclear Information System (INIS)
Salam, A.; Strathdee, J.
1977-12-01
Using the 0(3,2)-symmetric de Sitter solution of Einstein's equation describing a strongly interacting tensor field it is shown that hadronic bags confining quarks can be represented as de Sitter ''micro-universes'' with radii given 1/R 2 =lambdak 2 /6. Here k 2 and lambda are the strong coupling and the ''cosmological'' constant which apear in the Einstein equation used. Surprisingly the energy spectrum for the two-body hadronic states is the same as that for a harmonic oscillator potential, though the wave functions are completely different. The Einstein equation can be extended to include colour for the tensor fields
A non-perturbative argument for the non-abelian Higgs mechanism
Energy Technology Data Exchange (ETDEWEB)
De Palma, G. [Scuola Normale Superiore, Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy); Strocchi, F., E-mail: franco.strocchi@sns.it [INFN, Sezione di Pisa, Pisa (Italy)
2013-09-15
The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.
A non-perturbative argument for the non-abelian Higgs mechanism
International Nuclear Information System (INIS)
De Palma, G.; Strocchi, F.
2013-01-01
The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion
Field-theoretical investigations in nonlinear realizations of gauge symmetry
International Nuclear Information System (INIS)
Lee, Chenhan.
1989-01-01
A review of both linear realization and non-linear realization of gauge symmetries is given and the connection between the two recipes is carefully examined. The author then constructs both linear and non-linear realizations for of supersymmetric theories. The supermultiplets of the Goldstone modes contain Goldstone bosons, quasi-Goldstone bosons and quasi-Goldstone fermions. He makes an attempt to construct a specific model of a supersymmetric non-linear realization for the Nambu-Goldstone superfields and the quasi-Goldstone fermions are identified with the quarks and leptons. Further, he discusses a mechanism by which the components of the Nambu-Goldstone supermultiplets are given non-zero mass splittings by the coupling to a hidden sector. Next, he turns to anti-symmetric tensor gauge theories, which are shown to be classically equivalent to the non-linear models describing the complete symmetry breakdown. To study the quantum mechanical equivalence of these two models, he carries out the tensor gauge fixing and the quantization procedures for the anti-symmetric tensor theories and establish the global symmetry currents which connect the two models. He then builds the supersymmetric extensions of the anti-symmetric tensor gauge theories in both abelian and non-abelian versions. Such super-tensor gauge theories are shown, by using the superfield equations of motion, to be equivalent to the fully doubled supersymmetric non-linear models of complete symmetry breakdown
Finite N=1 SUSY gauge field theories
International Nuclear Information System (INIS)
Kazakov, D.I.
1986-01-01
The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established
Gauge field theories. Part three. Renormalization
International Nuclear Information System (INIS)
Frampon, P.H.
1978-01-01
The renormalization of nonabelian gauge theories both with exact symmetry and with spontaneous symmetry breaking is discussed. The method of dimensional regularization is described and used in the ensuing discussion. Triangle anomalies and their implications and the method for cancellation of anomalies in an SU(2) x U(1) theory, introduction of the BRS form of local gauge transformation and its use for the iterative proof of renormalizability to all orders for pure Yang--Mills and with fermion and scalar matter fields are considered. Lastly for massive vectors arising from spontaneous breaking, the demonstration of renormalizability is given, using the 't Hooft gauges introduced first in 1971. While the treatment is not totally rigorous, all the principle steps are given. 108 references
Generalized Proca action for an Abelian vector field
International Nuclear Information System (INIS)
Allys, Erwan; Peter, Patrick; Rodríguez, Yeinzon
2016-01-01
We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature
International Nuclear Information System (INIS)
Quadri, Andrea
2006-01-01
We elucidate the geometry of the polynomial formulation of the non-Abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) differential exists allowing to implement the constraint on the σ field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (Abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-Abelian gauge fields. As all versions of the Stueckelberg theory, also the Abelian embedding formulation yields a nonpower-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the Abelian embedding formalism
Shadow fields and local supersymmetric gauges
International Nuclear Information System (INIS)
Baulieu, L.; Bossard, G.; Sorella, S.P.
2006-01-01
To control supersymmetry and gauge invariance in super-Yang-Mills theories we introduce new fields, called shadow fields, which enable us to enlarge the conventional Faddeev-Popov framework and write down a set of useful Slavnov-Taylor identities. These identities allow us to address and answer the issue of the supersymmetric Yang-Mills anomalies, and to perform the conventional renormalization programme in a fully regularization-independent way
Directory of Open Access Journals (Sweden)
K.J.B. Ghosh
2018-01-01
Full Text Available We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U(1 gauge fields Aμ(x which depend on all four spacetime coordinates (including the coordinate x4∈S1 of the compact dimension and have vanishing components A4(x (implying trivial holonomies in the 4-direction. Our calculation shows that the effective gauge-field action contains a local Chern–Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli–Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg–Wilson fermions.
Ghosh, K. J. B.; Klinkhamer, F. R.
2018-01-01
We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology R3 ×S1 and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian U (1) gauge fields Aμ (x) which depend on all four spacetime coordinates (including the coordinate x4 ∈S1 of the compact dimension) and have vanishing components A4 (x) (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.
Stability of infinite derivative Abelian Higgs models
Ghoshal, Anish; Mazumdar, Anupam; Okada, Nobuchika; Villalba, Desmond
2018-04-01
Motivated by the stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability; the Yukawa coupling between the scalar and the fermion, the gauge coupling, and the self interaction of the Higgs yields exponentially suppressed running at high energies, showing that such class of theory never suffers from vacuum instability. We briefly discuss its implications for the early Universe cosmology.
Gauge field configurations in curved spacetimes (II)
International Nuclear Information System (INIS)
Boutaleb-Joutei, H.; Chakrabarti, A.; Comtet, A.
1979-05-01
One continues the study of gauge field configurations in curved spaces, using the formalism and results of a previous paper. A class of static, finite action, selfdual solutions of SU(2) gauge fields on a Euclidean section of de Sitter space is presented. The action depends on a continuous parameter. The spin connection solution is obtained as a particular case and a certain passage to the limiting case of a flat space is shown to reproduce the Euclidean Prasad-Sommerfield solution. The significance and possible interest of such solutions are discussed. The results are then generalized to a non-Einstein but conformally flat space, including de Sitter space as an Einstein limit. Next Baecklund type transformations are constructed starting from selfduality constraints for such curved spaces. These transformations are applied to the above mentioned solutions. The last two sections contain remarks on solutions with a background Robinson-Bertotti metric and on static, axially symmetric solutions respectively
Zero energy gauge fields and the phases of a gauge theory
International Nuclear Information System (INIS)
Guendelman, E.I.
1990-01-01
A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism
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 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.)
A note on the fate of the Landau–Yang theorem in non-Abelian gauge theories
Directory of Open Access Journals (Sweden)
Matteo Cacciari
2016-02-01
Full Text Available Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N Yang–Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
A note on the fate of the Landau–Yang theorem in non-Abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Cacciari, Matteo [Université Paris Diderot, F-75013 Paris (France); Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005 Paris (France); CNRS, UMR 7589, LPTHE, F-75005 Paris (France); CERN, PH-TH, CH-1211 Geneva 23 (Switzerland); Del Debbio, Luigi [Higgs Centre for Theoretical Physics, School of Physics & Astronomy, University of Edinburgh, Edinburgh EH9 3FD (United Kingdom); CERN, PH-TH, CH-1211 Geneva 23 (Switzerland); Espinosa, José R. [ICREA, Institució Catalana de Recerca i Estudis Avançats, Barcelona (Spain); IFAE, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); Polosa, Antonio D., E-mail: antonio.polosa@roma1.infn.it [Dipartimento di Fisica and INFN, ‘Sapienza’ Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma (Italy); Testa, Massimo [Dipartimento di Fisica and INFN, ‘Sapienza’ Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma (Italy)
2016-02-10
Using elementary considerations of Lorentz invariance, Bose symmetry and BRST invariance, we argue why the decay of a massive color-octet vector state into a pair of on-shell massless gluons is possible in a non-Abelian SU(N) Yang–Mills theory, we constrain the form of the amplitude of the process and offer a simple understanding of these results in terms of effective-action operators.
Linear b-gauges for open string fields
International Nuclear Information System (INIS)
Kiermaier, Michael; Zwiebach, Barton; Sen, Ashoke
2008-01-01
Motivated by Schnabl's gauge choice, we explore open string perturbation theory in gauges where a linear combination of antighost oscillators annihilates the string field. We find that in these linear b-gauges different gauge conditions are needed at different ghost numbers. We derive the full propagator and prove the formal properties which guarantee that the Feynman diagrams reproduce the correct on-shell amplitudes. We find that these properties can fail due to the need to regularize the propagator, and identify a large class of linear b-gauges for which they hold rigorously. In these gauges the propagator has a non-anomalous Schwinger representation and builds Riemann surfaces by adding strip-like domains. Projector-based gauges, like Schnabl's, are not in this class of gauges but we construct a family of regular linear b-gauges which interpolate between Siegel gauge and Schnabl gauge
Geometrodynamics of gauge fields on the geometry of Yang-Mills and gravitational gauge theories
Mielke, Eckehard W
2016-01-01
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter t...
Gauss decomposition, Wakimoto realisation and gauged WZNW models
International Nuclear Information System (INIS)
Arfaei, H.; Mohammedi, N.
1993-10-01
The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging an abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables. (orig.)
Gauge-invariant intense-field approximations to all orders
International Nuclear Information System (INIS)
Faisal, F H M
2007-01-01
We present a gauge-invariant formulation of the so-called strong-field KFR approximations in the 'velocity' and 'length' gauges and demonstrate their equivalence in all orders. The theory thus overcomes a longstanding discrepancy between the strong-field velocity and the length-gauge approximations for non-perturbative processes in intense laser fields. (fast track communication)
Gauge theory and renormalization
Hooft, G. 't
1996-01-01
Early developments leading to renormalizable non-Abelian gauge theories for the weak, electromagnetic and strong interactions, are discussed from a personal viewpoint. They drastically improved our view of the role of field theory, symmetry and topology, as well as other branches of mathematics, in
Relations between correlation functions in gauge field theory
International Nuclear Information System (INIS)
Simonov, Yu. A.; Shevchenko, V. I.
1997-01-01
Exact relations between vacuum correlations of non-Abelian field strengths are obtained. With the aid of exterior differentiation, the invariant parts of a given correlation function are expressed in terms of higher order correlation functions. The corollaries of these relations for the behavior of nonperturbative correlation functions at small and large distances are deduced
A gauge field theory of fermionic continuous-spin particles
Energy Technology Data Exchange (ETDEWEB)
Bekaert, X., E-mail: xavier.bekaert@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science, Daejeon (Korea, Republic of); Najafizadeh, M., E-mail: mnajafizadeh@gmail.com [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of); Setare, M.R., E-mail: rezakord@ipm.ir [Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of)
2016-09-10
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
A gauge field theory of fermionic continuous-spin particles
International Nuclear Information System (INIS)
Bekaert, X.; Najafizadeh, M.; Setare, M.R.
2016-01-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Gauge field theories. 3. enl. ed.
International Nuclear Information System (INIS)
Frampton, Paul H.
2008-01-01
Gauge theories provide a unified framework to describe three of the four universal forces known so far: the quantum field theories of electromagnetism, the weak force and the strong force. They are an essential part of the so-called standard model of particles and matter. The first edition of this work was quickly adopted by universities and other institutions of higher learning around the world. Completely updated, this third edition continues to be an ideal reference on the subject. In total, more than a quarter of the content has been changed or added. The tried-and-tested logical structuring of the material on gauge invariance, quantization, and renormalization has been retained, while the chapters on electroweak interactions and model building have been revised. Completely new is the chapter on conformality. As in the past, Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research: - gauge invariance, - quantization, - renormalization, - electroweak forces, - renormalization group, - quantum chromodynamics, - model building, - conformality. (orig.)
Gravitational Goldstone fields from affine gauge theory
Tresguerres, Romualdo; Mielke, Eckehard W.
2000-08-01
In order to facilitate the application of standard renormalization techniques, gravitation should be described, in the pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincaré or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills-type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden'' piece within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide the general mathematical scheme for the foundation of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric no longer constitutes an independent gravitational potential, since its degrees of freedom reveal a correspondence to eliminateable Goldstone bosons. This may be an important advantage for quantization.
String field theory-inspired algebraic structures in gauge theories
International Nuclear Information System (INIS)
Zeitlin, Anton M.
2009-01-01
We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.
Gauge-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
(Non-)Abelian Kramers-Wannier duality and topological field theory
Severa, Pavol
2002-01-01
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for higher-dimensional cases. In this form they lead to simple TFTs with boundary coloured in two colours. The statistical models live on the boundary of these TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie T-duality) suggest a non-abelian generalization in the 2dcase, with abelian groups replaced by quantum groups. Amazingly, the TFT formulation solves the problem without computation: quantum groups appear in pictures, independently of the classical motivation. Connection with Chern-Simons theory appears at the symplectic level, and also in the pictures of the Drinfeld double: Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the double, are included in these TFTs. All this suggests nice phenomena in higher dimensions.
Local gauge coupling running in supersymmetric gauge theories on orbifolds
International Nuclear Information System (INIS)
Hillenbach, M.
2007-01-01
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
Local gauge coupling running in supersymmetric gauge theories on orbifolds
Energy Technology Data Exchange (ETDEWEB)
Hillenbach, M.
2007-11-21
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
A new approach to non-Abelian hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Fernández-Melgarejo, Jose J. [Center for the Fundamental Laws of Nature, Harvard University,Cambridge, MA 02138 (United States); Rey, Soo-Jong [School of Physics & Astronomy and Center for Theoretical Physics, Seoul National University,Seoul, 08826 (Korea, Republic of); Department of Fundamental Sciences, University of Science and Technology,Daejeon, 34113 (Korea, Republic of); Center for Gauge, Gravity & Strings, Institute for Basic Sciences,Daejeon, 34047 (Korea, Republic of); Surówka, Piotr [Center for the Fundamental Laws of Nature, Harvard University,Cambridge, MA 02138 (United States); Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, D-80805 Munich (Germany)
2017-02-23
We present a new approach to describe hydrodynamics carrying non-Abelian macroscopic degrees of freedom. Based on the Kaluza-Klein compactification of a higher-dimensional neutral dissipative fluid on a manifold of non-Abelian isometry, we obtain a four-dimensional colored dissipative fluid coupled to Yang-Mills gauge field. We derive transport coefficients of resulting colored fluid, which feature non-Abelian character of color charges. In particular, we obtain color-specific terms in the gradient expansions and response quantities such as the conductivity matrix and the chemical potentials. We argue that our Kaluza-Klein approach provides a robust description of non-Abelian hydrodynamics, and discuss some links between this system and quark-gluon plasma and fluid/gravity duality.
A new approach to non-Abelian hydrodynamics
International Nuclear Information System (INIS)
Fernández-Melgarejo, Jose J.; Rey, Soo-Jong; Surówka, Piotr
2017-01-01
We present a new approach to describe hydrodynamics carrying non-Abelian macroscopic degrees of freedom. Based on the Kaluza-Klein compactification of a higher-dimensional neutral dissipative fluid on a manifold of non-Abelian isometry, we obtain a four-dimensional colored dissipative fluid coupled to Yang-Mills gauge field. We derive transport coefficients of resulting colored fluid, which feature non-Abelian character of color charges. In particular, we obtain color-specific terms in the gradient expansions and response quantities such as the conductivity matrix and the chemical potentials. We argue that our Kaluza-Klein approach provides a robust description of non-Abelian hydrodynamics, and discuss some links between this system and quark-gluon plasma and fluid/gravity duality.
Magnetic monopoles and the dual London equation in SU(3) lattice gauge theory
International Nuclear Information System (INIS)
Skala, P.; Faber, M.; Zach, M.
1996-01-01
The dual superconductor model of confinement in non-Abelian gauge theories is studied in a gauge invariant formulation. We propose a method for the determination of magnetic monopole currents in non-Abelian gauge theories which does not need a projection to Abelian degrees of freedom. With this definition we are able to determine the distribution of magnetic currents and electric fields for the gluonic flux tube between a pair of static charges. Further we check the validity of the dual London equation in a gauge invariant formulation. (orig.)
International Nuclear Information System (INIS)
Galilo, Bogdan V.; Nedelko, Sergei N.
2011-01-01
The one-loop quark contribution to the QCD effective potential for the homogeneous Abelian gluon field in the presence of an external strong electromagnetic field is evaluated. The structure of extrema of the potential as a function of the angles between chromoelectric, chromomagnetic, and electromagnetic fields is analyzed. In this setup, the electromagnetic field is considered as an external one while the gluon field represents domain structured nonperturbative gluon configurations related to the QCD vacuum in the confinement phase. Two particularly interesting gluon configurations, (anti-)self-dual and crossed orthogonal chromomagnetic and chromoelectric fields, are discussed specifically. Within this simplified framework it is shown that the strong electromagnetic fields can play a catalyzing role for a deconfinement transition. At the qualitative level, the present consideration can be seen as a highly simplified study of an impact of the electromagnetic fields generated in relativistic heavy ion collisions on the strongly interacting hadronic matter.
Localization in abelian Chern-Simons theory
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed...
Noether's theorem for local gauge transformations
International Nuclear Information System (INIS)
Karatas, D.L.; Kowalski, K.L.
1989-01-01
The variational methods of classical field theory may be applied to any theory with an action which is invariant under local gauge transformations. What is the significance of the resulting Noether current? This paper examines such currents for both Abelian and non-Abelian gauge theories and provides an explanation for their form and limited range of physical significance on a level accessible to those with a basic knowledge of classical field theory. Several of the more subtle aspects encountered in the application of the residual local gauge symmetry found by Becchi, Rouet, Stora, and Tyutin are also considered in detail in a self-contained manner. 23 refs
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
Some physico-geometrical remarks on gauge fields
International Nuclear Information System (INIS)
Ikeda, S.
1976-01-01
The gauge fields introduced to accomplish gauge invariance under Poincare and Weyl gauge transformations in general relativity are found a new to be absorbed into the covariant derivative operators. Some torsional properties associated with them are also discussed in connection with the principle of minimally coupling and the equivalence principle
Spin dynamics under local gauge fields in chiral spin-orbit coupling systems
International Nuclear Information System (INIS)
Tan, S.G.; Jalil, M.B.A.; Fujita, T.; Liu, X.J.
2011-01-01
Research highlights: → We derive a modified LLG equation in magnetic systems with spin-orbit coupling (SOC). → Our results are applied to magnetic multilayers, and DMS and magnetic Rashba systems. → SOC mediated magnetization switching is predicted in rare earth metals (large SOC). → The magnetization trajectory and frequency can be modulated by applied voltage. → This facilitates potential application as tunable microwave oscillators. - Abstract: We present a theoretical description of local spin dynamics in magnetic systems with a chiral spin texture and finite spin-orbit coupling (SOC). Spin precession about the relativistic effective magnetic field in a SOC system gives rise to a non-Abelian SU(2) gauge field reminiscent of the Yang-Mills field. In addition, the adiabatic relaxation of electron spin along the local spin yields an U(1) x U(1) topological gauge (Berry) field. We derive the corresponding equation of motion i.e. modified Landau-Lifshitz-Gilbert (LLG) equation, for the local spin under the influence of these effects. Focusing on the SU(2) gauge, we obtain the spin torque magnitude, and the amplitude and frequency of spin oscillations in this system. Our theoretical estimates indicate significant spin torque and oscillations in systems with large spin-orbit coupling, which may be utilized in technological applications such as current-induced magnetization-switching and tunable microwave oscillators.
Dual gauge field theory of quantum liquid crystals in three dimensions
International Nuclear Information System (INIS)
Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai; Zaanen, Jan
2017-01-01
The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two, or three directions, leading to the quantum analogues of columnar, smectic, or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes, while compressional stress remains massless. Rotational Goldstone modes emerge whenever translational symmetry is restored. Lastly, we also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.
Dual gauge field theory of quantum liquid crystals in three dimensions
Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai; Zaanen, Jan
2017-10-01
The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two, or three directions, leading to the quantum analogues of columnar, smectic, or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes, while compressional stress remains massless. Rotational Goldstone modes emerge whenever translational symmetry is restored. We also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.
Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
Energy Technology Data Exchange (ETDEWEB)
Cartas-Fuentevilla, R. [Universidad Autonoma de Puebla, Instituto de Fisica, Puebla, Pue. (Mexico); Meza-Aldama, O. [Universidad Autonoma de Puebla, Facultad de Ciencias Fisico-Matematicas, Puebla, Pue. (Mexico)
2016-02-15
Inspired by the appearance of split-complex structures in the dimensional reduction of string theory, and in the theories emerging as byproducts, we study the hypercomplex formulation of Abelian gauge field theories by incorporating a new complex unit to the usual complex one. The hypercomplex version of the traditional Mexican hat potential associated with the U(1) gauge field theory, corresponds to a hybrid potential with two real components, and with U(1) x SO(1,1) as symmetry group. Each component corresponds to a deformation of the hat potential, with the appearance of a new degenerate vacuum. Hypercomplex electrodynamics will show novel properties, such as spontaneous symmetry breaking scenarios with running masses for the vectorial and scalar Higgs fields, and such as Aharonov-Bohm type strings defects as exact solutions; these topological defects may be detected only by quantum interference of charged particles through gauge invariant loop integrals. In a particular limit, the hyperbolic electrodynamics does not admit topological defects associated with continuous symmetries. (orig.)
Vacuum structure of the SU(3) gauge field theory in the Coulomb gauge
International Nuclear Information System (INIS)
Yee, J.H.; Viswanathan, K.S.
1978-01-01
The SU(3) gauge field is studied in the Coulomb gauge. The Gribov ambiguities arising in the Coulomb gauge are analysed. Restricting to a class of spherically symmetric vacua it is shown that there exist non-trivial vacua characterized by a topological number eta=0, +-1/2, and +-2. This must be contrasted with the spherically symmetric SU(2) vacua which are characterized by eta=0, +-1/2. (Auth.)
International Nuclear Information System (INIS)
Cheng Hung; Tsai Ercheng
1986-01-01
We give a correspondence formula which equates transition amplitudes in a quantum gauge field theory without ghost fields to those in a quantum theory with the gauge fields covariantly quantized and coupled to ghost fields. (orig.)
Metric interpretation of gauge fields in noncommutative geometry
International Nuclear Information System (INIS)
Martinetti, P.
2007-01-01
We shall give an overview of the metric interpretation of gauge fields in noncommutative geometry, via Connes distance formula. Especially we shall focus on the Higgs fields in the standard model, and gauge fields in various models of fiber bundle. (author)
Gauge-invariant Yang-Mills fields and the role of Lorentz gauge condition
International Nuclear Information System (INIS)
Skachkov, N.B.; Shevchenko, O.Yu.
1985-01-01
A new class of gauge-invariant (G.I.) fields is constructed. The inversion formulae that express these fields through the G.I. strength tensor are obtained. It is shown that for the G.I. fields the Lorentz gauge condition appears as the secondary constraint. These fields coincide with the usual ones in some definite gauges. The Dyson-Schwinger equations for the G.I. spinor propagator are derived. It is found that in QED this propagator has a simple pole singularity (p-m) -1 in the infrared limit
International Nuclear Information System (INIS)
Wang Fan; Chen Xiangsong; Lue Xiaofu; Sun Weiming; Goldman, T.
2010-01-01
It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However, we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relations. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relations, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.
Multigrid methods for the computation of propagators in gauge fields
International Nuclear Information System (INIS)
Kalkreuter, T.
1992-11-01
In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. We discuss proper averaging operations for bosons and for staggered fermions. An efficient algorithm for computing C numerically is presented. The averaging kernels C can be used not only in deterministic multigrid computations, but also in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies of gauge theories. Actual numerical computations of kernels and propagators are performed in compact four-dimensional SU(2) gauge fields. (orig./HSI)
Markov, Yu. A.; Shishmarev, A. A.
2010-11-01
Based on the most general principles of materiality, gauge, and re-parameterized invariance, the problem of constructing an action describing the dynamics of a classical color-charged particle moving in external non-Abelian gauge and fermion fields is considered. The case of a linear Lagrangian dependence on the external fermion fields is discussed. Within the framework of the description of the color degree of freedom of the particle with half-integer spin by the Grassmann color charges, a new concept of the Grassmann color source of the particle being a fermion analog of the conventional color current is introduced.
Gauge principle for hyper(para) fields
Energy Technology Data Exchange (ETDEWEB)
Govorkov, A.B. (Joint Inst. for Nuclear Research, Dubna (USSR))
1983-04-01
A special representation for parafields is considered which is based on the use of the Clifford hypernumbers. The principle of gauge invariance under hypercomplex phase transformations of parafields is formulated. A special role of quaternion hyperfields and corresponding Yang-Mills lagrangian with the gauge SO(3)-symmetry is pointed out.
Introduction to gauge theories and unification
International Nuclear Information System (INIS)
Das, A.
1990-01-01
This paper contains the following lectures on gauge theories: basic notations; dimensional regularization; complex scalar field theory; scalar field theory; self-interacting scalar field theory; Noether's theorem; spontaneous symmetry breaking; dirac field theories; local symmetry; quantum electrodynamics; Higgs mechanism; non-Abelian symmetries; and Weinberg-Salam-Glashow theory
International Nuclear Information System (INIS)
Knight, D.W.
1976-01-01
Reasons are given for studying the form factor and a method for constructing all believed-to-be leading form factor diagrams in a certain class of non-Abelian gauge theories (NAGT's) in typical kinematic limits. The possibility that the form factor ''exponentiates'' in NAGT's (as it does in QED) is discussed. A method is given for constructing all 1CI planar diagrams (this is, all 1PI diagrams except those which separate upon cutting at a vertex) directly from one's heat--that is, without the need to refer to tables, et cetera. It is noted that the material is believed to be essentially completely original, that is, the technique for constructing all 1CI planar diagrams in an iterative fashion is completely new. Of course, one can construct them in an essentially random fashion, but this technique is slow and extremely error prone compared with the iterative technique given. The idea of associating an elastic resonance with a complex pole in the analytic scattering amplitude, T(E), is discussed. Calculations of the pole position and the residue of the Δ 33 resonance are given, along with an analysis of experimentally induced error in the pole position
Noncommutative gauge theories and Kontsevich's formality theorem
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.; Wess, J.
2001-01-01
The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor
From critical phenomena to gauge gields
International Nuclear Information System (INIS)
Le Bellac, M.
1988-01-01
In this book the author gives an introduction to the following questions: critical phenomena (Landau theory, renormalization group, two dimensional models); Perturbation theory and renormalization, scalar euclidian field (Feynman diagrams, Callan-Symanzik equations); Quantum theory of scalar fields (path integrals in quantum mechanics and statistical mechanics, green functions and S matrix, quantization of Klein-Gordon field); Gauge theories (quantization of Dirac field and electromagnetic field, quantum electrodynamics, non-abelian gauge theories) [fr
Nonabelian gauge fields in the background of magnetic strings
International Nuclear Information System (INIS)
Wieczorek, E.
1993-01-01
Quantized nonabelian gauge fields are studied in the external classical background of a linear magnetic string. The determination of the gauge field propagator demands a specification of the string by suitable physical limiting procedures. The vacuum energy density is obtained after transforming the background problem into a Casimir problem. (orig.)
New gauge symmetries in Witten's Ramond string field theory
International Nuclear Information System (INIS)
Kugo, Taichiro; Terao, Haruhiko
1988-01-01
Witten's Raymond string field theory is observed to possess new gauge symmetries, which guarantee the consistency and the equivalence of Witten's theory to the other formulation based on the constrained string field. The projection operator into the gauge-invariant sector is explicitly constructed using an operator similar to the picture changing operator. (orig.)
Gauge field entanglement in Kitaev's honeycomb model
Dóra, Balázs; Moessner, Roderich
2018-01-01
A spin fractionalizes into matter and gauge fermions in Kitaev's spin liquid on the honeycomb lattice. This follows from a Jordan-Wigner mapping to fermions, allowing for the construction of a minimal entropy ground-state wave function on the cylinder. We use this to calculate the entanglement entropy by choosing several distinct partitionings. First, by partitioning an infinite cylinder into two, the -ln2 topological entanglement entropy is reconfirmed. Second, the reduced density matrix of the gauge sector on the full cylinder is obtained after tracing out the matter degrees of freedom. This allows for evaluating the gauge entanglement Hamiltonian, which contains infinitely long-range correlations along the symmetry axis of the cylinder. The matter-gauge entanglement entropy is (Ny-1 )ln2 , with Ny the circumference of the cylinder. Third, the rules for calculating the gauge sector entanglement of any partition are determined. Rather small correctly chosen gauge partitions can still account for the topological entanglement entropy in spite of long-range correlations in the gauge entanglement Hamiltonian.
Abelian Chern endash Simons theory. II. A functional integral approach
International Nuclear Information System (INIS)
Manoliu, M.
1998-01-01
Following Witten, [Commun. Math. Phys. 21, 351 endash 399 (1989)] we approach the Abelian quantum Chern endash Simons (CS) gauge theory from a Feynman functional integral point of view. We show that for 3-manifolds with and without a boundary the formal functional integral definitions lead to mathematically proper expressions that agree with the results from the rigorous construction [J. Math. Phys. 39, 170 endash 206 (1998)] of the Abelian CS topological quantum field theory via geometric quantization. copyright 1998 American Institute of Physics
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.)
On the hyperbolicity of Einstein's and other gauge field equations
International Nuclear Information System (INIS)
Friedrich, H.
1985-01-01
It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)
Appearance of gauge structure in simple dynamical systems
Wilczek, F.; Zee, A.
1984-01-01
By generalizing a construction of Berry and Simon, it is shown that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.
Black holes with su(N) gauge field hair and superconducting horizons
Energy Technology Data Exchange (ETDEWEB)
Shepherd, Ben L.; Winstanley, Elizabeth [Consortium for Fundamental Physics, School of Mathematics and Statistics,The University of Sheffield,Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom)
2017-01-16
We present new planar dyonic black hole solutions of the su(N) Einstein-Yang-Mills equations in asymptotically anti-de Sitter space-time, focussing on su(2) and su(3) gauge groups. The magnetic part of the gauge field forms a condensate close to the planar event horizon. We compare the free energy of a non-Abelian hairy black hole with that of an embedded Reissner-Nordström-anti-de Sitter (RN-AdS) black hole having the same Hawking temperature and electric charge. We find that the hairy black holes have lower free energy. We present evidence that there is a phase transition at a critical temperature, above which the only solutions are embedded RN-AdS black holes. At the critical temperature, an RN-AdS black hole can decay into a hairy black hole, and it is thermodynamically favourable to do so. Working in the probe limit, we compute the frequency-dependent conductivity, and find that enlarging the gauge group from su(2) to su(3) eliminates a divergence in the conductivity at nonzero frequency.
Black holes with su(N) gauge field hair and superconducting horizons
International Nuclear Information System (INIS)
Shepherd, Ben L.; Winstanley, Elizabeth
2017-01-01
We present new planar dyonic black hole solutions of the su(N) Einstein-Yang-Mills equations in asymptotically anti-de Sitter space-time, focussing on su(2) and su(3) gauge groups. The magnetic part of the gauge field forms a condensate close to the planar event horizon. We compare the free energy of a non-Abelian hairy black hole with that of an embedded Reissner-Nordström-anti-de Sitter (RN-AdS) black hole having the same Hawking temperature and electric charge. We find that the hairy black holes have lower free energy. We present evidence that there is a phase transition at a critical temperature, above which the only solutions are embedded RN-AdS black holes. At the critical temperature, an RN-AdS black hole can decay into a hairy black hole, and it is thermodynamically favourable to do so. Working in the probe limit, we compute the frequency-dependent conductivity, and find that enlarging the gauge group from su(2) to su(3) eliminates a divergence in the conductivity at nonzero frequency.
Quantized Abelian principle connections on Lorentzian manifolds
International Nuclear Information System (INIS)
Benini, Marco; Schenkel, Alexander
2013-03-01
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers- Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the full subcategory of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Euler class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.
Quantized Abelian principle connections on Lorentzian manifolds
Energy Technology Data Exchange (ETDEWEB)
Benini, Marco [Pavia Univ. (Italy); Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Dappiaggi, Claudio [Pavia Univ. (Italy); Istituto Nazionale di Fisica Nucleare, Pavia (Italy); Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Mathematik
2013-03-15
We construct a covariant functor from a category of Abelian principal bundles over globally hyperbolic spacetimes to a category of *-algebras that describes quantized principal connections. We work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group, namely the group of vertical principal bundle automorphisms. Properties of our functor are investigated in detail and, similar to earlier works, it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated. Furthermore, we prove that, for Abelian structure groups containing a nontrivial compact factor, the gauge invariant Borchers- Uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections. We introduce a topological generalization of the concept of locally covariant quantum fields. As examples, we construct for the full subcategory of principal U(1)-bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the Euler class and the electric charge. In this case we also prove that the electric charges can be consistently set to zero, which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory.
Renormalization of nonabelian gauge theories with tensor matter fields
International Nuclear Information System (INIS)
Lemes, Vitor; Renan, Ricardo; Sorella, Silvio Paolo
1996-03-01
The renormalizability of a nonabelian model describing the coupling between antisymmetric second rank tensor matter fields and Yang-Mills gauge fields is discussed within the BRS algebraic framework. (author). 12 refs
Noncommutative gauge field theories: A no-go theorem
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-06-01
Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
Some formal problems in gauge theories
International Nuclear Information System (INIS)
Magpantay, J.A.
1980-01-01
The concerns of this thesis are the problems due to the extra degrees of freedom in gauge-invariant theories. Since gauge-invariant Lagrangians are singular, Dirac's consistency formalism and Fadeev's extension are first reviewed. A clarification on the origin of primary constraints is given, and some of the open problems in singular Lagrangian theory are discussed. The criteria in choosing a gauge, i.e., attainability, maintainability and Poincare invariance are summarized and applied to various linear gauges. The effects of incomplete removal of all gauge freedom on the criteria for gauge conditions are described. A simple example in point mechanics that contains some of the features of gauge field theories is given. Finally, we describe a method of constructing gauge-invariant variables in various gauge field theories. For the Abelian theory, the gauge-invariant, transverse potential and Dirac's gauge-invariant fermion field was derived. For the non-Abelian case we introduce a local set of basis vectors and gauge transformations are interpreted as rotations of the basis vectors introduced. The analysis leads to the reformulation of local SU(2) field theory in terms of path-dependent U(1) x U(1) x U(1). However, the analysis fails to include the matter fields as of now
Manipulating novel quantum phenomena using synthetic gauge fields
Zhang, Shao-Liang; Zhou, Qi
2017-11-01
The past few years have seen fascinating progress in the creation and utilization of synthetic gauge fields for charge-neutral ultracold atoms. Whereas the synthesis of gauge fields in itself is readily interesting, it is more exciting to explore the new era that will be brought by the interplay between synthetic gauge fields and many other degrees of freedom of highly tunable ultracold atoms. This topical review surveys recent developments in using synthetic gauge fields to manipulate novel quantum phenomena that are not easy to access in other systems. We first summarize current experimental methods of creating synthetic gauge fields, including the use of Raman schemes, shaken lattices, and Raman-dressed lattices. We then discuss how synthetic gauge fields bring new physics to non-interacting systems, including degenerate single-particle ground states, quartic dispersions, topological band structures in lattices, and synthetic dimensions. As for interacting systems, we focus on novel quantum many-body states and quantum macroscopic phenomena induced by interactions in the presence of unconventional single-particle dispersions. For bosons, we discuss how a quartic dispersion leads to non-condensed bosonic states at low temperatures and at the ground state. For fermions, we discuss chiral superfluids in the presence of attractive s-wave interaction, where high partial-wave interactions are not required. Finally, we discuss the challenges in current experiments, and conclude with an outlook for what new exciting developments synthetic gauge fields may bring us in the near future.
Non-Abelian bosonization as a nonholonomic transformation from a flat to a curved field space
International Nuclear Information System (INIS)
Kleinert, H.
1997-01-01
There exists a simple rule by which path integrals for the motion of a point particle in a flat space can be transformed correctly into those in a curved space. This rule arose from well-established methods in the theory of plastic deformations, where crystals with defects are described mathematically by applying active nonholonomic coordinate transformations to ideal crystals. In the context of time-sliced path integrals, this has given rise to a quantum equivalence principle which determines the short-time action and functional integration measure of fluctuating orbits in spaces with curvature and torsion. The nonholonomic transformations have a nontrivial Jacobian which in curved spaces produces an additional energy proportional to the curvature scalar, thereby canceling an equal term found earlier by DeWitt in his formulation of Feynman close-quote s time-sliced path integral in curved space. The importance of this cancelation has been documented in various systems (H-atom, particle on the surface of a sphere, spinning top). Here we point out its relevance to the bosonization of a non-Abelian one-dimensional quantum field theory, whose fields live in a flat field space. The bosonized version is a quantum-mechanical path integral of a point particle moving in a space with constant curvature. The additional term introduced by the Jacobian is crucial for the identity between original and bosonized theory. A useful bosonization tool is the so-called Hubbard endash Stratonovich formula for which we find a nonabelian version. copyright 1997 Academic Press, Inc
Energy Technology Data Exchange (ETDEWEB)
Smiseth, Jo
2005-07-01
The critical properties of three-dimensional U(1)-symmetric lattice gauge theories have been studied. The models apply to various physical systems such as insulating phases of strongly correlated electron systems as well as superconducting and superfluid states of liquid metallic hydrogen under extreme pressures. The thesis contains an introductory part and a collection of research papers of which seven are published works and one is submitted for publication. The outline of this thesis is as follows. In Chapter 2 the theory of phase transitions is discussed with emphasis on continuous phase transitions, critical phenomena and phase transitions in gauge theories. In the next chapter the phases of the abelian Higgs model are presented, and the critical phenomena are discussed. Furthermore, the multicomponent Ginzburg-Landau theory and the applications to liquid metallic hydrogen are presented. Chapter 4 contains an overview of the Monte Carlo integration scheme, including the Metropolis algorithm, error estimates, and re weighting techniques. This chapter is followed by the papers I-VIII. Paper I: Criticality in the (2+1)-Dimensional Compact Higgs Model and Fractionalized Insulators. Paper II: Phase structure of (2+1)-dimensional compact lattice gauge theories and the transition from Mott insulator to fractionalized insulator. Paper III: Compact U(1) gauge theories in 2+1 dimensions and the physics of low dimensional insulating materials. Paper IV: Phase structure of Abelian Chern-Simons gauge theories. Paper V: Critical Properties of the N-Color London Model. Paper VI: Field- and temperature induced topological phase transitions in the three-dimensional N-component London superconductor. Paper VII: Vortex Sublattice Melting in a Two-Component Superconductor. Paper VIII: Observation of a metallic superfluid in a numerical experiment (ml)
Massive and massless gauge fields of any spin and symmetry
International Nuclear Information System (INIS)
Hussain, F.; Jarvis, P.D.
1988-05-01
An analysis of the BRST approach to massive and massless gauge fields of any spin and symmetry is presented. Previous results on massless gauge fields are extended to totally antisymmetric massless tensors and Kaehler-Dirac particles. Two methods for arriving at a BRST invariant, massive theory from the corresponding massless one are discussed. The first allows for an interpretation in terms of dimensional reduction, while the second keeps the BRST operator of the massless theory, but employs gauge invariant fields. (author). 10 refs
Towards a unified picture for gauge and Higgs fields
International Nuclear Information System (INIS)
Mecklenburg, W.
1981-01-01
A scheme for a geometrical unification of gauge and Higgs fields, previously given for SU 2 , is generalized to include arbitrary semisimple gauge groups. Gauge and physical Higgs fields appear as different components of the same tensor in a high dimensional manifold, the higher dimensions being comprised by the group coordinates. Their respective inhomogeneous transformation behaviour is derived from the same principle. The number of Higgs fields is restricted. The form of the Higgs potential is fixed and the mass of the Higgs particle is predicted in terms of the vector boson mass. (author)
Extended monopoles in gauge field theories
International Nuclear Information System (INIS)
Horvath, Z.; Palla, L.
1977-04-01
The paper gives a review of the 't Hooft monopole and briefly discusses the general topological considerations connected with monopoles. A method is presented for constructing explicit monopole solutions in any gauge theory. Some stability questions and time-dependent problems are also considered
Non-Abelian magnetized blackholes and unstable attractors
International Nuclear Information System (INIS)
Mosaffa, A.E.; Randjbar-Daemi, S.; Sheikh-Jabbari, M.M.
2006-12-01
Fluctuations of non-Abelian gauge fields in a background magnetic flux contain tachyonic modes and hence the background is unstable. We extend these results to the cases where the background flux is coupled to Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of Reissner-Nordstroem blackholes or the AdS 2 x S 2 , are also unstable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes. (author)
Conformal Gauge-Yukawa Theories away From Four Dimensions
DEFF Research Database (Denmark)
Codello, Alessandro; Langaeble, Kasper; Litim, Daniel
2016-01-01
We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD$...
Two-time physics with gravitational and gauge field backgrounds
International Nuclear Information System (INIS)
Bars, Itzhak
2000-01-01
It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d dimensions (one time) can be described in the language of two-time physics in a spacetime with d+2 dimensions. This is obtained by generalizing the world line formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from d+2 dimensions to (d-1)+1 dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target (d+2)-dimensional spacetime. The gravitational background obeys a closed homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher (d+2)-dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden
Gauge fields in algebraically special space-times
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1985-01-01
It is shown that in an algebraically special space-time which admits a congruence of null strings, a source-free gauge field aligned with the congruence is determined by a matrix potential which has to satisfy a second-order differential equation with quadratic nonlinearities. The Einstein--Yang--Mills equations are then reduced to a scalar and two matrix equations. In the case of self-dual gauge fields in a self-dual space-time, the existence of an infinite set of conservation laws, of an associated linear system, and of infinitesimal Baecklund transformations is demonstrated. All the results apply for an arbitrary gauge group
Point-splitting as a regularization method for λφ4-type vertices: Abelian case
International Nuclear Information System (INIS)
Moura-Melo, Winder A.; Helayel Neto, J.A.
1998-11-01
We obtained regularized Abelian Lagrangians containing λφ 4 -type vertices by means of a suitable point-splitting procedure. The calculation is developed in details for a general Lagrangian, whose fields (gauge and matter ones) satisfy certain conditions. We illustrates our results by considering some special cases, such as the Abelian Higgs, the (ψ-barψ) 2 and the Avdeev-Chizov (real rank-2 antisymmetric tensor as matter fields) models. We also discuss some features of the obtained Lagrangian such as the regularity and non-locality of its new integrating terms. Moreover, the resolution of the Abelian case may teach us some useful technical aspects when dealing with the non-Abelian one. (author)
Non-Abelian color dielectric - towards the effective model of the low energy QCD
International Nuclear Information System (INIS)
Wereszczynski, A.; Slusarczyk, M.
2005-01-01
Lattice motivated triplet color scalar field theory is analyzed. We consider non-minimal as well as covariant derivative coupling with SU(2) gauge fields. Field configurations generated by external electric sources are presented. Moreover non-Abelian magnetic monopoles are found. Dependence on the spatial coordinates in the obtained solutions is identical as in the usual Abelian case. We show also that after a decomposition of the fields a modified Faddeev-Niemi action can be obtained. It contains explicit O(3) symmetry breaking term parameterized by the condensate of an isoscalar field. Due to that Goldstone bosons observed in the original Faddeev-Niemi model are removed. (orig.)
Dual geometric-gauge field aspects of gravity
International Nuclear Information System (INIS)
Huei Peng; Wang, K.
1992-01-01
We propose that the geometric and standard gauge field aspects of gravity are equally essential for a complete description of gravity and can be reconciled. We show that this dualism of gravity resolves the dimensional Newtonian constant problem in both quantum gravity and unification schemes involving gravity (i.e., the Newtonian constant is no longer the coupling constant in the gauge aspect of gravity) and reveals the profound similarity between gravity and other fields. 23 refs., 3 tabs
On quantization of the electromagnetic field in radiation gauge
International Nuclear Information System (INIS)
Burzynski, A.
1982-01-01
This paper contains a detailed description of quantization of the electromagnetic field (in radiation gauge) and quantization of some basic physical variables connected with radiation field as energy, momentum and spin. The dynamics of the free quantum radiation field and the field interacting with external classical sources is described. The canonical formalism is not used explicity. (author)
Near-field photon wave mechanics in the Lorenz gauge
International Nuclear Information System (INIS)
Keller, Ole
2007-01-01
Optical near-field interactions are studied theoretically in the perspective of photon wave mechanics paying particular attention to the dynamics in the wave-vector time domain. A unitary transformation is used to replace the scalar and longitudinal photon variables by so-called near-field and gauge photon variables. Dynamical equations are established for these types of photon variables, and it is shown that these equations are invariant against gauge transformations within the Lorenz gauge. The near-field photon is absent in the free-field limit, and the gauge photon can be eliminated by a suitable gauge transformation. Implicit solutions for the near-field, gauge, and transverse photon variables are obtained and discussed. The general theory is applied to an investigation of transverse photon propagation in a uniform solid-state plasma dominated by the diamagnetic field-matter interaction. It is found that the diamagnetic response can be incorporated in a quantum mechanical wave equation for a massive transverse photon. The Compton wave number of the massive photon equals the plasma wave number of the electron system. A dynamical equation describing the emission of a massive transverse photon from a mesoscopic source embedded in the plasma is finally established
Colour magnetic currents and the dual London equation in SU(3) lattice gauge theory
International Nuclear Information System (INIS)
Skala, P.; Faber, M.; Zach, M.
1997-01-01
We propose a method for the determination of magnetic currents in non-Abelian gauge theories which does not need a projection to Abelian degrees of freedom. With this definition we are able to determine the distribution of magnetic currents and electric fields for the gluonic flux tube between a pair of static charges. Further we check the validity of the Gauss law and the dual London equation in a gauge-invariant formulation. (orig.)
Magnetic Monopoles and the Dual London Equation in SU(3) Lattice Gauge Theory
Skala, Peter; Faber, Manfried; Zach, Martin
1996-01-01
We propose a method for the determination of magnetic monopole currents in non-Abelian gauge theories which does not need a projection to Abelian degrees of freedom. With this definition we are able to determine the distribution of magnetic currents and electric fields for the gluonic flux tube between a pair of static charges. Further we check the validity of the Gauss law and the dual London equation in a gauge invariant formulation.
Remarks on an equation common to Weyl's gauge field, Yang-Mills field and Toda lattice
International Nuclear Information System (INIS)
Nishioka, M.
1984-01-01
In this letter a remark is presented on an equation of a gauge-invariant Weyl's gauge field and it is shown that the equation is common to Yang's approach to the self-duality condition for SU 2 gauge field and the simplest Toda lattice
Hyperunified field theory and gravitational gauge-geometry duality
International Nuclear Information System (INIS)
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Energy Technology Data Exchange (ETDEWEB)
Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)
2018-01-15
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)
Hyperunified field theory and gravitational gauge-geometry duality
Wu, Yue-Liang
2018-01-01
A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.
On whole Abelian model dynamics
Energy Technology Data Exchange (ETDEWEB)
Chauca, J.; Doria, R. [CBPF, Rio de Janeiro (Brazil); Aprendanet, Petropolis, 25600 (Brazil)
2012-09-24
Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics oriented through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.
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...
New features of the maximal abelian projection
International Nuclear Information System (INIS)
Bornyakov, V.G.; Polikarpov, M.I.; Syritsyn, S.N.; Schierholz, G.; Suzuki, T.
2005-12-01
After fixing the Maximal Abelian gauge in SU(2) lattice gauge theory we decompose the nonabelian gauge field into the so called monopole field and the modified nonabelian field with monopoles removed. We then calculate respective static potentials and find that the potential due to the modified nonabelian field is nonconfining while, as is well known, the monopole field potential is linear. Furthermore, we show that the sum of these potentials approximates the nonabelian static potential with 5% or higher precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the modified nonabelian field potential describes the string fluctuations. Similar decomposition was observed to work for the adjoint static potential. A check was also made of the center projection in the direct center gauge. Two static potentials, determined by projected Z 2 and by modified nonabelian field without Z 2 component were calculated. It was found that their sum is a substantially worse approximation of the SU(2) static potential than that found in the monopole case. It is further demonstrated that similar decomposition can be made for the flux tube action/energy density. (orig.)
Meta fluid dynamic as a gauge field theory
International Nuclear Information System (INIS)
Mendes, A.C.R.; Neves, C.; Oliveira, W.; Takakura, F.I.
2003-01-01
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the meta fluid dynamics, is extended in order to reformulate the meta fluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the meta fluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed. (author)
Inflationary dynamics of kinetically-coupled gauge fields
DEFF Research Database (Denmark)
Ferreira, Ricardo J. Z.; Ganc, Jonathan
2015-01-01
We investigate the inflationary dynamics of two kinetically-coupled massless U(1) gauge fields with time-varying kinetic-term coefficients. Ensuring that the system does not have strongly coupled regimes shrinks the parameter space. Also, we further restrict ourselves to systems that can be quant......We investigate the inflationary dynamics of two kinetically-coupled massless U(1) gauge fields with time-varying kinetic-term coefficients. Ensuring that the system does not have strongly coupled regimes shrinks the parameter space. Also, we further restrict ourselves to systems that can...... be quantized using the standard creation, annihilation operator algebra. This second constraint limits us to scenarios where the system can be diagonalized into the sum of two decoupled, massless, vector fields with a varying kinetic-term coefficient. Such a system might be interesting for magnetogenesis...... because of how the strong coupling problem generalizes. We explore this idea by assuming that one of the gauge fields is the Standard Model U(1) field and that the other dark gauge field has no particles charged under its gauge group. We consider whether it would be possible to transfer a magnetic field...
Interaction of orientable object fields with gauge fields
International Nuclear Information System (INIS)
Gitman, D M; Shelepin, A L
2011-01-01
We consider a scalar field f(g) on the Poincaré group M(3, 1). This scalar field describes objects that are characterized by a position x and an orientation z, g=(x,z). The field f(x, z) admits two kinds of transformations, corresponding to a change of the space-fixed reference frame, as well as to a change of the body-fixed reference frame, which form the group M(3, 1) ext ×M(3, 1) int , and also phase transformations U(1) ch of orientational variables z. Elementary particles considered as elementary orientable objects are described by the scalar functions transforming according to irreps of the group M(3, 1) ext ×M(3, 1) int ×U(1) ch . Correspondingly, their continuous symmetries can be divided into external, which form the Poincaré group M(3, 1) ext , and internal M(3, 1) int ×U(1) ch . The assumption that the internal symmetries in the theory of orientable objects are gauge ones allows one to obtain important features of the known fundamental interactions—the electroweak and the gravitational. Localization of the group of the right translations T(4) int leads to the teleparallel theory of gravity, which is equivalent to general relativity. Localization of the compact subgroup SU(2) int ×U(1) ch leads to the theory of electroweak interactions. Thus, the suggested approach can be considered as a possible way to gravitational-electroweak unification.
Gauge field propagator and the number of fermion fields
International Nuclear Information System (INIS)
Oehme, R.; Zimmermann, W.
1980-01-01
The structure of the transverse gluon propagator D of massless quantum chromodynamics is considered in the Landau gauge. The essential differences in the weak-coupling limit g → 0 for γ 0 /β 0 >0 and γ 0 /β 0 0 and β 0 are coefficients of lowest-order terms of the anomalous dimension and of the β function. For SU(3) as the color group and quark triplets, the corresponding flavor conditions are N/sub F/ 0 /β 0 >0 there are inconsistencies with the postulates of local quantum field theory and the requirement that the positive-norm contribution D/sub +/ to D should approach its free-field value for g → 0. In the present paper, it is investigated in detail how this requirement is violated assuming that the other postulates hold, including invariance under the renormalization group. Using a specific, simple projection into a subspace of positive norm, it is shown that D/sub +/ diverges like (g 2 )/sup -gamma/0/sup /beta/0, while the free-field value and higher-order terms of D are entirely due to contributions from negative-norm states. In contradistinction, the required dominance of positive-norm states in the weak-coupling limit prevails for γ 0 /β 0 2 → 0
Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics
1975-03-01
General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.
Multigrid Methods for the Computation of Propagators in Gauge Fields
Kalkreuter, Thomas
Multigrid methods were invented for the solution of discretized partial differential equations in order to overcome the slowness of traditional algorithms by updates on various length scales. In the present work generalizations of multigrid methods for propagators in gauge fields are investigated. Gauge fields are incorporated in algorithms in a covariant way. The kernel C of the restriction operator which averages from one grid to the next coarser grid is defined by projection on the ground-state of a local Hamiltonian. The idea behind this definition is that the appropriate notion of smoothness depends on the dynamics. The ground-state projection choice of C can be used in arbitrary dimension and for arbitrary gauge group. We discuss proper averaging operations for bosons and for staggered fermions. The kernels C can also be used in multigrid Monte Carlo simulations, and for the definition of block spins and blocked gauge fields in Monte Carlo renormalization group studies. Actual numerical computations are performed in four-dimensional SU(2) gauge fields. We prove that our proposals for block spins are “good”, using renormalization group arguments. A central result is that the multigrid method works in arbitrarily disordered gauge fields, in principle. It is proved that computations of propagators in gauge fields without critical slowing down are possible when one uses an ideal interpolation kernel. Unfortunately, the idealized algorithm is not practical, but it was important to answer questions of principle. Practical methods are able to outperform the conjugate gradient algorithm in case of bosons. The case of staggered fermions is harder. Multigrid methods give considerable speed-ups compared to conventional relaxation algorithms, but on lattices up to 184 conjugate gradient is superior.
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
New scheme for color confinement and violation of the non-Abelian Bianchi identities
Suzuki, Tsuneo; Ishiguro, Katsuya; Bornyakov, Vitaly
2018-02-01
A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities is proposed. The violation of the non-Abelian Bianchi identities (VNABI) Jμ is equal to Abelian-like monopole currents kμ defined by the violation of the Abelian-like Bianchi identities. Although VNABI is an adjoint operator satisfying the covariant conservation law DμJμ=0 , it satisfies, at the same time, the Abelian-like conservation law ∂μJμ=0 . The Abelian-like conservation law ∂μJμ=0 is also gauge-covariant. There are N2-1 conserved magnetic charges in the case of color S U (N ). The charge of each component of VNABI is quantized à la Dirac. The color-invariant eigenvalues λμ of VNABI also satisfy the Abelian conservation law ∂μλμ=0 and the magnetic charges of the eigenvalues are also quantized à la Dirac. If the color invariant eigenvalues condense in the QCD vacuum, each color component of the non-Abelian electric field Ea is squeezed by the corresponding color component of the solenoidal current Jμa. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. This confinement picture is completely new in comparison with the previously studied monopole confinement scenario based on an Abelian projection after some partial gauge-fixing, where Abelian neutral states can survive as physical. To check if the scenario is realized in nature, numerical studies are done in the framework of lattice field theory by adopting pure S U (2 ) gauge theory for simplicity. Considering Jμ(x )=kμ(x ) in the continuum formulation, we adopt an Abelian-like definition of a monopole following DeGrand-Toussaint as a lattice version of VNABI, since the Dirac quantization condition of the magnetic charge is satisfied on lattice partially. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum. Smooth gauge fixings such as the maximal center gauge (MCG), block
Fermion number non-conservation and cold neutral fermionic matter in (V-A) gauge theories
International Nuclear Information System (INIS)
Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Tokarev, V.F.
1987-01-01
It is shown that in four-dimensional abelian (V-A) theories, the ground state of cold neutral fermionic matter is an anomalous state containing domains of abnormal phase surrounded by the normal vacuum. Inside these domains, there exists a gauge field condensate which makes real fermions disappear both inside and outside the domains. In non-abelian theories, the abnormal matter is unstable in its turn, and the system rolls back down into the normal state with a small number of fermions above the topologically non-trivial vacuum. Thus, in several non-abelian gauge theories, the fermion number density of cold neutral matter cannot exceed some critical value. (orig.)
Massive propagators in instanton fields
International Nuclear Information System (INIS)
Brown, L.S.; Lee, C.
1978-01-01
Green's functions for massive spinor and vector particles propagating in a self-dual but otherwise arbitrary non-Abelian gauge field are shown to be completely determined by the corresponding Green's functions of massive scalar particles
Dynamics of Gauge Fields at High Temperature
Nauta, B.J.
2000-01-01
An effective description of dynamical Bose fields is provided by the classical (high-temperature) limit of thermal field theory. The main subject of this thesis is to improve the ensuing classical field theory, that is, to include the dominant quantum corrections and to add counter terms for the
Non-uniqueness of the source for singular gauge fields
International Nuclear Information System (INIS)
Lanyi, G.; Pappas, R.
1977-01-01
It is shown that the singular Wu-Yang solution for SU(2) gauge fields may be interpreted as due to a point source at the origin. However, the electric or magnetic nature of the source depends on whether one approaches the singularity by means of a 'smeared' potential or a 'smeared' field strength. (Auth.)
Hotplate precipitation gauge calibrations and field measurements
Zelasko, Nicholas; Wettlaufer, Adam; Borkhuu, Bujidmaa; Burkhart, Matthew; Campbell, Leah S.; Steenburgh, W. James; Snider, Jefferson R.
2018-01-01
First introduced in 2003, approximately 70 Yankee Environmental Systems (YES) hotplate precipitation gauges have been purchased by researchers and operational meteorologists. A version of the YES hotplate is described in Rasmussen et al. (2011; R11). Presented here is testing of a newer version of the hotplate; this device is equipped with longwave and shortwave radiation sensors. Hotplate surface temperature, coefficients describing natural and forced convective sensible energy transfer, and radiative properties (longwave emissivity and shortwave reflectance) are reported for two of the new-version YES hotplates. These parameters are applied in a new algorithm and are used to derive liquid-equivalent accumulations (snowfall and rainfall), and these accumulations are compared to values derived by the internal algorithm used in the YES hotplates (hotplate-derived accumulations). In contrast with R11, the new algorithm accounts for radiative terms in a hotplate's energy budget, applies an energy conversion factor which does not differ from a theoretical energy conversion factor, and applies a surface area that is correct for the YES hotplate. Radiative effects are shown to be relatively unimportant for the precipitation events analyzed. In addition, this work documents a 10 % difference between the hotplate-derived and new-algorithm-derived accumulations. This difference seems consistent with R11's application of a hotplate surface area that deviates from the actual surface area of the YES hotplate and with R11's recommendation for an energy conversion factor that differs from that calculated using thermodynamic theory.
Anomalous gauge theories revisited
International Nuclear Information System (INIS)
Matsui, Kosuke; Suzuki, Hiroshi
2005-01-01
A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact U(1) link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear. (author)
Abelian versus non-abelian Higgs model in three dimensions
International Nuclear Information System (INIS)
Buchmueller, W.; Philipsen, O.
1995-04-01
We study the phase structure of the abelian Higgs model in three dimensions based on perturbation theory and a set of gauge independent gap equations for Higgs boson and vector boson masses. Contrary to the non-abelian Higgs model, the vector boson mass vanishes in the symmetric phase. In the Higgs phase the gap equations yield masses consistent with perturbation theory. The phase transition is first-order for small values of the scalar self-coupling λ, where the employed loop expansion is applicable. (orig.)
Gibbs perturbations of a two-dimensional gauge field
International Nuclear Information System (INIS)
Petrova, E.N.
1981-01-01
Small Gibbs perturbations of random fields have been investigated up to now for a few initial fields only. Among them there are independent fields, Gaussian fields and some others. The possibility for the investigation of Gibbs modifications of a random field depends essentially on the existence of good estimates for semiinvariants of this field. This is the reason why the class of random fields for which the investigation of Gibbs perturbations with arbitrary potential of bounded support is possible is rather small. The author takes as initial a well-known model: a two-dimensional gauge field. (Auth.)
Local gauge invariant Lagrangeans in classical field theories
International Nuclear Information System (INIS)
Grigore, D.R.
1982-07-01
We investigate the most general local gauge invariant Lagrangean in the framework of classical field theory. We rederive esentially Utiyama's result with a slight generalization. Our proof makes clear the importance of the so called current conditions, i.e. the requirement that the Noether currents are different from zero. This condition is of importance both in the general motivation for the introduction of the Yang-Mills fields and for the actual proof. Some comments are made about the basic mathematical structure of the problem - the gauge group. (author)
Lattice formulations of supersymmetric gauge theories with matter fields
International Nuclear Information System (INIS)
Joseph, Anosh
2014-12-01
Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.
Gauge-independent decoherence models for solids in external fields
Wismer, Michael S.; Yakovlev, Vladislav S.
2018-04-01
We demonstrate gauge-invariant modeling of an open system of electrons in a periodic potential interacting with an optical field. For this purpose, we adapt the covariant derivative to the case of mixed states and put forward a decoherence model that has simple analytical forms in the length and velocity gauges. We demonstrate our methods by calculating harmonic spectra in the strong-field regime and numerically verifying the equivalence of the deterministic master equation to the stochastic Monte Carlo wave-function method.
International Nuclear Information System (INIS)
Nguyen Quoc Thang
2006-12-01
We prove some new results on Corestriction principle for non-abelian cohomology of group schemes over the rings of integers of local and global fields. Some connections with Grothendieck - Serre's conjecture are indicated, and applications to the study of class groups of algebraic groups over global fields are given. (author)
Wormholes, emergent gauge fields, and the weak gravity conjecture
Energy Technology Data Exchange (ETDEWEB)
Harlow, Daniel [Center for the Fundamental Laws of Nature, Physics Department, Harvard University,Cambridge MA, 02138 (United States)
2016-01-20
This paper revisits the question of reconstructing bulk gauge fields as boundary operators in AdS/CFT. In the presence of the wormhole dual to the thermofield double state of two CFTs, the existence of bulk gauge fields is in some tension with the microscopic tensor factorization of the Hilbert space. I explain how this tension can be resolved by splitting the gauge field into charged constituents, and I argue that this leads to a new argument for the “principle of completeness”, which states that the charge lattice of a gauge theory coupled to gravity must be fully populated. I also claim that it leads to a new motivation for (and a clarification of) the “weak gravity conjecture”, which I interpret as a strengthening of this principle. This setup gives a simple example of a situation where describing low-energy bulk physics in CFT language requires knowledge of high-energy bulk physics. This contradicts to some extent the notion of “effective conformal field theory”, but in fact is an expected feature of the resolution of the black hole information problem. An analogous factorization issue exists also for the gravitational field, and I comment on several of its implications for reconstructing black hole interiors and the emergence of spacetime more generally.
Determining and uniformly estimating the gauge potential corresponding to a given gauge field on M4
International Nuclear Information System (INIS)
Mostow, M.; Shnider, S.; Ben-Gurion Univ. of the Negev, Beersheba
1986-01-01
In an earlier paper on the field copy problem, we proved that there exists a generic set of connections (gauge potentials) on a principle bundle with a semi-simple structure group over a four-dimensional base manifold for which the connection is uniquely determined by its curvature (gauge field). We conjectured that there exists a smaller, but still generic, set of connections for which the curvature map sending a connection to its curvature admits a continuous inverse with respect to the appropriate function space topologies. The conjecture says, in other words, that restricting to certain generic curvature 2-forms, one can determine and uniformly estimate the connection and its derivatives from the curvature and uniform estimates of its derivatives. In this Letter we give an affirmative answer to the conjecture and show, moreover, that the set of such connections contains an open dense set in the Whitney C ∞ topology. (orig.)
Nonabelian Gauged Linear Sigma Model
Institute of Scientific and Technical Information of China (English)
Yongbin RUAN
2017-01-01
The gauged linear sigma model (GLSM for short) is a 2d quantum field theory introduced by Witten twenty years ago.Since then,it has been investigated extensively in physics by Hori and others.Recently,an algebro-geometric theory (for both abelian and nonabelian GLSMs) was developed by the author and his collaborators so that he can start to rigorously compute its invariants and check against physical predications.The abelian GLSM was relatively better understood and is the focus of current mathematical investigation.In this article,the author would like to look over the horizon and consider the nonabelian GLSM.The nonabelian case possesses some new features unavailable to the abelian GLSM.To aid the future mathematical development,the author surveys some of the key problems inspired by physics in the nonabelian GLSM.
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
Operation of cold-cathode gauges in high magnetic fields
International Nuclear Information System (INIS)
Thomas, S.R. Jr.; Goerz, D.A.; Pickles, W.L.
1985-01-01
The Mirror Fusion Test Facility (MFTF-B), under construction at LLNL, requires measurement of the neutral gas density in high magnetic fields near the plasma at several axial regions. This Background Gas Pressure (BGP) diagnostic will help us understand the role of background neutrals in particle and power balance, particularly in the maintenance of the cold halo plasma that shields the hot core plasma from the returning neutrals. It consists of several cold-cathode, magnetron-type gauges stripped of their permanent magnets, and utilizes the MFTF-B ambient B-field in strengths of 5 to 25 kG. Similar gauges have operated in TMX-U in B-fields up to 3 kG. To determine how well the gauges will perform, we assembled a test stand which operated magnetron gauges in an external, uniform magnetic field of up to 30 kG, over a pressure range of 1E-8 T to 1E-5 T, at several cathode voltages. This paper describes the test stand and presents the results of the tests
Gauge field back reaction on a black hole
International Nuclear Information System (INIS)
Hochberg, D.; Kephart, T.W.
1993-01-01
The order-ℎ fluctuations of gauge fields in the vicinity of a black hole can create a repulsive antigravity region extending out beyond the renormalized Schwarzschild horizon. If the strength of this repulsive force increases as higher orders in the back reaction are included, the formation of a wormholelike object could occur
Gauge field governing parallel transport along mixed states
International Nuclear Information System (INIS)
Uhlmann, A.
1990-01-01
At first a short account is given of some basic notations and results on parallel transport along mixed states. A new connection form (gauge field) is introduced to give a geometric meaning to the concept of parallelity in the theory of density operators. (Author) 11 refs
Gauge/string duality in confining theories
International Nuclear Information System (INIS)
Edelstein, J.D.; Portugues, R.
2006-01-01
This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Gauge/string duality in confining theories
Energy Technology Data Exchange (ETDEWEB)
Edelstein, J.D. [Departamento de Fi sica de Particulas, Universidade de Santiago de Compostela and Instituto Galego de Fisica de Altas Enerxias (IGFAE), 15782 Santiago de Compostela (Spain); Instituto de Fisica de La Plata (IFLP), Universidad Nacional de La Plata, La Plata (Argentina); Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile); Portugues, R. [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
2006-07-03
This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
On classical solutions of SU(3) gauge field equations
International Nuclear Information System (INIS)
Chakrabarti, A.
1975-01-01
Static classical solutions of SU(3) gauge field equations are studied. The roles of the O(3) subgroup and of the quadrupole generators are discussed systematically. The general form thus obtained leads, through-out, to a high degree of symmetry in the results. This brings in some simplifying features. An octet of scalar mesons is finally added. Certain classes of exact solutions are given that are singular at the origin. A generalized gauge condition is pointed out. The relation of the general form to known particular cases is discussed [fr
Lawther, R
2018-01-01
In this work the author lets \\Phi be an irreducible root system, with Coxeter group W. He considers subsets of \\Phi which are abelian, meaning that no two roots in the set have sum in \\Phi \\cup \\{ 0 \\}. He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to the action of W: for each W-orbit of maximal abelian sets we provide an explicit representative X, identify the (setwise) stabilizer W_X of X in W, and decompose X into W_X-orbits. Abelian sets of roots are closely related to abelian unipotent subgroups of simple algebraic groups, and thus to abelian p-subgroups of finite groups of Lie type over fields of characteristic p. Parts of the work presented here have been used to confirm the p-rank of E_8(p^n), and (somewhat unexpectedly) to obtain for the first time the 2-ranks of the Monster and Baby Monster sporadic groups, together with the double cover of the latter. Root systems of classical type are dealt with quickly here; the vast majority of the present work con...
Interplay between topology, gauge fields and gravity
Corichi Rodriguez Gil, Alejandro
In this thesis we consider several physical systems that illustrate an interesting interplay between quantum theory, connections and knot theory. It can be divided into two parts. In the first one, we consider the quantization of the free Maxwell field. We show that there is an important role played by knot theory, and in particular the Gauss linking number, in the quantum theory. This manifestation is twofold. The first occurs at the level of the algebra of observables given by fluxes of electric and magnetic field across surfaces. The commutator of the operators, and thus the basic uncertainty relations, are given in terms of the linking number of the loops that bound the surfaces. Next, we consider the quantization of the Maxwell field based on self-dual connections in the loop representation. We show that the measure which determines the quantum inner product can be expressed in terms of the self linking number of thickened loops. Therefore, the linking number manifests itself at two key points of the theory: the Heisenberg uncertainty principle and the inner product. In the second part, we bring gravity into play. First we consider quantum test particles on certain stationary space-times. We demonstrate that a geometric phase exists for those space-times and focus on the example of a rotating cosmic string. The geometric phase can be explicitly computed, providing a fully relativistic gravitational Aharonov-Bohm effect. Finally, we consider 3-dimensional gravity with non-vanishing cosmological constant in the connection dynamics formulation. We restrict our attention to Lorentzian gravity with positive cosmological constant and Euclidean signature with negative cosmological constant. A complex transformation is performed in phase space that makes the constraints simple. The reduced phase space is characterized as the moduli space of flat complex connections. We construct the quantization of the theory when the initial hyper-surface is a torus. Two important
Measurement of gravity and gauge fields using quantum mechanical probes
International Nuclear Information System (INIS)
Anandan, J.
1986-01-01
The author considers the question of which quantities are observed when the gravitational and gauge fields are measured by a quantum mechanical probe. The motion of a quantum mechanical particle can be constructed, via Huyghens' principle, by the interference of secondary wavelets. Three types of interference phenomena are considered: interference of two coherent beams separated in space-time during part of their motion; interference of two coherent beams which are in the same region in spacetime but differ in energy or mass; and the Josphson effect and its generalization. The author shows how to determine the gravitational field by means of quantum interference. The corresponding problem for gauge fields is treated and a simple proof of the previously proved theorem for the reconstruction of the connection from the holonomy transformations is presented. A heuristic principle for the gravitational interaction of two quantum mechanical particles is formulated which implies the equivalence of inertial and active gravitational masses
Strong coupling in a gauge invariant field theory
Energy Technology Data Exchange (ETDEWEB)
Johnson, K. [Physics Department, Massachusetts Institute of Technology, Cambridge, MA (United States)
1963-01-15
I would like to discuss some approximations which may be significant in the domain of strong coupling in a field system analogous to quantum electrodynamics. The motivation of this work is the idea that the strong couplings and elementary particle spectrum may be the consequence of the dynamics of a system whose underlying description is in terms of a set of Fermi fields gauge invariantly coupled to a single (''bare'') massless neutral vector field. The basis of this gauge invariance would of course be the exact conservation law of baryons or ''nucleonic charge''. It seems to me that a coupling scheme based on an invariance principle is most attractive if that invariance is an exact one. It would then be nice to try to account for the approximate invariance principles in the same way one would describe ''accidental degeneracies'' in any quantum system.
Broken Weyl symmetry. [Gauge model, coupling, Higgs field
Energy Technology Data Exchange (ETDEWEB)
Domokos, G.
1976-05-01
It is argued that conformal symmetry can be properly understood in the framework of field theories in curved space. In such theories, invariance is required under general coordinate transformations and conformal rescalings. A gauge model coupled to a Higgs field is examined. In the tree approximation, the vacuum solution exhibits two Higgs phenomena; both the phase (Goldstone boson) and the coordinate dependent part of the radial component of the scalar field can be removed by a Higgs-Kibble transformation. The resulting vacuum solution corresponds to a space of constant curvature and constant vacuum expectation value of the scalar field.
A gauge quantum field theory of confined quarks and gluons
International Nuclear Information System (INIS)
Voelkel, A.H.
1983-01-01
A SU(3)-gauge quantum field theory with a quark triplet, an antiquark triplet and a self-conjugate gluon octet as basic fields is investigated. In virtue of a non trivial coupling between the representation of the translation group and the SU(3)-colour charge of the basic fields it is proved: (i) The basic quark, antiquark and gluon fields are confined. (ii) Every statevector of the physical Hilbert space is a SU(3)-colour singlet state. (iii) Poincare invariance holds in the physical Hilbert space. (orig.)
Hamiltonian formulation of QCD in the Schwinger gauge
International Nuclear Information System (INIS)
Schutte, D.
1989-01-01
The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed
The extended local gauge invariance and the BRS symmetry in stochastic quantization of gauge fields
International Nuclear Information System (INIS)
Nakazawa, Naohito.
1989-05-01
We investigate the BRS invariance of the first-class constrained systems in the context of the stochastic quantization. For the first-class constrained systems, we construct the nilpotent BRS transformation and the BRS invariant stochastic effective action based on the D+1 dimensional field theoretical formulation of stochastic quantization. By eliminating the multiplier field of the gauge fixing condition and an auxiliary field, it is shown that there exists a truncated BRS transformation which satisfies the nilpotency condition. The truncated BRS invariant stochastic action is also derived. As the examples of the general formulation, we investigate the BRS invariant structure in the massless and massive Yang-Mills fields in stochastic quantization. (author)
Duality transformations for general abelian systems
International Nuclear Information System (INIS)
Savit, R.
1982-01-01
We describe the general structure of duality transformations for a very broad set of abelian statistical and field theoretic systems. This includes theories with many different types of fields and a large variety of kinds of interactions including, but not limited to nearest neighbor, next nearest neighbor, multi-spin interactions, etc. We find that the dual form of a theory does not depend directly on the dimensionality of the theory, but rather on the number of fields and number of different kinds of interactions. The dual forms we find have a generalized gauge symmetry and posses the usual property of having a temperature (or coupling constant) which is inverted from that of the original theory. Our results reduce to the well-known results in those particular cases that have heretofore been studied. Our procedure also suggests variations capable of generating other forms of the dual theory which may be useful in various specific cases. (orig.)
Enhanced gauge symmetry and winding modes in double field theory
Energy Technology Data Exchange (ETDEWEB)
Aldazabal, G. [Centro Atómico Bariloche,8400 S.C. de Bariloche (Argentina); Instituto Balseiro (CNEA-UNC) and CONICET,8400 S.C. de Bariloche (Argentina); Graña, M. [Institut de Physique Théorique, CEA/ Saclay,91191 Gif-sur-Yvette Cedex (France); Iguri, S. [Instituto de Astronomía y Física del Espacio (CONICET-UBA), Universidad de Buenos Aires,1428 Buenos Aires (Argentina); Mayo, M. [Centro Atómico Bariloche,8400 S.C. de Bariloche (Argentina); Instituto Balseiro (CNEA-UNC) and CONICET,8400 S.C. de Bariloche (Argentina); Nuñez, C. [Instituto de Astronomía y Física del Espacio (CONICET-UBA), Universidad de Buenos Aires,1428 Buenos Aires (Argentina); Departamento de Física, FCEN, Universidad de Buenos Aires,C.C. 67 - Suc. 28, 1428 Buenos Aires (Argentina); Rosabal, J.A. [Departamento de Física, FCEN, Universidad de Buenos Aires,C.C. 67 - Suc. 28, 1428 Buenos Aires (Argentina)
2016-03-15
We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1)×U(1) symmetry to SU(2)×SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with ((O(d+3,d+3))/(O(d+3)×O(d+3))) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.
Fuchs, László
2015-01-01
Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of undecidability problems. The treatment of the latter trend includes Shelah’s seminal work on the undecidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups, and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, th...
Polarization-dependent optics using gauge-field metamaterials
International Nuclear Information System (INIS)
Liu, Fu; Xiao, Shiyi; Li, Jensen; Wang, Saisai; Hang, Zhi Hong
2015-01-01
We show that effective gauge field for photons with polarization-split dispersion surfaces, being realized using uniaxial metamaterials, can be used for polarization control with unique opportunities. The metamaterials with the proposed gauge field correspond to a special choice of eigenpolarizations on the Poincaré sphere as pseudo-spins, in contrary to those from either conventional birefringent crystals or optical active media. It gives rise to all-angle polarization control and a generic route to manipulate photon trajectories or polarizations in the pseudo-spin domain. As demonstrations, we show beam splitting (birefringent polarizer), all-angle polarization control, unidirectional polarization filter, and interferometer as various polarization control devices in the pseudo-spin domain. We expect that more polarization-dependent devices can be designed under the same framework
Symmetry breaking by Wilson loops in gauge field theory
International Nuclear Information System (INIS)
Dowker, J.S.; Jadhav, S.P.
1989-01-01
An analysis is presented of the gauge symmetry breaking caused by Wilson loops on a space-time whose spatial section is openR/sup d/ x S 3 /Γ, for all those fundamental groups Γ that give a homogeneous space. We concentrate on pure SU(3) and SU(5) gauge field theories and find that symmetry breaking can occur when d = 0, for all Γ. If d = 3, the extra minimal scalars prevent any breaking and one must include other fields to achieve this. Explicit forms for the vacuum energies are exhibited in the case of lens and prism spaces, the former for SU(n). For Γ = Z/sub m/, when m and the radius of the sphere become infinite, we recover the results on the space-time openR/sup d//sup +3/ x S 1
Light cone sum rules in nonabelian gauge field theory
Energy Technology Data Exchange (ETDEWEB)
Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik
1981-03-24
The author examines, in the context of nonabelian gauge field theory, the derivation of the light cone sum rules which were obtained earlier on the assumption of dominance of canonical singularity in the current commutator on the light cone. The retarded scaling functions appearing in the sum rules are numbers known in terms of the charges of the quarks and the number of quarks and gluons in the theory. Possible applications of the sum rules are suggested.
Gauge field geometry from complex and harmonic analyticities
International Nuclear Information System (INIS)
Gal'perin, A.S.; Ivanov, E.A.; Ogievetsky, V.I.; Sokatchev, E.
1987-01-01
The analyticity preservation principle is employed to demonstrate and impressive affinity between field theories with intrinsic analytic structure and superfield gauge theories. The defining constraints of the former theories are interpreted as the integrability conditions for the existence of appropriate analytic subspaces and are solved by passing to the basis with manifest analyticity. We prefer to work within the analytic basis. This allows, e.g., to replace the nonlinear splitting problem of twistor approach by solving a linear equation
Yang-Mills-Vlasov system in the temporal gauge
International Nuclear Information System (INIS)
Choquet-Bruhat, Y.; Noutchegueme, N.
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction [fr
Henneaux, Marc; Vasiliev, Mikhail A
2017-01-01
Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at an international workshop in Singapore in November 2015 where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories i...
On discrete symmetries for a whole Abelian model
International Nuclear Information System (INIS)
Chauca, J.; Doria, R.
2012-01-01
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {D μ ,X i μ } and the physical basis {G μI }. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {G μI } manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.
Gauge transformations with fractional winding numbers
International Nuclear Information System (INIS)
Abouelsaood, A.
1996-01-01
The role which gauge transformations of noninteger winding numbers might play in non-Abelian gauge theories is studied. The phase factor acquired by the semiclassical physical states in an arbitrary background gauge field when they undergo a gauge transformation of an arbitrary real winding number is calculated in the path integral formalism assuming that a θFF term added to the Lagrangian plays the same role as in the case of integer winding numbers. Requiring that these states provide a representation of the group of open-quote open-quote large close-quote close-quote gauge transformations, a condition on the allowed backgrounds is obtained. It is shown that this representability condition is only satisfied in the monopole sector of a spontaneously broken gauge theory, but not in the vacuum sector of an unbroken or a spontaneously broken non-Abelian gauge theory. It is further shown that the recent proof of the vanishing of the θ parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed because certain gauge transformations needed for the proof, and whose existence is assumed, are either spontaneously broken or cannot be globally defined as a result of a topological obstruction. copyright 1996 The American Physical Society
Introduction to Abelian varieties
Murty, V Kumar
1993-01-01
The book represents an introduction to the theory of abelian varieties with a view to arithmetic. The aim is to introduce some of the basics of the theory as well as some recent arithmetic applications to graduate students and researchers in other fields. The first part contains proofs of the Abel-Jacobi theorem, Riemann's relations and the Lefschetz theorem on projective embeddings over the complex numbers in the spirit of S. Lang's book Introduction to algebraic and abelian functions. Then the Jacobians of Fermat curves as well as some modular curves are discussed. Finally, as an application, Faltings' proof of the Mordell conjecture and its intermediate steps, the Tate conjecture and the Shafarevich conjecture, are sketched. - H. Lange for MathSciNet.
Domaratzki, Michael; Rampersad, Narad
2011-01-01
We investigate Abelian primitive words, which are words that are not Abelian powers. We show that unlike classical primitive words, the set of Abelian primitive words is not context-free. We can determine whether a word is Abelian primitive in linear time. Also different from classical primitive words, we find that a word may have more than one Abelian root. We also consider enumeration problems and the relation to the theory of codes. Peer reviewed
International Nuclear Information System (INIS)
Chernodub, M.N.; Feldmann, R.; Schiller, A.; Ilgenfritz, E.-M.
2005-01-01
The confining and topological properties of the compact Abelian Higgs model with doubly-charged Higgs field in three space-time dimensions are studied. We consider the London limit of the model. We show that the monopoles are forming chainlike structures (kept together by Abrikosov-Nielsen-Olesen vortices), the presence of which is essential for getting simultaneously permanent confinement of singly-charged particles and breaking of the string spanned between doubly-charged particles. In the confinement phase, the chains are forming percolating clusters, while in the deconfinement (Higgs) phase, the chains are of finite size. The described picture is in close analogy with the synthesis of the Abelian monopole and the center vortex pictures in confining non-Abelian gauge models. The screening properties of the vacuum are studied by means of the photon propagator in the Landau gauge
Modulation of the waterfall by a gauge field
International Nuclear Information System (INIS)
Lyth, David H.; Karčiauskas, Mindaugas
2013-01-01
We present the first complete calculation of the curvature perturbation generated during the hybrid inflation waterfall, caused by the coupling of the waterfall field to a gauge field A whose kinetic function f 2 depends on the inflaton field. We impose an upper bound on the field A≡fA which ensures that it has a negligible effect before the waterfall. We confirm the claim of Soda and Yokoyama, that the perturbation δB generates a statistically anisotropic spectrum and bispectrum, which could easily be observable. We also discover a new phenomenon, whereby the time-dependent 'varyon' field B causes the inflaton contribution to vary during the waterfall. The varyon mechanism might be implemented also with a scalar field and might not involve the waterfall
Globally conformal invariant gauge field theory with rational correlation functions
Nikolov, N M; Todorov, I T; CERN. Geneva; Todorov, Ivan T.
2003-01-01
Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields $V_{\\kappa} (x_1, x_2)$ of dimension $(\\kappa, \\kappa)$. For a {\\it globally conformal invariant} (GCI) theory we write down the OPE of $V_{\\kappa}$ into a series of {\\it twist} (dimension minus rank) $2\\kappa$ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field. We argue that the theory of a GCI hermitian scalar field ${\\cal L} (x)$ of dimension 4 in $D = 4$ Minkowski space such that the 3-point functions of a pair of ${\\cal L}$'s and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density ${\\cal L} (x)$.
Strings - Links between conformal field theory, gauge theory and gravity
International Nuclear Information System (INIS)
Troost, J.
2009-05-01
String theory is a candidate framework for unifying the gauge theories of interacting elementary particles with a quantum theory of gravity. The last years we have made considerable progress in understanding non-perturbative aspects of string theory, and in bringing string theory closer to experiment, via the search for the Standard Model within string theory, but also via phenomenological models inspired by the physics of strings. Despite these advances, many deep problems remain, amongst which a non-perturbative definition of string theory, a better understanding of holography, and the cosmological constant problem. My research has concentrated on various theoretical aspects of quantum theories of gravity, including holography, black holes physics and cosmology. In this Habilitation thesis I have laid bare many more links between conformal field theory, gauge theory and gravity. Most contributions were motivated by string theory, like the analysis of supersymmetry preserving states in compactified gauge theories and their relation to affine algebras, time-dependent aspects of the holographic map between quantum gravity in anti-de-Sitter space and conformal field theories in the bulk, the direct quantization of strings on black hole backgrounds, the embedding of the no-boundary proposal for a wave-function of the universe in string theory, a non-rational Verlinde formula and the construction of non-geometric solutions to supergravity
Supersymmetric gauge theories, quantization of Mflat, and conformal field theory
International Nuclear Information System (INIS)
Teschner, J.; Vartanov, G.S.
2013-02-01
We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.
Extended BRST symmetries in the gauge field theory
International Nuclear Information System (INIS)
Babalean, Aurel; Constantinescu, Radu; Ionescu, Carmen
2001-01-01
The BRST procedure provides one of the most powerful methods for the quantum description of the gauge field theories. As already stated, the unphysical degrees of freedom that appear in this case can be easily canceled by the introduction of the ghost type variables. In the Hamiltonian formalism, the structure of the ghost that must be used mainly depends on two factors: - the type of the theory, that this the relations among the constraints of the theory; - the extension of the symmetry to be implemented. The paper presents the structure of the extended phase space suitable for the BRST canonical quantization of a 1- reducible gauge theory in the frame of a BRST symmetry of order three. The corresponding BRST charges and the extended Hamiltonian are also constructed. (authors)
International Nuclear Information System (INIS)
Nakawaki, Yuji; McCartor, Gary
2006-01-01
We construct a new perturbative formulation of pure space-like axial gauge QED in which the inherent infrared divergences are regularized by residual gauge fields. For this purpose, we carry out our calculations in the coordinates x μ =(x + , x - , x 1 , x 2 ), where x + =x 0 sinθ + x 3 cosθ and x - = x 0 cosθ - x 3 sinθ. Here, A=A 0 cosθ + A 3 sinθ = n·A=0 is taken as the gauge fixing condition. We show in detail that, in perturbation theory, infrared divergences resulting from the residual gauge fields cancel infrared divergences resulting from the physical parts of the gauge field. As a result, we obtain the gauge field propagator proposed by Mandelstam and Leibbrandt. By taking the limit θ→π/4, we are able to construct a light-cone formulation that is free from infrared divergences. With that analysis complete, we next calculate the one-loop electron self-energy, something not previously done in the light-cone quantization and light-cone gauge. (author)
Gravitational waves in bouncing cosmologies from gauge field production
Energy Technology Data Exchange (ETDEWEB)
Ben-Dayan, Ido, E-mail: ido.bendayan@gmail.com [Department of Physics, Ben-Gurion University of the Negev, P.O. Box 653, Be' er-Sheva 8410500 (Israel)
2016-09-01
We calculate the gravitational waves (GW) spectrum produced in various Early Universe scenarios from gauge field sources, thus generalizing earlier inflationary calculations to bouncing cosmologies. We consider generic couplings between the gauge fields and the scalar field dominating the energy density of the Universe. We analyze the requirements needed to avoid a backreaction that will spoil the background evolution. When the scalar is coupled only to F F-tilde term, the sourced GW spectrum is exponentially enhanced and parametrically the square of the vacuum fluctuations spectrum, P {sup s} {sub T} ∼ (P {sup v} {sub T} ){sup 2}, giving an even bluer spectrum than the standard vacuum one. When the scalar field is also coupled to F {sup 2} term, the amplitude is still exponentially enhanced, but the spectrum can be arbitrarily close to scale invariant (still slightly blue), n {sub T} ∼> 0, that is distinguishable form the slightly red inflationary one. Hence, we have a proof of concept of observable GW on CMB scales in a bouncing cosmology.
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.)
A multiscale view of propagators in gauge fields
Energy Technology Data Exchange (ETDEWEB)
Baeker, M
1995-07-01
The Iteratively Smoothing Unigrid (ISU) is presented and studied in detail. An appropriate definition of smoothness in the presence of disordered gauge fields is given on which the algorith is based. ISU uses an iterative process to determ is based. ISU uses an iterative process to determine the interpolation operators as the eigenvectors to the lowest eigenvalues on blocks of larger and larger sizes. We always used the algorith in two dim in two dimensions, usually with SU(2) gauge fields. The ISU algorith perform performs extreely well for the case of the covariant Laplace equation with arbitrarily large disorder. For the Dirac equation, critical slowing down is elimely well for the case of the covariant Laplace equation with arbitrarily large disorder. For the Dirac equation, critical slowing down is eliminated in the continuu lim limit, but when {beta} is kept fixed and the lattice size is increased the critical exponent is estiated to z{approx}1.6. (orig.) methods prove that the problem is due to the many eigenmodes of the Dirac operator that have low eigenvalues and can not be approximated well by the used localized interpolation operators. That the Laplace equation is solved efficiently is caused by the phenomenon of Localization: The lowest modes of the Laplace operator are strongly localized when the disorder of the gauge field is large. We also present an explanation of this phenomenon. For the Dirac operator in two dimension, no localization is found; the reasons for this are not known. It is explained in detail why localization helps to improve the convergence of the algorithm. After having analyzed the problems of the algorithm for the Dirac equation, we try to invent a cure. It consists of two parts: We change the shapes of the supports of the interpolation operators and we introduce the possibility of having more than one interpolation operators per block-lattice point. (Abstract Truncated)
Role of gauge invariance in a variational and mean-field calculation
International Nuclear Information System (INIS)
Masperi, L.; Omero, C.
1981-08-01
We show that the implementation of gauge invariance is essential for a variational treatment to correctly reproduce all the features of the phase diagram for the Z(2) lattice gauge theory with matter field. (author)
Effective Einsteinian gravity from Poincare gauge field theory
International Nuclear Information System (INIS)
Baekler, P.; Mielke, E.W.
1985-10-01
The Poincare gauge theory of gravity should apply in the microphysical domain. Here we investigate its implications for macrophysics. Weakly self double dual Riemann-Cartan curvature is assumed throughout. It is shown that the metrical background is then determined by Einstein's field equations with the Belinfante-Rosenfeld symmetrized energy-momentum current amended by spin squared terms. Moreover, the effective cosmological constant can be reconciled with the empirical data by absorbing the corresponding constant curvature part into the dynamical torsion of recently found exact solutions. Macroscopically this extra torsion remains undetectable. (author)
Body fixed frame, rigid gauge rotations and large N random fields in QCD
International Nuclear Information System (INIS)
Levit, S.
1995-01-01
The ''body fixed frame'' with respect to local gauge transformations is introduced. Rigid gauge ''rotations'' in QCD and their Schroedinger equation are studied for static and dynamic quarks. Possible choices of the rigid gauge field configuration corresponding to a non-vanishing static colormagnetic field in the ''body fixed'' frame are discussed. A gauge invariant variational equation is derived in this frame. For large number N of colors the rigid gauge field configuration is regarded as random with maximally random probability distribution under constraints on macroscopic-like quantities. For the uniform magnetic field the joint probability distribution of the field components is determined by maximizing the appropriate entropy under the area law constraint for the Wilson loop. In the quark sector the gauge invariance requires the rigid gauge field configuration to appear not only as a background but also as inducing an instantaneous quark-quark interaction. Both are random in the large N limit. (orig.)
Mean fields and self consistent normal ordering of lattice spin and gauge field theories
International Nuclear Information System (INIS)
Ruehl, W.
1986-01-01
Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
International Nuclear Information System (INIS)
Pernici, M.; Pilch, K.; Van Nieuwenhuizen, P.
1985-01-01
The complete gauged nonlinear N=8 d=5 supergravity action and supersymmetry transformation laws (without four- and three-fermion terms) are presented. They are obtained from the ungauged model by reinterpreting part of the field strengths of the abelian vector fields as real self-dual second-rank antisymmetric tensors. The complete set of T-tensor indentities are given and their validity is checked numerically. The model has a local Yang-Mills SO(6) and a local composite USp(8) symmetry. The self-duality is essential for the consistent coupling of the antisymmetric tensors to the nonabelian gauge fields. (orig.)
From topological quantum field theories to supersymmetric gauge theories
International Nuclear Information System (INIS)
Bossard, G.
2007-10-01
This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the β function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)
Massive Higher Dimensional Gauge Fields as Messengers of Supersymmetry Breaking
International Nuclear Information System (INIS)
Chacko, Z.; Luty, Markus A.; Ponton, Eduardo
2000-01-01
We consider theories with one or more compact dimensions with size r > 1/M, where M is the fundamental Planck scale, with the visible and hidden sectors localized on spatially separated 3 -branes''. We show that a bulk U(1) gauge field spontaneously broken on the hidden-sector 3-brane is an attractive candidate for the messenger of supersymmetry breaking. In this scenario scalar mass-squared terms are proportional to U(1) charges, and therefore naturally conserve flavor. Arbitrary flavor violation at the Planck scale gives rise to exponentially suppressed flavor violation at low energies. Gaugino masses can be generated if the standard gauge fields propagate in the bulk; μ and Bμ terms can be generated by the Giudice-Masiero or by the VEV of a singlet in the visible sector. The latter case naturally solves the SUSY CP problem. Realistic phenomenology can be obtained either if all microscopic parameters are order one in units of M, or if the theory is strongly coupled at the scale M. (For the latter case, we estimate parameters by extending n aive dimensional analysis'' to higher-dimension theories with branes.) In either case, the only unexplained hierarchy is the l arge'' size of the extra dimensions in fundamental units, which need only be an order of magnitude. All soft masses are naturally within an order of magnitude of m 3/2 , and trilinear scalar couplings are negligible. Squark and slepton masses can naturally unify even in the absence of grand unification. (author)
Restricted gravity: Abelian projection of Einstein's theory
International Nuclear Information System (INIS)
Cho, Y.M.
2013-01-01
Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection Γμ into the restricted connection made of the potential of the maximal Abelian subgroup H of Lorentz group G and the valence connection made of G/H part of the potential which transforms covariantly under Lorentz gauge transformation. With this we show that Einstein's theory can be decomposed into the restricted gravity made of the restricted connection which has the full Lorentz gauge invariance which has the valence connection as gravitational source. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory,
Elastic gauge fields and Hall viscosity of Dirac magnons
Ferreiros, Yago; Vozmediano, María A. H.
2018-02-01
We analyze the coupling of elastic lattice deformations to the magnon degrees of freedom of magnon Dirac materials. For a honeycomb ferromagnet we find that, as happens in the case of graphene, elastic gauge fields appear coupled to the magnon pseudospinors. For deformations that induce constant pseudomagnetic fields, the spectrum around the Dirac nodes splits into pseudo-Landau levels. We show that when a Dzyaloshinskii-Moriya interaction is considered, a topological gap opens in the system and a Chern-Simons effective action for the elastic degrees of freedom is generated. Such a term encodes a phonon Hall viscosity response, entirely generated by quantum fluctuations of magnons living in the vicinity of the Dirac points. The magnon Hall viscosity vanishes at zero temperature, and grows as temperature is raised and the states around the Dirac points are increasingly populated.
Calibration and characterization of Bayard-Alpert gauges operating in high magnetic fields
International Nuclear Information System (INIS)
Pickles, W.L.; Hunt, A.L.
1985-11-01
Standard Bayard-Alpert gauges have been successfully operated for several months in the 0.3 to 0.7 T magnetic fields near the plasma edge of the Tandem Mirror Experiment-Upgrade (TMX-U). The gauges clearly measure gas pressure and maintain calibration within 10% during operation. The gauge filaments are tungsten and are heated with DC. The gauge housing allows operation in the low density plasma outside the limiter radius by thermalizing the neutral gas that enters the gauge and by preventing plasma from entering the gauge. Changing the orientation of the gauge with respect to the magnetic field changes the gauge calibration, or effective sensitivity, by as much as a factor of 100. Only some orientations of the filament collector plane with respect to the magnetic field direction allow calibrated operation as a pressure gauge. This range of angles is approximately from 20 to 50 degrees. The gauge is oriented to produce the desired sensitivity, then calibrated for the magnetic field effects for that position. The correction to sensitivity for magnet field is not strongly species dependent. The gauge species sensitivities for CH 4 , Xe,and Kr measured in the high magnetic fields were found to be close to the published values measured in no magnetic field
Stochastic quantization and gauge theories
International Nuclear Information System (INIS)
Kolck, U. van.
1987-01-01
Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author) [pt
Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models
International Nuclear Information System (INIS)
Steinacker, Harold
2009-01-01
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.
Gauge boson mass without a Higgs field: a simple model
International Nuclear Information System (INIS)
Nicholson, A.F.; Kennedy, D.C.
1997-02-01
A simple, anomaly-free chiral gauge theory can be perturbatively quantized and renormalized in such a way as to generate fermion and gauge boson masses. This development exploits certain freedoms inherent in choosing the unperturbed Lagrangian and in the renormalization procedure. Apart from its intrinsic interest, such a mechanism might be employed in electroweak gauge theory to generate fermion and gauge boson masses without a Higgs sector. 38 refs
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
Implementability of gauge transformations and quantization of fermions in external fields
International Nuclear Information System (INIS)
Grosse, H.; Karner, G.
1986-01-01
Quantization of fermions in an external soliton field, leading to a representation of the CAR which is inequivalent to the representation connected to the massive Dirac operator, is studied. We determine classes of gauge and axial gauge transformations which can be unitarily implemented. In the latter case quantization conditions for gauge functions are obtained; integers entering can be interpreted as winding numbers. (Author)
Quantum theory of gauge fields and rigid processes calculation
International Nuclear Information System (INIS)
Andreev, I.V.
1981-01-01
Elementary statement of the basic data on the nature of quark interactions and their role in the high energy processes is presented in the first part of the paper. The second part of the paper deals with gauge theory (GT) of strong interactions (chromodynamics (CD)) and its application in calculation of rigid processes with quark participation. It is based on the method of functional integration (MFI). A comparatively simple representation of the MFI in the quantum theory and formulation of the perturbation theory for gauge fields are given. A derivation of the rules of diagram technique is presented. Renormalization invariance of the theory and the basic for CD phenomenon of asymptotical freedom are discussed. Theory application in calculation of certain effects at high energies is considered. From the CD view point considered is a parton model on the base of which ''rigid'' stage of evolution of quark and gluon jets produced at high energies can be quantitatively described and some quantitative experimental tests of the CD are suggested [ru
Gauge and matter fields coupled to N=2 supergravity
International Nuclear Information System (INIS)
Wit, B. de; Lauwers, P.G.; Philippe, R.; Su, S.-Q.; Proeyen, A. van.
1983-07-01
The authors consider the potential of a general matter system of N=2 vector and scalar multiplets coupled to supergravity. For lagrangians that are initially quadratic in the matter fields the potential is proved to be either positive or unbounded from below. The results have been obtained in the framework of a superconformal multiplet calculus, and it has been verified that they can be derived from each of the three off-shell representations. As an example the authors consider SO(6) Yang-Mills theory coupled to scalar multiplets in the 10+10 representation, which, for suitably chosen parameters, leads to the potential of gauged N=8 supergravity. Finally, a discussion of the possibility to set residual nonabelian symmetry groups after breaking of N=8 supersymmetry to N=1 or 2 is presented. (Auth.)
Gauge invariance of a particle in an external magnetic field
International Nuclear Information System (INIS)
Ekstein, H.
1978-12-01
In the accepted theory of a nonrelativistic particle in an external field, as well as in the Dirac equation, the canonical momentum p plays a strangely elusive role: contrary to the position q, it has no physical interpretation, yet it is a member of the algebra of observables; nor does it have a well-defined meaning as a translation generator. This paper proposes an observation procedure for p which entails a definite choice for the vector potential A: the radiation gauge divergence of A=0. The canonical momentum, so defined operationally, is shown to be the image of the generator of space translations, in the sense of presymmetry, as the position q is the image of the generator of Galilei boosts in nonrelativistic theories
Full spectrum of Lyapunov exponents in gauge field theories
International Nuclear Information System (INIS)
Biro, T.S.; Markum, H.; Pullirsch, R.
2003-01-01
Full text: Results are presented for the full spectrum of Lyapunov exponents of the compact U(1) gauge system in classical field theory. Instead of the determination of the largest Lyapunov exponent by the rescaling method we now use the monodromy matrix approach. The Lyapunov spectrum L i is expressed in terms of the eigenvalues Λ i of the monodromy matrix M. In the confinement phase the eigenvalues lie on either the real or on the imaginary axes. This is a nice illustration of a strange attractor of a chaotic system. Positive Lyapunov exponents eject the trajectories from oscillating orbits provided by the imaginary eigenvalues. Negative Lyapunov exponents attract the trajectories keeping them confined in the basin. Latest studies concern the time (in)dependence of the monodromy matrix. Further, we show that monopoles are created and annihilated in pairs as a function of real time in access to a fixed average monopole number. (author)
Chiral gauged Wess-Zumino-Witten theories and coset models in conformal field theory
International Nuclear Information System (INIS)
Chung, S.; Tye, S.H.
1993-01-01
The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by G L direct-product G R . In the standard gauged WZW theory, vector gauge fields (i.e., with vector gauge couplings) are in the adjoint representation of the subgroup H contained-in G. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R where H L and H R can be different groups. In the special case where H L =H R , the theory is equivalent to vector gauged WZW theory. For general groups H L and H R , an examination of the correlation functions (or more precisely, conformal blocks) shows that the chiral gauged WZW theory is equivalent to (G/H L ) L direct-product(G/H R ) R coset models in conformal field theory
Comment on ''Topologically Massive Gauge Theories''
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
1988-01-01
In a recent paper by R. Pisarski and S. Rao concerning topologically massive quantum Yang--Mills theory, the expression of the P-even part of the non-Abelian gauge field self-energy at one-loop order is shown to obey a consistency condition, which is not fulfilled by the formula originally presented by S. Deser, R. Jackiw, and S. Templeton. In this comment, I present a recalculation which agress with Pisarski and Rao. copyright 1988 Academic Press, Inc
Non-Abelian magnetized blackholes and unstable attractors
Energy Technology Data Exchange (ETDEWEB)
Mosaffa, A.E. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: mosaffa@theory.ipm.ac.ir; Randjbar-Daemi, S. [The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11 34014, Trieste (Italy)], E-mail: seif@ictp.trieste.it; Sheikh-Jabbari, M.M. [Institute for Studies in Theoretical Physics and Mathematics (IPM), PO Box 19395-5531, Tehran (Iran, Islamic Republic of)], E-mail: jabbari@theory.ipm.ac.ir
2008-01-21
Fluctuations of non-Abelian gauge fields in a background magnetic charge contain 'tachyonic' modes which as we will show cause an instability of the background. We extend this result to the cases where the background charge (flux) is coupled to four-dimensional Einstein gravity and show that the corresponding spherically symmetric geometries, which in the absence of a cosmological constant are of the form of (colored) Reissner-Nordstroem blackholes or the AdS{sub 2}xS{sup 2}, are also unstable unless the flux assumes its smallest allowed value, in which case the configuration is stable. We discuss the relevance of these instabilities to several places in string theory including various string compactifications and the attractor mechanism. Our results for the latter imply that the attractor mechanism shown to work for the extremal Abelian charged blackholes, cannot be applied in a straightforward way to the extremal non-Abelian colored blackholes, with the exception of the minimally charged stable ones.
Dynamics of particle production by strong electric fields in non-Abelian plasmas
International Nuclear Information System (INIS)
Dawson, John F.; Mihaila, Bogdan; Cooper, Fred
2010-01-01
We develop methods for computing the dynamics of fermion pair production by strong color electric fields including backreaction using the semiclassical Boltzmann-Vlasov (B-V) equation. We implement the Schwinger pair production by inserting a source term in the B-V equation which includes Pauli-Blocking effects. We present numerical results for a model with SU(2) symmetries in (1+1) Cartesian dimensions.
On the 4D generalized Proca action for an Abelian vector field
Energy Technology Data Exchange (ETDEWEB)
Allys, Erwan [Institut d’Astrophysique de Paris, UMR 7095, UPMC Université Paris 6 et CNRS,98 bis boulevard Arago, 75014 Paris (France); Almeida, Juan P. Beltrán [Departamento de Física, Universidad Antonio Nariño,Cra 3 Este # 47A-15, Bogotá D.C. 110231 (Colombia); Peter, Patrick [Institut d’Astrophysique de Paris, UMR 7095, UPMC Université Paris 6 et CNRS,98 bis boulevard Arago, 75014 Paris (France); Institut Lagrange de Paris,UPMC Université Paris 6 et CNRS,Sorbonne Universités, Paris (France); Rodríguez, Yeinzon [Centro de Investigaciones en Ciencias Básicas y Aplicadas, Universidad Antonio Nariño, Cra 3 Este # 47A-15, Bogotá D.C. 110231 (Colombia); Escuela de Física, Universidad Industrial de Santander,Ciudad Universitaria, Bucaramanga 680002 (Colombia); Simons Associate at The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151, Trieste (Italy)
2016-09-19
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated StÃ¼ckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the StÃ¼ckelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A{sub μ}, the Faraday tensor F{sub μν} and its Hodge dual F-tilde{sub μν}.
On the 4D generalized Proca action for an Abelian vector field
International Nuclear Information System (INIS)
Allys, Erwan; Almeida, Juan P. Beltrán; Peter, Patrick; Rodríguez, Yeinzon
2016-01-01
We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated StÃ¼ckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the StÃ¼ckelberg field describing the longitudinal mode, which is in agreement with the results of http://dx.doi.org/10.1088/1475-7516/2014/05/015 and http://dx.doi.org/10.1016/j.physletb.2016.04.017 and complements those of http://dx.doi.org/10.1088/1475-7516/2016/02/004. We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field A_μ, the Faraday tensor F_μ_ν and its Hodge dual F-tilde_μ_ν.
International Nuclear Information System (INIS)
Evett, S.R.; Steiner, J.L.
1995-01-01
Soil water content gauges based on neutron scattering (NS) have been a valuable tool for soil water investigations for some 40 yr. However, licensing, training, and safety regulations pertaining to the radioactive source in these gauges makes their use expensive and prevents use in some situations such as unattended monitoring. A capacitance probe (CP) gauge has characteristics that would seem to make it an ideal replacement for NS gauges. We determined the relative precision of two brands of NS gauges (three gauges of each) and a brand of CP gauge (four gauges) in a field calibration exercise. Both brands of NS gauges were calibrated vs. volumetric soil water content with coefficients of determination (r2) ranging from 0.97 to 0.99 and root mean squared errors (RMSE) 0.012 m3 m-3 water content. Calibrations for the CP gauges resulted in r2 ranging from 0.68 to 0.71 and RMSE of 0.036 m3 m-3 water content. Average 95% confidence intervals on predictions were three to five times higher for the CP gauges than for the NS gauges, ranging from 0.153 to 0.161 and 0.032 to 0.052 m3 m-3, respectively. Although poorly correlated with soil water content, readings were reproducible among the four CP gauges. The poor correlation for CP gauges may be due to small-scale soil water content variations within the measurement volume of the gauge. The NS gauges provide acceptable precision but the CP gauge has poor precision and is unacceptable for routine soil water content measurements
A Third-Rank Tensor Field Based on a U(1) Gauge Theory in Loop Space
Shinichi, DEGUCHI; Tadahito, NAKAJIMA; Department of Physics and Atomic Energy Research Institute College of Science and Technology; Department of Physics and Atomic Energy Research Institute College of Science and Technology
1995-01-01
We derive the Stueckelberg formalism extended to a third-rank tensor field from a U(1) gauge theory in loop space, the space of all loops in space-time. The third-rank tensor field is regarded as a constrained U(1) gauge field on the loop space.
Heterotic non-Abelian orbifolds
Energy Technology Data Exchange (ETDEWEB)
Fischer, Maximilian [Technische Univ. Muenchen, Garching (Germany). Physik-Department; Ramos-Sanchez, Saul [UNAM, Mexico (Mexico). Dept. of Theoretical Physics; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non-Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard embedding based on higher dimensional supersymmetry, we compute the Hodge numbers for all recently classified 331 non-Abelian orbifold geometries which yield N=1 supersymmetry for heterotic compactifications. Surprisingly, most Hodge numbers follow the empiric pattern h{sup (1,1)}-h{sup (2,1)}=0 mod 6, which might be related to the number of three standard model generations. Furthermore, we study the fundamental groups in order to identify the possibilities for non-local gauge symmetry breaking. Three examples are discussed in detail: the simplest non-Abelian orbifold S{sub 3} and two more elaborated examples, T{sub 7} and {Delta}(27), which have only one untwisted Kaehler and no untwisted complex structure modulus. Such models might be especially interesting in the context of no-scale supergravity. Finally, we briefly discuss the case of orbifolds with vanishing Euler numbers in the context of enhanced (spontaneously broken) supersymmetry.
String theory duals of Lifshitz–Chern–Simons gauge theories
International Nuclear Information System (INIS)
Balasubramanian, Koushik; McGreevy, John
2012-01-01
We propose candidate gravity duals for a class of non-Abelian z = 2 Lifshitz Chern–Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern–Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang–Mills theory. Using the holographic dictionary, we identify the bulk fields of type IIB supergravity that are dual to these deformations. The geometries describing the groundstates of the non-Abelian LCS gauge theories realized here exhibit a mass gap. (paper)
On the dynamics of gauge potential
International Nuclear Information System (INIS)
Tao Jiafu; Li Yuanjie; Zhang Jinru
1992-01-01
The gauge potential is resolved into gauge potential of strength and gauge potential of phase. The phase gauge potential can be described with an equivalent potential of inertial force. A Lagrangian density with phase gauge potential is given and some examples are discussed. The method proposed has been extended to the case of the non-Abelian group
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.)
Tumbling in two djmensional gauge theories
International Nuclear Information System (INIS)
Banks, T.; Yankielowicz, S.; Frishman, Y.
1981-05-01
The ideas of Tumbling and Most Attractive Channel condensation are confronted in two dimensional chiral gauge theories. The performance of a gauge invariant regularization is first demonstrated. Exact results about the spectra in both abelian and non abelian cases are then found. These conflict with the predictions of Tumbling and MAC. (author)
Noncommutative gauge theory for Poisson manifolds
Energy Technology Data Exchange (ETDEWEB)
Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de
2000-09-25
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.
Noncommutative gauge theory for Poisson manifolds
International Nuclear Information System (INIS)
Jurco, Branislav; Schupp, Peter; Wess, Julius
2000-01-01
A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem
Non-Abelian duality and confinement in N=2 supersymmetric QCD
International Nuclear Information System (INIS)
Shifman, M.; Yung, A.
2009-01-01
In N=2 supersymmetric QCD with the U(N) gauge group and N f >N we study the crossover transition from the weak coupling regime at large ξ to strong coupling at small ξ, where ξ is the Fayet-Iliopoulos parameter. We find that at strong coupling a dual non-Abelian weakly coupled N=2 theory exists, which describes low-energy physics at small ξ. The dual gauge group is U(N f -N), and the dual theory has N f flavors of light dyons, to be compared with N f quarks in the originalU(N) theory. Both, the original and dual theories are Higgsed and share the same global symmetry SU(N)xSU(N f -N)xU(1), albeit the physical meaning of the SU(N) and SU(N f -N) factors is different in the large- and small-ξ regimes. Both regimes support non-Abelian semilocal strings. In each of these two regimes particles that are in the adjoint representations with respect to one of the factor groups exist in two varieties: elementary fields and composite states bound by strings. These varieties interchange upon transition from one regime to the other. We conjecture that the composite stringy states can be related to Seiberg's M fields. The bulk duality that we observed translates into a two-dimensional duality on the world sheet of the non-Abelian strings. At large ξ the internal dynamics of the semilocal non-Abelian strings is described by the sigma model of N orientational and (N f -N) size moduli, while at small ξ the roles of orientational and size moduli interchange. The Bogomol'nyi-Prasad-Sommerfield spectra of two dual sigma models (describing confined monopoles/dyons of the bulk theory) coincide. It would be interesting to trace parallels between the non-Abelian duality we found and string theory constructions.
Cosmology in Gauge Field Theory and String Theory
International Nuclear Information System (INIS)
Garcia Compean, H
2005-01-01
This new book is intended for students and researchers who want to go into the interplay between cosmology and high-energy physics. It assumes a prior knowledge of these subjects such as some of the topics contained in the previous books by the authors, Introduction to Gauge Field Theory (1993 Bristol: Institute of Physics Publishing) and Supersymmetric Gauge Field Theory and String Theory (1994 Bristol: Institute of Physics Publishing). However, the book is intended to be self-contained, explaining, from a modern perspective, some background material mainly in standard cosmology, topological defects, baryogenesis, inflationary cosmology and, at the end of the book, some of the basics of string theory. What is distinctively new about this book is that it lies in the interplay between cosmology and high-energy physics typically above 100 GeV (10 15 K). Often these subjects are presented in regular textbooks in a disconnected way, or in research papers, proceedings and review papers but usually not in a pedagogical style. Thus, in this sense, the book is unique and deserves a special place in the recent literature. The book starts by reviewing the standard material of the early universe. The standard model of cosmology from a modern perspective is revised in chapter 1. In chapter 2, phase transitions in different models are discussed, Higgs, electroweak, GUTs, supersymmetric GUTs and supergravity, by using quantum field theory at finite temperature. Chapter 3 is devoted to a general account of topological defects and discusses how they arise as possible remnants of these phase transitions in GUTs. Other relics, such as neutrinos and axions, are introduced in chapter 5 and their impact in cosmology is assessed. In chapter 4, some of the most relevant mechanisms of baryogenesis are discussed in the context of the different GUTs and the minimal supersymmetric standard model (MSSM). Inflation is also discussed in the context of GUTs. In chapter 6, the authors introduce
International Nuclear Information System (INIS)
Moura-Melo, Winder A.; Panza, N.; Helayel Neto, J.A.
1998-12-01
An Abelian gauge model, with vector and 2-form potential; fields linked by a topological mass term that mixes the two Abelian factors, is shown to exhibit Dirac-like magnetic monopoles in the presence of a matter background. In addition, considering a 'non-minimal coupling' between the fermions and the tensor fields, we obtain a generalized quantisation condition that involves, among others, the mass parameter. Also, it is explicitly shown that 1 loop (finite) corrections do no shift the value of such a mass parameter. (author)
Energy Technology Data Exchange (ETDEWEB)
Moura-Melo, Winder A.; Panza, N.; Helayel Neto, J.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1998-12-01
An Abelian gauge model, with vector and 2-form potential; fields linked by a topological mass term that mixes the two Abelian factors, is shown to exhibit Dirac-like magnetic monopoles in the presence of a matter background. In addition, considering a 'non-minimal coupling' between the fermions and the tensor fields, we obtain a generalized quantisation condition that involves, among others, the mass parameter. Also, it is explicitly shown that 1{sub loop} (finite) corrections do no shift the value of such a mass parameter. (author)
Light-cone gauge approach to arbitrary spin fields, currents and shadows
International Nuclear Information System (INIS)
Metsaev, R R
2014-01-01
Totally symmetric arbitrary spin fields in AdS space, conformal fields, conformal currents, and shadow fields in flat space are studied. Light-cone gauge formulations for such fields, currents and shadows are obtained. Use of the Poincaré parametrization of AdS space and ladder operators allows us to treat fields in flat and AdS spaces on an equal footing. Light-cone gauge realization of relativistic symmetries for fields, currents and shadows is also obtained. The light-cone gauge formulation for fields is obtained by using the gauge invariant Lagrangian which is presented in terms of modified de Donder divergence, while the light-cone gauge formulation for currents and shadows is obtained by using the gauge invariant approach to currents and shadows. This allows us to demonstrate explicitly how the ladder operators entering the gauge invariant formulation of fields, currents and shadows manifest themselves in the light-cone gauge formulation for fields, currents and shadows. (paper)
Non-Abelian hydrodynamics and the flow of spin in spin-orbit coupled substances
International Nuclear Information System (INIS)
Leurs, B.W.A.; Nazario, Z.; Santiago, D.I.; Zaanen, J.
2008-01-01
Motivated by the heavy ion collision experiments there is much activity in studying the hydrodynamical properties of non-Abelian (quark-gluon) plasmas. A major question is how to deal with color currents. Although not widely appreciated, quite similar issues arise in condensed matter physics in the context of the transport of spins in the presence of spin-orbit coupling. The key insight is that the Pauli Hamiltonian governing the leading relativistic corrections in condensed matter systems can be rewritten in a language of SU(2) covariant derivatives where the role of the non-Abelian gauge fields is taken by the physical electromagnetic fields: the Pauli system can be viewed as Yang-Mills quantum-mechanics in a 'fixed frame', and it can be viewed as an 'analogous system' for non-Abelian transport in the same spirit as Volovik's identification of the He superfluids as analogies for quantum fields in curved space time. We take a similar perspective as Jackiw and coworkers in their recent study of non-Abelian hydrodynamics, twisting the interpretation into the 'fixed frame' context, to find out what this means for spin transport in condensed matter systems. We present an extension of Jackiw's scheme: non-Abelian hydrodynamical currents can be factored in a 'non-coherent' classical part, and a coherent part requiring macroscopic non-Abelian quantum entanglement. Hereby it becomes particularly manifest that non-Abelian fluid flow is a much richer affair than familiar hydrodynamics, and this permits us to classify the various spin transport phenomena in condensed matter physics in an unifying framework. The 'particle based hydrodynamics' of Jackiw et al. is recognized as the high temperature spin transport associated with semiconductor spintronics. In this context the absence of faithful hydrodynamics is well known, but in our formulation it is directly associated with the fact that the covariant conservation of non-Abelian currents turns into a disastrous non
Gauged BRST symmetry and the occurence of higher cocycles in quantum field theory
International Nuclear Information System (INIS)
Baulieu, L.; Grossman, B.; Stora, R.
1986-06-01
The BRST symmetry of Yang Mills theories can be gauged via the introduction of an anticommuting single gauge field. There follows the construction of a local BRST operation which allows an algebraic analysis of the BRST current algebra. This construction provides, in particular, a field theory interpretation of most higher cocycles which accompany the usual chiral anomaly
Ultraviolet stability of three-dimensional lattice pure gauge field theories
International Nuclear Information System (INIS)
Balaban, T.
1985-01-01
We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories. (orig.)
Introduction to gauge theories of electroweak interactions
International Nuclear Information System (INIS)
Ecker, G.
1982-01-01
Intended as a lecture for physicists who are not familiar with the sophisticated theoretical models in particle physics. Starting with the standard gauge model of electromagnetic, weak and strong interactions the recent developments of a unified gauge theory of electroweak interactions are shown. Shortcomings in the unitarity problem of the V-A fermi theory of charged intermediate vector bosons. Presented are the spontaneous symmetry breaking in quantum mechanics, the abelian higgs model as an example of a spontaneously broken gauge field theory, the minimal gauge group of electroweak interactions, the fermion mass generation. Further on the anomalies in quantum field theory are discussed and the radiative corrections to the vector boson masses are considered. (H.B.)
Gauge fields in nonlinear group realizations involving two-dimensional space-time symmetry
International Nuclear Information System (INIS)
Machacek, M.E.; McCliment, E.R.
1975-01-01
It is shown that gauge fields may be consistently introduced into a model Lagrangian previously considered by the authors. The model is suggested by the spontaneous breaking of a Lorentz-type group into a quasiphysical two-dimensional space-time and one internal degree of freedom, loosely associated with charge. The introduction of zero-mass gauge fields makes possible the absorption via the Higgs mechanism of the Goldstone fields that appear in the model despite the fact that the Goldstone fields do not transform as scalars. Specifically, gauge invariance of the Yang-Mills type requires the introduction of two sets of massless gauge fields. The transformation properties in two-dimensional space-time suggest that one set is analogous to a charge doublet that behaves like a second-rank tensor in real four-dimensional space time. The other set suggests a spin-one-like charge triplet. Via the Higgs mechanism, the first set absorbs the Goldstone fields and acquires mass. The second set remains massless. If massive gauge fields are introduced, the associated currents are not conserved and the Higgs mechanism is no longer fully operative. The Goldstone fields are not eliminated, but coupling between the Goldstone fields and the gauge fields does shift the mass of the antisymmetric second-rank-tensor gauge field components
Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system
International Nuclear Information System (INIS)
Kawabe, Tetsuji
2003-01-01
Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition
Physical principles, geometrical aspects, and locality properties of gauge field theories
International Nuclear Information System (INIS)
Mack, G.; Hamburg Univ.
1981-01-01
Gauge field theories, particularly Yang - Mills theories, are discussed at a classical level from a geometrical point of view. The introductory chapters are concentrated on physical principles and mathematical tools. The main part is devoted to locality problems in gauge field theories. Examples show that locality problems originate from two sources in pure Yang - Mills theories (without matter fields). One is topological and the other is related to the existence of degenerated field configurations of the infinitesimal holonomy groups on some extended region of space or space-time. Nondegenerate field configurations in theories with semisimple gauge groups can be analysed with the help of the concept of a local gauge. Such gauges play a central role in the discussion. (author)
Cosmological bounds on non-Abelian dark forces
Forestell, Lindsay; Morrissey, David E.; Sigurdson, Kris
2018-04-01
Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early Universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the standard model through nonrenormalizable operators. These operators will transfer energy between the dark and visible sectors, and they allow some or all of the dark glueballs to decay. In this work we investigate the cosmological evolution and decays of dark glueballs in the presence of connector operators to the standard model. Dark glueball decays can modify cosmological and astrophysical observables, and we use these considerations to put very strong limits on the existence of pure non-Abelian dark forces. On the other hand, if one or more of the dark glueballs are stable, we find that they can potentially make up the dark matter of the Universe.
Once more about the topologically massive gauge theory
International Nuclear Information System (INIS)
Kogan, Ya.I.
1989-01-01
The general properties of the three-dimensional gauge theory with the topological mass is discussed namely the long-range interaction of the Aharonov-Bohm type. It is argued that Chern-Simons gauge theories must be considered as the infrared limit of the topologically massive theories. The analogy between the Landau problem of a charged particle in a magnetic field and quantization of this gauge theory is considered, as well as the quantization condition for the Abelian Chern-Simons term. 38 refs.; 5 figs
Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field
International Nuclear Information System (INIS)
Mandal, Anirban; Hunt, Katharine L. C.
2016-01-01
In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term H m and a field term H f , and show that both H m and H f have gauge-independent expectation values. Any gauge may be chosen for the calculations; but
Metal–insulator crossover in high Tc cuprates: A gauge field approach
Indian Academy of Sciences (India)
plane resistivity of underdoped cuprates and a range of superconducting cuprates in the presence of a strong magnetic field suppressing superconductivity. We propose an explanation for this phenomenon based on a gauge field theory approach ...
Symmetry breaking in Landau gauge. A comment to a paper by T. Kennedy and C. King
International Nuclear Information System (INIS)
Borgs, C.; Nill, F.
1986-01-01
The authors generalize the result of T. Kennedy and C. King (Princeton preprint, 1985) on the non-compact abelian lattice Higgs model in Landau gauge in order to show that there are states parameterized by an angle such that the expectation value of the Higgs field is described by a phase factor and a value which is uniformly bounded away from zero. (HSI)
International Nuclear Information System (INIS)
Okun, Lev B
2010-01-01
V A Fock, in 1926, was the first to have the idea of an Abelian gradient transformation and to discover that the electromagnetic interaction of charged particles has a gradient invariance in the framework of quantum mechanics. These transformation and invariance were respectively named Eichtransformation and Eichinvarianz by H Weyl in 1929 (the German verb zu eichen means to gauge). The first non-Abelian gauge theory was suggested by O Klein in 1938; and in 1954, C N Yang and R L Mills rediscovered the non-Abelian gauge symmetry. Gauge invariance is the underlying principle of the current Standard Model of strong and electroweak interactions. (from the history of physics)
Yuji, NAKAWAKI; Azuma, TANAKA; Kazuhiko, OZAKI; Division of Physics and Mathematics, Faculty of Engineering Setsunan University; Junior College of Osaka Institute of Technology; Faculty of General Education, Osaka Institute of Technology
1994-01-01
Gauge Equivalence of the A_3=0 (axial) gauge to the Coulomb gauge is directly verified in QED. For that purpose a pair of conjugate zero-norm fields are introduced. This enables us to construct a canonical formulation in the axial gauge embedded in the indefinite metric Hilbert space in such a way that the Feynman rules are not altered. In the indefinite metric Hilbert space we can implement a gauge transformation, which otherwise has to be carried out only by hand, as main parts of a canonic...
Stochastic quantization and gauge-fixing of the linearized gravitational field
International Nuclear Information System (INIS)
Hueffel, H.; Rumpf, H.
1984-01-01
Due to the indefiniteness of the Euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gravitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization. (Author)
Towards a coupled-cluster treatment of SU(N) lattice gauge field theory
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
Noncontractible hyperloops in gauge models with Higgs fields in the fundamental representation
Burzlaff, Jürgen
1984-11-01
We study finite-energy configurations in SO( N) gauge theories with Higgs fields in the fundamental representation. For all winding numbers, noncontractible hyperloops are constructed. The corresponding energy density is spherically symmetric, and the configuration with maximal energy on each hyperloop can be determined. Noncontractible hyperloops with an arbitrary winding number for SU(2) gauge theory are also given.
Noncontractible hyperloops in gauge models with Higgs fields in the fundamental representation
International Nuclear Information System (INIS)
Burzlaff, J.
1984-01-01
We study finite-energy configurations in SO(N) gauge theories with Higgs fields in the fundamental representation. For all winding numbers, noncontractible hyperloops are constructed. The corresponding energy density is spherically symmetric, and the configuration with maximal energy on each hyperloop can be determined. Noncontractible hyperloops with an arbitrary winding number for SU(2) gauge theory are also given. (orig.)
Noncontractible hyperloops in gauge models with Higgs fields in the fundamental representation
Energy Technology Data Exchange (ETDEWEB)
Burzlaff, J. (Dublin Inst. for Advanced Studies (Ireland). School of Theoretical Physics)
1984-11-01
We study finite-energy configurations in SO(N) gauge theories with Higgs fields in the fundamental representation. For all winding numbers, noncontractible hyperloops are constructed. The corresponding energy density is spherically symmetric, and the configuration with maximal energy on each hyperloop can be determined. Noncontractible hyperloops with an arbitrary winding number for SU(2) gauge theory are also given.