Infrared and ultraviolet behaviour of effective scalar field theory

CERN Document Server

Ball, R D

1995-01-01

We consider the infrared and ultraviolet behaviour of the effective quantum field theory of a single Z_2 symmetric scalar field. In a previous paper we proved to all orders in perturbation theory the renormalizability of massive effective scalar field theory using Wilson's exact renormalization group equation. Here we show that away from exceptional momenta the massless theory is similarly renormalizable, and we prove detailed bounds on Green's functions as arbitrary combinations of exceptional Euclidean momenta are approached. As a corollary we also prove Weinberg's Theorem for the massive effective theory, in the form of bounds on Green's functions at Euclidean momenta much greater than the particle mass but below the naturalness scale of the theory.

Experimental signature of scaling violation implied by field theories

International Nuclear Information System (INIS)

Tung, W.

1975-01-01

Renormalizable field theories are found to predict a surprisingly specific pattern of scaling violation in deep inelastic scattering. Comparison with experiments is discussed. The feasibility of distinguishing asymptotically free field theories from conventional field theories is evaluated

Renormalizability and model-independent description of Z' signals at low energies

International Nuclear Information System (INIS)

Gulov, A.V.; Skalozub, V.V.

2000-01-01

The model-independent search for signals of heavy Z' gauge bosons in low-energy four-fermion processes is analyzed. It is shown that the renormalizability of the underlying theory containing Z', formulated as a scattering in the field of heavy virtual states, can be implemented in specific relations between different processes. Considering the two-Higgs-doublet model as the low-energy basis theory, the two types of Z' interactions with light particles are found to be compatible with the renormalizability. They are called the Abelian and the ''chiral'' couplings. Observables giving the possibility to uniquely detect Z' in both cases are introduced. (orig.)

On the renormalizability of noncommutative U(1) gauge theory-an algebraic approach

International Nuclear Information System (INIS)

Vilar, L C Q; Tedesco, D G; Lemes, V E R; Ventura, O S

2010-01-01

We investigate the quantum effects of the nonlocal gauge invariant operator 1/D 2 F μν * 1/D 2 F μν in the noncommutative U(1) action and its consequences to the infrared sector of the theory. Nonlocal operators of such kind were proposed to solve the infrared problem of the noncommutative gauge theories evading the questions on the explicit breaking of the Lorentz invariance. More recently, a first step in the localization of this operator was accomplished by means of the introduction of an extra tensorial matter field, and the first loop analysis was carried out (Blaschke et al (2009 Eur. Phys. J. C 62 433-43)). We will complete this localization avoiding the introduction of new degrees of freedom beyond those of the original action by using only BRST doublets. This will allow us to conduct a complete BRST algebraic study of the renormalizability of the theory, following Zwanziger's method of localization of nonlocal operators in QFT.

New perturbative approach to renormalizable field theories

International Nuclear Information System (INIS)

Dhar, A.; Gupta, V.

1984-01-01

A new method for obtaining perturbative predictions in quantum field theory is developed. Our method gives finite predictions, which are free from scheme ambiguities, for any quantity of interest (like a cross section or a Green's function) starting directly from the bare regularized Lagrangian. The central idea in our approach is to incorporate directly the consequences of dimensional transmutation for the predictions of the theory. We thus completely bypass the conventional renormalization procedure and the ambiguities associated with it. The case of massless theories with a single dimensionless coupling constant is treated in detail to illustrate our approach

Features of finite quantum field theories

International Nuclear Information System (INIS)

Boehm, M.; Denner, A.

1987-01-01

We analyse general features of finite quantum field theories. A quantum field theory is considered to be finite, if the corresponding renormalization constants evaluated in the dimensional regularization scheme are free from divergences in all orders of perturbation theory. We conclude that every finite renormalizable quantum field theory with fields of spin one or less must contain both scalar fields and fermion fields and nonabelian gauge fields. Some secific nonsupersymmetric models are found to be finite at the one- and two-loop level. (orig.)

Covariant Renormalizable Modified and Massive Gravity Theories on (Non) Commutative Tangent Lorentz Bundles

CERN Document Server

Vacaru, Sergiu I

2014-01-01

The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to nonholonomic frames with 2 (or 3) +2+2+... spacetime decompositions. This allows us to construct exact solutions with generic off--diagonal metrics depending on all spacetime coordinates via generating and integration functions containing (un-) broken symmetry parameters. Such nonholonomic configurations/ models have a nice ultraviolet behavior and seem to be ghost free and (super) renormalizable in a sense of covariant and/or massive modifications of HL gravity. The apparent noncommutativity and breaking of Lorentz invariance by quantum effects can be encoded into fibers of noncommutative tangent Lorentz bundles for corresponding "partner" anisotropically induced theories. We show how the constructions can be extended to include conjectured covariant reonormalizable models with...

Scattering and short-distance properties in field theory models

International Nuclear Information System (INIS)

Iagolnitzer, D.

1987-01-01

The aim of constructive field theory is not only to define models but also to establish their general properties of physical interest. We here review recent works on scattering and on short-distance properties for weakly coupled theories with mass gap such as typically P(φ) in dimension 2, φ 4 in dimension 3 and the (renormalizable, asymptotically free) massive Gross-Neveu (GN) model in dimension 2. Many of the ideas would apply similarly to other (possibly non renormalizable) theories that might be defined in a similar way via phase-space analysis

Towards quantum gravity via quantum field theory. Problems and perspectives

Energy Technology Data Exchange (ETDEWEB)

Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)

2016-07-01

General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.

Renormalizability of N = 1/2 Wess-Zumino model in superspace

International Nuclear Information System (INIS)

Romagnoni, Alberto

2003-01-01

In this letter we use the spurion field approach adopted in [6] in order to show that by adding F and F 2 terms to the original lagrangian, the N 1/2 Wess-Zumino model is renormalizable to all orders in perturbation theory. We reformulate in superspace language the proof given in the recent work [7] in terms of component fields. (author)

Extension of the renormalizability criterion to the case of arbitrary unperturbed Lagrangian

International Nuclear Information System (INIS)

Grozin, A.G.

1979-01-01

Extension of the renormalizability criterium of the perturbation theory is generalized in the case, when an unperturbed lagrangian is not a lagrangian of free fields L 0 . The derivating functional of the Green function, written in the form of a function integral is disintegrated by the perturbed lagrangian L 1 when building the perturbation theory. Described are ultraviolet divergences and possibilities of their elimination in eucledian space. The criterion permits to state extension renormalizability of the perturbation theory for eVery point L 0 and the direction L 1 assigned in this point in linear space of different lagrangians. According to the Weinberg theorem the grade asymptotics of Green functions is not changed at slight shift from the initial point in the supernormalized direction. For any point and any direction the extension of the perturbation theory is supernormalized in this space

Quantum field theory with infinite component local fields as an alternative to the string theories

Science.gov (United States)

Krasnikov, N. V.

1987-09-01

We show that the introduction of the infinite component local fields with higher-order derivatives in the interaction makes the theory completely ultraviolet finite. For the γ5-anomalous theories the introduction of the infinite component field makes the theory renormalizable or even superrenormalizable. I am indebted to J. Ambjōrn, P. Di Vecchia, H.B. Nielsen and L. Rozhansky for useful discussions. It is a pleasure to thank the Niels Bohr Institute (Copenhagen) where this work was completed for kind hospitality.

Field theories with subcanonical fields

International Nuclear Information System (INIS)

Bigi, I.I.Y.

1976-01-01

The properties of quantum field theories with spinor fields of dimension less than the canonical value of 3/2 are studied. As a starting point for the application of common perturbation theory we look for the linear version of these theories. A gange-interaction is introduced and with the aid of power counting the renormalizability of the theory is shown. It follows that in the case of a spinor-field with negative dimension renormalization can only be attained if the interaction has a further symmetry. By this symmetry the theory is determined in an unequivocal way. The gange-interaction introduced in the theory leads to a spontaneous breakdown of scale invariance whereby masses are produced. At the same time the spinor-field operators can now be separated in two orthogonal sections with opposite norm. It is proposed to use the section with negative (positive) norm to describe hadrons (leptons) respectively. (orig./WL) [de

Renormalization of gauge theories in the background-field approach arXiv

CERN Document Server

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.

Renormalization in the stochastic quantization of field theories

International Nuclear Information System (INIS)

Brunelli, J.C.

1991-01-01

In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)

Abelian embedding formulation of the Stueckelberg model and its power-counting renormalizable extension

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

Perturbation Theory of Massive Yang-Mills Fields

Science.gov (United States)

Veltman, M.

1968-08-01

Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.

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

Gaussian processes and constructive scalar field theory

International Nuclear Information System (INIS)

Benfatto, G.; Nicolo, F.

1981-01-01

The last years have seen a very deep progress of constructive euclidean field theory, with many implications in the area of the random fields theory. The authors discuss an approach to super-renormalizable scalar field theories, which puts in particular evidence the connections with the theory of the Gaussian processes associated to the elliptic operators. The paper consists of two parts. Part I treats some problems in the theory of Gaussian processes which arise in the approach to the PHI 3 4 theory. Part II is devoted to the discussion of the ultraviolet stability in the PHI 3 4 theory. (Auth.)

Finiteness of quantum field theories and supersymmetry

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We study the consequences of finiteness for a general renormalizable quantum field theory by analysing the finiteness conditions resulting from the requirement of absence of divergent contributions to the renormalizations of the parameters of an arbitrary gauge theory. In all cases considered, the well-known two-loop finite supersymmetric theories prove to be the unique solution of the finiteness criterion. (Author)

Super-renormalizable or finite Lee–Wick quantum gravity

Directory of Open Access Journals (Sweden)

Leonardo Modesto

2016-08-01

Full Text Available We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2=0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee–Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named “anti-gravitons” because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee–Wick standard model of particle physics.

Analysis of interacting quantum field theory in curved spacetime

International Nuclear Information System (INIS)

Birrell, N.D.; Taylor, J.G.

1980-01-01

A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green's functions are derived, special attention being paid to the possibility that the ''in'' and ''out'' vacuum states may not be equivalent. Green's functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for lambdaphi 3 /sub() 4,6/ field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, phi 3 /sub( 4 ) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes

Algebraic renormalization of Yang-Mills theory with background field method

International Nuclear Information System (INIS)

Grassi, P.A.

1996-01-01

In this paper the renormalizability of Yang-Mills theory in the background gauge fixing is studied. By means of Ward identities of background gauge invariance and Slavnov-Taylor identities, in a regularization-independent way, the stability of the model under radiative corrections is proved and its renormalizability is verified. In particular, it is shown that the splitting between background and quantum field is stable under radiative corrections and this splitting does not introduce any new anomalies. (orig.)

Extended BPH renormalization of cutoff scalar field theories

International Nuclear Information System (INIS)

Chalmers, G.

1996-01-01

We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg close-quote s convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green close-quote s functions are the same as in ordinary Φ 4 theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group. copyright 1996 The American Physical Society

Calculating Casimir energies in renormalizable quantum field theory

International Nuclear Information System (INIS)

Milton, Kimball A.

2003-01-01

Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges were studied by several authors. Quite recently, Graham et al. have reexamined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well known that in two space dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general spatial dimension D not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for curved boundaries. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in D and in three dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations

Effective Field Theories and the Role of Consistency in Theory Choice

CERN Document Server

Wells, James D

2012-01-01

Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the importance of these attributes pales in comparison with consistency, both observational and mathematical consistency, which propels the effective theory to be superior to its simpler truncated version of finite terms, whether that theory be renormalizable (e.g., Standard Model of particle physics) or nonrenormalizable (e.g., gravity). Some implications for the Large Hadron Collider and beyond are discussed, including comments on how directly acknowledging the preeminence of consistency can affect future theory work.

Neutrix calculus and finite quantum field theory

International Nuclear Information System (INIS)

Ng, Y Jack; Dam, H van

2005-01-01

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like quantum electrodynamics are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT, obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework. (letter to the editor)

Schroedinger representation in quantum field theory

International Nuclear Information System (INIS)

Luescher, M.

1985-01-01

Until recently, the Schroedinger representation in quantum field theory had not received much attention, even more so because there were reasons to believe that in the presence of interactions it did not exist in a mathematically well-defined sense. When Symanzik set out to solve this problem, he was motivated by a special 2-dimensional case, the relativistic string model, in which the Schroedinger wave functionals are the primary objects of physical interest. Also, he knew that if it were possible to demonstrate the existence of the Schroedinger representation, the (then unproven) ultraviolet finiteness of the Casimir force in renormalizable quantum field theories would probably follow. (orig./HSI)

High-energy behavior of field-strength interactions

International Nuclear Information System (INIS)

Levin, D.N.

1976-01-01

It is known that spontaneously broken gauge theories are the only renormalizable theories of massive spin-one particles with mass dimension less than or equal to 4. This paper describes a search for renormalizable interactions with higher mass dimension. Specifically, we examine the high-energy behavior of a class of models which involve field-strength interactions. Power counting shows that the high-energy behavior of these models is no worse than the naively estimated high-energy behavior of a gauge theory in the U gauge. Therefore, there may be a ''soft'' symmetry-breaking mechanism (for instance, a soft divergence of an antisymmetric tensor current) which enforces renormalizable high-energy behavior in the same way that spontaneously broken gauge invariance guarantees the renormalizability of gauge theories. This hope is supported by the existence of ''gauge theories'' of strings, which describe analogous interactions of strings and field strengths. Unfortunately, this idea is tarnished by explicit calculations in which renormalizability is imposed in the form of unitarity bounds. These unitarity bounds imply that all possible field-strength couplings must be zero and that the remaining interactions describe a spontaneously broken gauge theory. Thus this result supports an earlier conjecture that gauge theories are the only renormalizable theories of massive vector bosons

A Unitary and Renormalizable Theory of the Standard Model in Ghost-Free Light-Cone Gauge

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.

2002-02-15

Light-front (LF) quantization in light-cone (LC) gauge is used to construct a unitary and simultaneously renormalizable theory of the Standard Model. The framework derived earlier for QCD is extended to the Glashow, Weinberg, and Salam (GWS) model of electroweak interaction theory. The Lorentz condition is automatically satisfied in LF-quantized QCD in the LC gauge for the free massless gauge field. In the GWS model, with the spontaneous symmetry breaking present, we find that the 't Hooft condition accompanies the LC gauge condition corresponding to the massive vector boson. The two transverse polarization vectors for the massive vector boson may be chosen to be the same as found in QCD. The non-transverse and linearly independent third polarization vector is found to be parallel to the gauge direction. The corresponding sum over polarizations in the Standard model, indicated by K{sub {mu}{nu}}(k); has several simplifying properties similar to the polarization sum D{sub {mu}{nu}}(k) in QCD. The framework is ghost-free, and the interaction Hamiltonian of electroweak theory can be expressed in a form resembling that of covariant theory, except for few additional instantaneous interactions which can be treated systematically. The LF formulation also provides a transparent discussion of the Goldstone Boson (or Electroweak) Equivalence Theorem, as the illustrations show.

A renormalizable extension of the NJL-model

International Nuclear Information System (INIS)

Langfeld, K.; Kettner, C.; Reinhardt, H.

1996-01-01

The Nambu-Jona-Lasinio model is supplemented by the quark interaction generated by the one-gluon exchange. The employed gluon propagator exhibits the correct large-momentum behavior of QCD, whereas the Landau pole at low energies is screened. The emerging constituent quark model is one-loop renormalizable and interpolates between the phenomenologically successful Nambu-Jona-Lasinio model (modified by a transversal projector) at low energies and perturbative QCD at high momenta. Consequently, the momentum dependence of the quark self-energy at high energy coincides with the prediction from perturbative QCD. The chiral phase transition is studied in dependence on the low-energy four-quark interaction strength in the Dyson-Schwinger equation approach. The critical exponents of the quark self-energy and the quark condensate are obtained. The latter exponent deviates from the NJL-result. Pion properties are addressed by means of the Bethe-Salpeter equation. The validity of the Gell-Mann-Oakes-Renner relation is verified. Finally, we study the conditions under which the Nambu-Jona-Lasinio model is a decent approximation to our renormalizable theory as well as the shortcoming of the NJL-model due to its inherent non-renormalizability. (orig.)

Microcanonical quantum field theory

International Nuclear Information System (INIS)

Strominger, A.

1983-01-01

Euclidean quantum field theory is equivalent to the equilibrium statistical mechanics of classical fields in 4+1 dimensions at temperature h. It is well known in statistical mechanics that the theory of systems at fixed temperature is embedded within the more general and fundamental theory of systems at fixed energy. We therefore develop, in precise analogy, a fixed action (macrocanonical) formulation of quantum field theory. For the case of ordinary renormalizable field theories, we show (with one exception) that the microcanonical is entirely equivalent to the canonical formulation. That is, for some particular fixed value of the total action, the Green's functions of the microcanonical theory are equal, in the bulk limit, to those of the canonical theory. The microcanonical perturbation expansion is developed in some detail for lambdaphi 4 . The particular value of the action for which the two formulations are equivalent can be calculated to all orders in perturbation theory. We prove, using Lehmann's Theorem, that this value is one-half Planck unit per degree of freedom, if fermionic degrees of freedom are counted negatively. This is the 4+1 dimensional analog of the equipartition theorem. The one exception to this is supersymmetric theories. A microcanonical formulation exists if and only if supersymmetry is broken. In statistical mechanics and in field theory there are systems for which the canonical description is pathological, but the microcanonical is not. An example of such a field theory is found in one dimension. A semiclassical expansion of the microcanonical theory is well defined, while an expansion of the canonical theory is hoplessly divergent

Canonical quantum theory of gravitational field with higher derivatives

International Nuclear Information System (INIS)

Kawasaki, Shoichiro; Kimura, Tadahiko; Kitago, Koichi.

1981-01-01

A renormalizable gravitational theory with higher derivatives is canonically quantized in the Landau gauge. Field equations and various equal-time commutation relations are explicitly given. The main results obtained in this work are 1) the equal-time commutation relations involving b sub(μ) exhibit the tensor-like behaviour and 2) the theory has the 16-dimensional Poincare-like superalgebra. These results are just the same as those discovered by Nakanishi in the Einstein case. (author)

Infrared problems in field perturbation theory

International Nuclear Information System (INIS)

David, Francois.

1982-12-01

The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr

Renormalization of quantum electrodynamics in an arbitrarily strong time independent external field. [Perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Dosch, H G [Heidelberg Univ. (F.R. Germany). Inst. fuer Theoretische Physik; Mueller, V F [Trier-Kaiserslautern Univ., Kaiserslautern (F.R. Germany). Fachbereich Physik

1975-01-01

Extending the inductive renormalization procedure of Epstein and Glaser which is essentially based on locality, we show that quantum electrodynamics in an external time independent electromagnetic field has a renormalizable formal perturbation expansion. The interaction involving the quantized radiation field but not the action of the external field is treated by perturbation theory. It turns out that vacuum polarization is undetermined in the framework of such a theory.

Quantum field theory in flat Robertson-Walker space-time functional Schrodinger picture

International Nuclear Information System (INIS)

Pi, S.Y.

1990-01-01

Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schrodinger picture provides a useful description. This paper discusses free and self-interacting bosonic quantum field theories: Schrodinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schrodinger picture. The technique introduced can be used to study various dynamical questions in early universe processes

Quantum field theory in flat Robertson-Walker space-time functional Schroedinger picture

International Nuclear Information System (INIS)

Pi, S.Y.

1989-01-01

Quantum field theory in Robertson-Walker space-time is intrinsically time-dependent and the functional Schroedinger picture provides a useful description. We discuss free and self-interacting bosonic quantum field theories: Schroedinger picture quantization, time-dependent Gaussian approximations based on variational principles describing time evolution of pure and mixed states, and renormalizability of the Schroedinger picture. The techniques introduced can be used to study various dynamical questions in early universe processes. (author)

Irreversibility and higher-spin conformal field theory

CERN Document Server

Anselmi, D

2000-01-01

I discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particular, the Newton constant should be viewed as a low-energy effect of the RG scale. This approach leads naturally to consider higher-spin conformal field theories, which are here classified, as candidate high-energy theories. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. The central charges c and a are well defined and positive. I calculate their values and study the operator-product structure. Fermionic theories have no gauge invariance and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a...

Long-range interactions in lattice field theory

International Nuclear Information System (INIS)

Rabin, J.M.

1981-06-01

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations

Long-range interactions in lattice field theory

Energy Technology Data Exchange (ETDEWEB)

Rabin, J.M.

1981-06-01

Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.

Exactly renormalizable model in quantum field theory. II. The physical-particle representation

NARCIS (Netherlands)

Ruijgrok, Th.W.

1958-01-01

For the simplified model of quantum field theory discussed in a previous paper it is shown how the physical particles can be properly described by means of the so-called asymptotically stationary (a.s.) states. It is possible by formulating the theory in terms of these a.s. states to express it

Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering

International Nuclear Information System (INIS)

Pavon Valderrama, M.

2011-01-01

We study the perturbative renormalizability of chiral two-pion exchange for singlet and triplet channels within effective field theory, provided that the one-pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed to obtain finite results when the cutoff is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that perturbative chiral two-pion exchange reproduce the data up to a center-of-mass momentum of k∼200-300 MeV in the singlet channel and k∼300-400 MeV in the triplet.

Twisted supersymmetry: Twisted symmetry versus renormalizability

International Nuclear Information System (INIS)

Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja

2011-01-01

We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.

Off-shell renormalization in Higgs effective field theories

Science.gov (United States)

Binosi, Daniele; Quadri, Andrea

2018-04-01

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.

Worldline approach to noncommutative field theory

International Nuclear Information System (INIS)

Bonezzi, R; Corradini, O; Viñas, S A Franchino; Pisani, P A G

2012-01-01

The study of the heat-trace expansion in non-commutative field theory has shown the existence of Moyal non-local Seeley–DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive at a master formula for the n-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the non-commutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other non-local operators. (paper)

Canonical quantum theory of gravitational field with higher derivatives, 3

International Nuclear Information System (INIS)

Kawasaki, Shoichiro; Kimura, Tadahiko

1983-01-01

A formulation which is invariant under an additional BRS transformation with nilpotency of order two is presented for the canonical theory of the renormalizable quantum gravity with higher derivatives. The canonical quantization is carried out and various equal time (anti-) commutation relations are derived. The asymptotic fields are reanalyzed. The physical particle contents are just the same as those obtained in previous papers. (author)

A simple proof of orientability in colored group field theory.

Science.gov (United States)

Caravelli, Francesco

2012-01-01

Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates colors to the faces of the simplices. The theory of crystallizations is instead a field at the boundary between graph theory and combinatorial topology and deals with n-simplices as colored graphs. Several techniques have been introduced in order to study the topology of the pseudo-manifold associated to the colored graph. Although of the similarity between colored group field theory and the theory of crystallizations, the connection between the two fields has never been made explicit. In this short note we use results from the theory of crystallizations to prove that color in group field theories guarantees orientability of the piecewise linear pseudo-manifolds associated to each graph generated perturbatively. Colored group field theories generate orientable pseudo-manifolds. The origin of orientability is the presence of two interaction vertices in the action of colored group field theories. In order to obtain the result, we made the connection between the theory of crystallizations and colored group field theory.

Is there a quantum theory of gravity

International Nuclear Information System (INIS)

Strominger, A.

1984-01-01

The paper concerns attempts to construct a unitary, renormalizable quantum field theory of gravity. Renormalizability and unitarity in quantum gravity; the 1/N expansion; 1/D expansions; and quantum gravity and particle physics; are all discussed. (U.K.)

Field theories with multiple fermionic excitations

International Nuclear Information System (INIS)

Crawford, J.P.

1978-01-01

The reason for the existence of the muon has been an enigma since its discovery. Since that time there has been a continuing proliferation of elementary particles. It is proposed that this proliferation of leptons and quarks is comprehensible if there are only four fundamental particles, the leptons ν/sub e/ and e - , and the quarks u and d. All other leptons and quarks are imagined to be excited states of these four fundamental entities. Attention is restricted to the charged leptons and the electromagnetic interactions only. A detailed study of a field theory in which there is only one fundamental charged fermionic field having two (or more) excitations is made. When the electromagnetic interactions are introduced and the theory is second quantized, under certain conditions this theory reproduces the S matrix obtained from usual OED. In this case no electromagnetic transitions are allowed. A leptonic charge operator is defined and a superselection rule for this leptonic charge is found. Unfortunately, the mass spectrum cannot be obtained. This theory has many renormalizable generalizations including non-abelian gauge theories, Yukawa-type theories, and Fermi-type theories. Under certain circumstances the Yukawa- and Fermi-type theories are finite in perturbation theory. It is concluded that there are no fundamental objections to having fermionic fields with more than one excitation

Field theory methods applied for the study of superconductivity in one-dimensional systems

International Nuclear Information System (INIS)

Martins, M.J.

1986-01-01

It is shown that the Froehlich's hamiltonian in one spatial dimension is identical to that of an exactly solvable field Theory. The spectrum of the theory is computed. A critical coupling is found above which the system becomes unstable, indicating a superconducting transition. It is also proposed and investigated a renormalizable relativistic field theory model in two space-time dimensions, with quartic self-interaction among N species of fermions, which undergoes dynamical generation of a superconducting gap and is asymptotically free. A finite temperature is introduced and, for N -> ∞ a critical value T c is found above which the gap vanishes. (author)

Models with oscillator terms in noncommutative quantum field theory

International Nuclear Information System (INIS)

Kronberger, E.

2010-01-01

The main focus of this Ph.D. thesis is on noncommutative models involving oscillator terms in the action. The first one historically is the successful Grosse-Wulkenhaar (G.W.) model which has already been proven to be renormalizable to all orders of perturbation theory. Remarkably it is furthermore capable of solving the Landau ghost problem. In a first step, we have generalized the G.W. model to gauge theories in a very straightforward way, where the action is BRS invariant and exhibits the good damping properties of the scalar theory by using the same propagator, the so-called Mehler kernel. To be able to handle some more involved one-loop graphs we have programmed a powerful Mathematica package, which is capable of analytically computing Feynman graphs with many terms. The result of those investigations is that new terms originally not present in the action arise, which led us to the conclusion that we should better start from a theory where those terms are already built in. Fortunately there is an action containing this complete set of terms. It can be obtained by coupling a gauge field to the scalar field of the G.W. model, integrating out the latter, and thus 'inducing' a gauge theory. Hence the model is called Induced Gauge Theory. Despite the advantage that it is by construction completely gauge invariant, it contains also some unphysical terms linear in the gauge field. Advantageously we could get rid of these terms using a special gauge dedicated to this purpose. Within this gauge we could again establish the Mehler kernel as gauge field propagator. Furthermore we where able to calculate the ghost propagator, which turned out to be very involved. Thus we were able to start with the first few loop computations showing the expected behavior. The next step is to show renormalizability of the model, where some hints towards this direction will also be given. (author) [de

On the problem of existence of quantum field theory

International Nuclear Information System (INIS)

Chaichian, M.; Hayashi, M.; Nelipa, N.F.; Pukhov, E.A.

1978-01-01

Existence of quantum field theory is considered for the four-dimensional phi 3 -model. The mathematical tool of contraction mapping principle is used to investigate the question of existence of solution for the infinite system of coupled equations for the Green functions of the theory in the Euclidean region. Formulation of the problem for this model with one divergent part is interesting in itself and provides the first attempt towards the study of other renormalizable quantum field theory models with infinite number of divergent graphs. For sufficiently small values of coupling constant, the theory has a unique solution for the truncated system of equations for the Green functions. However, for the complete, infinite set of equations, the Banach fixed point theorem admits a solution only when the coupling constant tends to zero. Possible reasons for such a result are discussed. (author)

Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

Breaking democracy with non renormalizable mass terms

CERN Document Server

Silva-Marcos, Joaquim I

2001-01-01

The exact democratic structure for the quark mass matrix, resulting from the action of the family symmetry group $A_{3L}\\times A_{3R}$, is broken by the vacuum expectation values of heavy singlet fields appearing in non renormalizable dimension 6 operators. Within this specific context of breaking of the family symmetry we formulate a very simple ansatz which leads to correct quark masses and mixings.

Non-renormalizability of supersymmetric non-linear sigma models in four dimensions

International Nuclear Information System (INIS)

Spence, B.

1985-01-01

The one-loop, on-shell, ultraviolet-divergent part of the effective action is calculated for the N=1 and 2 supersymmetric non-linear sigma models in four dimensions. These infinities cannot be absorbed into a redefinition of the bare Kaehler potential and the theories are not renormalizable. (orig.)

Cancellation of infrared and collinear singularities in relativistic thermal field theories. Pt. 2

International Nuclear Information System (INIS)

Le Bellac, M.; Reynaud, P.

1992-01-01

We study the infrared and collinear divergences of a renormalizable scalar field theory at finite temperature. We give the final results of an investigation undertaken in a previous work by showing the complete cancellation of all divergences at two-loop order in a physical process. This result makes the validity of the Kinoshita-Lee-Nauenberg theorem at finite temperature extremely plausible. (orig.)

Constructive tensorial group field theory II: the {U(1)-T^4_4} model

Science.gov (United States)

Lahoche, Vincent

2018-05-01

In this paper, we continue our program of non-pertubative constructions of tensorial group field theories (TGFT). We prove analyticity and Borel summability in a suitable domain of the coupling constant of the simplest super-renormalizable TGFT which contains some ultraviolet divergencies, namely the color-symmetric quartic melonic rank-four model with Abelian gauge invariance, nicknamed . We use a multiscale loop vertex expansion. It is an extension of the loop vertex expansion (the basic constructive technique for non-local theories) which is required for theories that involve non-trivial renormalization.

Renormalization of gauge theories of weak interactions

International Nuclear Information System (INIS)

Lee, B.W.

1973-01-01

The renormalizability of spontaneously broken gauge theories is discussed. A brief outline of the motivation for such an investigation is given, and the manner in which the renormalizability of such theories is proven is described. The renormalizability question of the unbroken gauge theory is considered, and the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories) is considered. (U.S.)

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

Energy Technology Data Exchange (ETDEWEB)

Chankowski, Piotr H. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Lewandowski, Adrian [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut),Mühlenberg 1, D-14476 Potsdam (Germany); Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland); Meissner, Krzysztof A. [Institute of Theoretical Physics, Faculty of Physics, University of Warsaw,Pasteura 5, 02-093 Warsaw (Poland)

2016-11-18

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional (MS)-bar scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the (MS)-bar scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

Unitary unified field theories

International Nuclear Information System (INIS)

Sudarshan, E.C.G.

1976-01-01

This is an informal exposition of some recent developments. Starting with an examination of the universality of electromagnetic and weak interactions, the attempts at their unification are outlined. The theory of unitary renormalizable self-coupled vector mesons with dynamical sources is formulated for a general group. With masses introduced as variable parameters it is shown that the theory so defined is indeed unitary. Diagrammatic rules are developed in terms of a chosen set of fictitious particles. A number of special examples are outlined including a theory with strongly interacting vector and axial vector mesons and weak mesons. Applications to weak interactions of strange particles is briefly outlined. (Auth.)

Quantum field theory II introductions to quantum gravity, supersymmetry and string theory

CERN Document Server

Manoukian, Edouard B

2016-01-01

This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author in...

Clifford algebra in finite quantum field theories

International Nuclear Information System (INIS)

Moser, M.

1997-12-01

We consider the most general power counting renormalizable and gauge invariant Lagrangean density L invariant with respect to some non-Abelian, compact, and semisimple gauge group G. The particle content of this quantum field theory consists of gauge vector bosons, real scalar bosons, fermions, and ghost fields. We assume that the ultimate grand unified theory needs no cutoff. This yields so-called finiteness conditions, resulting from the demand for finite physical quantities calculated by the bare Lagrangean. In lower loop order, necessary conditions for finiteness are thus vanishing beta functions for dimensionless couplings. The complexity of the finiteness conditions for a general quantum field theory makes the discussion of non-supersymmetric theories rather cumbersome. Recently, the F = 1 class of finite quantum field theories has been proposed embracing all supersymmetric theories. A special type of F = 1 theories proposed turns out to have Yukawa couplings which are equivalent to generators of a Clifford algebra representation. These algebraic structures are remarkable all the more than in the context of a well-known conjecture which states that finiteness is maybe related to global symmetries (such as supersymmetry) of the Lagrangean density. We can prove that supersymmetric theories can never be of this Clifford-type. It turns out that these Clifford algebra representations found recently are a consequence of certain invariances of the finiteness conditions resulting from a vanishing of the renormalization group β-function for the Yukawa couplings. We are able to exclude almost all such Clifford-like theories. (author)

1/N perturbation theory and quantum conservation laws for supersymmetrical chiral field. 2

International Nuclear Information System (INIS)

Aref'eva, I.Ya.; Krivoshchekov, V.K.; Medvedev, P.B.; Gosudarstvennyj Komitet Standartov Soveta Ministrov SSSR, Moscow; Gosudarstvennyj Komitet po Ispol'zovaniyu Atomnoj Ehnergii SSSR, Moscow. Inst. Teoreticheskoj i Ehksperimental'noj Fiziki)

1980-01-01

The renormalizability of the supersymmetric chiral model (supersymmetric nonlinear σ-model) is proved in the framework of the 1/N perturbation theory expansion proposed in the previous paper. The renormalizability proof is essentially based on the quantum supersymmetric chirality condition. The supersymmetric formulation of equations of motion is given. The first non-trivial quantum conservation laws are derived

Two loop effective Kahler potential of (non)-renormalizable supersymmetric models

International Nuclear Information System (INIS)

Groot Nibbelink, S.; Nyawelo, T.S.

2005-10-01

We perform a supergraph computation of the effective Kahler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kahler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kahler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics. (author)

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

International Nuclear Information System (INIS)

Baker, G.A. Jr.

1975-01-01

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

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)

Gauge theory and renormalization

NARCIS (Netherlands)

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

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

Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory

CERN Multimedia

CERN. Geneva

2015-01-01

The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.

Instantons in Lifshitz field theories

Energy Technology Data Exchange (ETDEWEB)

Fujimori, Toshiaki; Nitta, Muneto [Department of Physics, and Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)

2015-10-05

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for “the superpotential” defining “the detailed balance condition”. The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.

Irreversibility and higher-spin conformal field theory

Science.gov (United States)

Anselmi, Damiano

2000-08-01

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.

Renormalizability of a quark-gluon model with soft BRST breaking in the infrared region

CERN Document Server

Baulieu, L; Gomez, A J; Lemes, V E R; Sobreiro, R F; Sorella, S P

2010-01-01

We prove the renormalizability of a quark-gluon model with a soft breaking of the BRST symmetry, which accounts for the modification of the large distance behavior of the quark and gluon correlation functions. The proof is valid to all orders of perturbation theory, by making use of softly broken Ward identities.

Cosmological singularities in string and M-theory cosmology

NARCIS (Netherlands)

Vazquez-Mozo, M.A.; Ibanez, J.

2000-01-01

I discuss the point of view that non-renormalizability in General Relativity is a consequence of dealing with a low-energy effective field theory of the gravitational field, and how Einstein-Brans-Dicke gravity is retrieved from string/M-theory at low energies. After examining the role of stringy

The renormalizability and the asymptotically free behaviour of the extended Wess-Zumino models

International Nuclear Information System (INIS)

Ha Huy Bang; Hoang Ngoc Long.

1989-09-01

By using the path integral method for superfields the Ward identities and the Callan-Symanzik equations for the extended Wess-Zumino models are derived. From these the renormalizability and the asymptotically behaviour of all the extended Wess-Zumino models in d = 2,4 (mod 8)-dimensional space-time are studied. In particular, we will come to the conclusion that the supersymmetric Ward identities together with the broken chiral Ward identities imply that a single wave function renormalization is sufficient to renormalize the theory and that the theory is not asymptotically free. (author). 16 refs

Renormalizability of Reggeon field theory taking into account thresholds and ''mass'' terms at D = 2

International Nuclear Information System (INIS)

Eremyan, S.S.; Nazaryan, A.E.

1982-01-01

It is shown that the inclusion of the Reggeon production thresholds xi 0 = 1n(M 2 /s 0 )roughly-equal2 in Reggeon field theory causes the epsilon-c expansion to become analytic at epsilon-c = 2 and it becomes possible to simultaneously take epsilon-c → 2 and E → 0, which corresponds to the physical dimensionality of space in the limit of asymptotic energies. The introduction of thresholds makes it easier to carry out perturbative calculations at D = 2 by removing the ultraviolet divergences of the theory and is useful for a smooth joining of the perturbative and asymptotic solutions

Topics in field theory-higher spins, CFT, and gravity

International Nuclear Information System (INIS)

Yang, Z.

1990-01-01

Several topics in field theory are investigated. (1) Massive higher spin actions are obtained as gauge theories from the dimensional reduction of the corresponding massless ones. (2) The author considers a model of spin4 and spin2 interaction through the Bel-Robinson tensor of spin2 field, which in conserved at free level. The coupling is inconsistent, yet there are indications that adding still higher spin couplings would be a promising direction to achieve consistency. (3) Energy and Stability of Einstein-Gauss-Bonnet models of gravity are studied. It is shown that flat space is stable while AdS is not. (4) Gauged Wess-Zumino-Witten models are studied in detail. The equivalence to GKO construction of conformal field theory is considered. BRST quantization of the models is given. (5) Nonrenormalizability of quantum gravity is, in the binomial first order metric formulation, traced to a mismatch between the symmetries of its quadratic and cubic term. (6) The possibility that the gravitational model defined in D = 3 by an action which is the sum of Einstein and Chern-Simons terms is a viable quantum theory is investigated. It is shown that it is compatible with power-counting renormalizability. Gauge invariant regularizations, however, have not been found to exist. Detailed BRS analysis shows that there are possible anomalies

N=2, 4 supersymmetric gauge field theory in two-time physics

International Nuclear Information System (INIS)

Bars, Itzhak; Kuo, Y.-C.

2009-01-01

In the context of two-time physics in 4+2 dimensions we construct the most general N=2, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. When the equations of motion are used the SUSY transformations close to the supergroup SU(2,2|N) with N=1, 2, 4. The SU(2,2)=SO(4,2) subsymmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat 3+1 dimensions coincide with the well known counterpart N=1, 2, 4 supersymmetric massless renormalizable field theories in 3+1 dimensions. It is expected that our more symmetric new structures in 4+2 spacetime may be useful for nonperturbative or exact solutions of these theories.

From topological quantum field theories to supersymmetric gauge theories; Des theories quantiques de champ topologiques aux theories de jauge supersymetriques

Energy Technology Data Exchange (ETDEWEB)

Bossard, G

2007-10-15

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 {beta} 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)

Infrared finiteness in Yang--Mills theories

International Nuclear Information System (INIS)

Appelquist, T.; Carazzone, J.; Kluberg-Stern, H.; Roth, M.

1976-01-01

The infrared divergences of renormalizable theories with coupled massless fields (in particular, the Yang--Mills theory) are shown to cancel for transition probabilities corresponding to finite-energy-resolution detectors, just as in quantum electrodynamics. This result is established through lowest nontrivial order in perturbation theory for the detection of massive muons in a quantum electrodynamic theory containing massless electrons or the detection of massive quarks in a Yang--Mills theory

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

Effective field theories in the large-N limit

International Nuclear Information System (INIS)

Weinberg, S.

1997-01-01

Various effective field theories in four dimensions are shown to have exact nontrivial solutions in the limit as the number N of fields of some type becomes large. These include extended versions of the U (N) Gross-Neveu model, the nonlinear O(N) σ model, and the CP N-1 model. Although these models are not renormalizable in the usual sense, the infinite number of coupling types allows a complete cancellation of infinities. These models provide qualitative predictions of the form of scattering amplitudes for arbitrary momenta, but because of the infinite number of free parameters, it is possible to derive quantitative predictions only in the limit of small momenta. For small momenta the large-N limit provides only a modest simplification, removing at most a finite number of diagrams to each order in momenta, except near phase transitions, where it reduces the infinite number of diagrams that contribute for low momenta to a finite number. copyright 1997 The American Physical Society

A proposal of a renormalizable Nambu-Jona-Lasinio model

Science.gov (United States)

Cabo Montes de Oca, Alejandro

2018-03-01

A local and gauge invariant gauge field model including Nambu-Jona-Lasinio (NJL) and QCD Lagrangian terms in its action is introduced. Surprisingly, it becomes power counting renormalizable. This occurs thanks to the presence of action terms which modify the quark propagators, to become more decreasing that the Dirac one at large momenta in a Lee-Wick form, implying power counting renormalizability. The appearance of finite quark masses already in the tree approximation in the scheme is determined by the fact that the new action terms explicitly break chiral invariance. In this starting work we present the renormalized Feynman diagram expansion of the model and derive the formula for the degree of divergence of the diagrams. An explanation for the usual exclusion of the added Lagrangian terms is presented. In addition, the primitíve divergent graphs are identified. We start their evaluation by calculating the simpler contribution to the gluon polarization operator. The divergent and finite parts both result transverse as required by gauge invariance. The full evaluation of the various primitive divergences, which are required for completely defining the counterterm Feynman expansion will be considered in coming works, for further allowing to discuss the flavour symmetry breaking and unitarity.

Pion propagator in relativistic quantum field theories of the nuclear many-body problem

International Nuclear Information System (INIS)

Matsui, T.; Serot, B.D.

1982-01-01

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models; the scalar-vector theory of Walecka, extended to include π and rho mesons in a non-chiral fashion, and the linear sigma-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pions propagator is evaluated in the one-nucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual NN-bar loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the Lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model Lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored

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)

Nonperturbative bounds on in cutoff (lambdaphi/sup n/)/sub d/ field theory

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

Stochastic quantization is used to obtain upper and lower bounds on the vacuum expectation value of phi/sup n/ in a cutoff lambdaphi/sup n/ scalar theory in d dimensions. These determine the behavior of as the cutoff is removed. The results are given by formulas which depend on whether the values of n and d define a perturbatively superrenormalizable, strictly renormalizable, or nonrenormalizable theory

Possible role of torsion in gravitational theories

International Nuclear Information System (INIS)

Nieh, H.T.

1983-01-01

Torsion is of interest in an indirect way, in that it has the potential of being an important ingredient in a future successful quantum theory of gravitation. Einstein's theory of gravitation, despite its simplicity and elegance, and its successes in large-scale gravitational phenomena, can only be regarded as a macroscopic classical theory. It is a non-renormalizable quantum field theory, and, therefore, lacks the status of a good microscopic theory. It is the search for a successful quantum field theory of gravitation that poses as one of the great challenges to theoretical physics today. (Auth.)

Field theory methods applied for the study of superconductivity in one-dimensional systems; Metodos de teoria de campos no estudo da supercondutividade em sistemas unidimensionais

Energy Technology Data Exchange (ETDEWEB)

Martins, M J

1987-12-31

It is shown that the Froehlich`s hamiltonian in one spatial dimension is identical to that of an exactly solvable field Theory. The spectrum of the theory is computed. A critical coupling is found above which the system becomes unstable, indicating a superconducting transition. It is also proposed and investigated a renormalizable relativistic field theory model in two space-time dimensions, with quartic self-interaction among N species of fermions, which undergoes dynamical generation of a superconducting gap and is asymptotically free. A finite temperature is introduced and, for N -> {infinity} a critical value T{sub c} is found above which the gap vanishes. (author).

Renormalizable N=2 supersymmetric and gauge invariant interactions from the N=2 harmonic superspace with central charges

International Nuclear Information System (INIS)

Saidi, E.H.

1986-04-01

The N=2 harmonic-superspace in the presence of central charges is developed. Renormalizable interactions unusual in N=2 supersymmetric theories, are derived in a consistent way. Symmetries generated by the central charges are discussed. A certain equivalence between N=2 harmonic superspace with and without central charges is established. A non-abelian generalization of the model is given. (author)

Nonperturbative studies of quantum field theories on noncommutative spaces

International Nuclear Information System (INIS)

Volkholz, J.

2007-01-01

This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the λφ 4 model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized λφ 4 model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations. (orig.)

Nonperturbative studies of quantum field theories on noncommutative spaces

Energy Technology Data Exchange (ETDEWEB)

Volkholz, J.

2007-11-16

This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted

Examining a renormalizable supersymmetric SO(10) model

Energy Technology Data Exchange (ETDEWEB)

Chen, Zhi-Yong; Zhang, Da-Xin [Peking University, School of Physics and State Key Laboratory of Nuclear Physics and Technology, Beijing (China)

2017-10-15

We examine a renormalizable SUSY SO(10) model without fine-tuning. We show how to construct MSSM doublets and to predict proton decay. We find that in the minimal set of Yukawa couplings the model is consistent with the experiments, while including 120{sub H} to fit the data there are inconsistencies. (orig.)

Structure of UV divergences in maximally supersymmetric gauge theories

Science.gov (United States)

Kazakov, D. I.; Borlakov, A. T.; Tolkachev, D. M.; Vlasenko, D. E.

2018-06-01

We consider the UV divergences up to sub-subleading order for the four-point on-shell scattering amplitudes in D =8 supersymmetric Yang-Mills theory in the planar limit. We trace how the leading, subleading, etc divergences appear in all orders of perturbation theory. The structure of these divergences is typical for any local quantum field theory independently on renormalizability. We show how the generalized renormalization group equations allow one to evaluate the leading, subleading, etc. contributions in all orders of perturbation theory starting from one-, two-, etc. loop diagrams respectively. We focus then on subtraction scheme dependence of the results and show that in full analogy with renormalizable theories the scheme dependence can be absorbed into the redefinition of the couplings. The only difference is that the role of the couplings play dimensionless combinations like g2s2 or g2t2, where s and t are the Mandelstam variables.

Background field method in gauge theories and on linear sigma models

International Nuclear Information System (INIS)

van de Ven, A.E.M.

1986-01-01

This dissertation constitutes a study of the ultraviolet behavior of gauge theories and two-dimensional nonlinear sigma-models by means of the background field method. After a general introduction in chapter 1, chapter 2 presents algorithms which generate the divergent terms in the effective action at one-loop for arbitrary quantum field theories in flat spacetime of dimension d ≤ 11. It is demonstrated that global N = 1 supersymmetric Yang-Mills theory in six dimensions in one-loop UV-finite. Chapter 3 presents an algorithm which produces the divergent terms in the effective action at two-loops for renormalizable quantum field theories in a curved four-dimensional background spacetime. Chapter 4 presents a study of the two-loop UV-behavior of two-dimensional bosonic and supersymmetric non-linear sigma-models which include a Wess-Zumino-Witten term. It is found that, to this order, supersymmetric models on quasi-Ricci flat spaces are UV-finite and the β-functions for the bosonic model depend only on torsionful curvatures. Chapter 5 summarizes a superspace calculation of the four-loop β-function for two-dimensional N = 1 and N = 2 supersymmetric non-linear sigma-models. It is found that besides the one-loop contribution which vanishes on Ricci-flat spaces, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for superstrings are discussed. Chapters 6 and 7 treat the details of these calculations

In praise of quantum fields

International Nuclear Information System (INIS)

Shirkov, D.V.

1989-08-01

A comprehensive discussion of several topics vital for the structure of a modern Quantum Field Theory are discussed, namely: physical content of the notion of a Quantum Field; meaning of infinite renormalization; renormalizability as quantizability; the influence of several principles of quantum nature (quantizability, gauge dynamics, supersymmetry) on quantum fields dynamics; main trends of QFT evolution; present status of QFT and its frontier role in physics. (author). 15 refs, 1 fig

Energy-momentum tensor in quantum field theory

International Nuclear Information System (INIS)

Fujikawa, K.

1981-01-01

The definition of the energy-momentum tensor as a source current coupled to the background gravitational field receives an important modification in quantum theory. In the path-integral approach, the manifest covariance of the integral measure under general coordinate transformations dictates that field variables with weight 1/2 should be used as independent integration variables. An improved energy-momentum tensor is then generated by the variational derivative, and it gives rise to well-defined gravitational conformal (Weyl) anomalies. In the flat--space-time limit, all the Ward-Takahashi identities associated with space-time transformations including the global dilatation become free from anomalies in terms of this energy-momentum tensor, reflecting the general covariance of the integral measure; the trace of this tensor is thus finite at zero momentum transfer for renormalizable theories. The Jacobian for the local conformal transformation, however, becomes nontrivial, and it gives rise to an anomaly for the conformal identity. All the familiar anomalies are thus reduced to either chiral or conformal anomalies. The consistency of the dilatation and conformal identities at vanishing momentum transfer determines the trace anomaly of this energy-momentum tensor in terms of the renormalization-group b function and other parameters. In contrast, the trace of the conventional energy-momentum tensor generally diverges even at vanishing momentum transfer depending on the regularization scheme, and it is subtractively renormalized. We also explain how the apparently different renormalization properties of the chiral and trace anomalies arise

Properties of nuclear and neutron matter in a relativistic Hartree-Fock theory

International Nuclear Information System (INIS)

Horowitz, C.J.; Serot, B.D.

1983-01-01

Relativistic-Hartree-Fock (HF) equations are derived for an infinite system of mesons and baryons in the framework of a renormalizable relativistic quantum field theory. The derivation is based on a diagrammatic approach and Dyson's equation for the baryon propagator. The result is a set of coupled, nonlinear integral equations for the baryon self-energy with a self-consistency condition on the single-particle spectrum. The HF equations are solved for nuclear and neutron matter in the Walecka model, which contains neutral scalar and vector mesons. After renormalizing model parameters to reproduce nuclear matter saturation properties, HF results at low to moderate densities are similar to those in the mean-field (Hartree) approximation. Self-consistent exchange corrections to the Hartree equation of state become negligible at high densities. Rho- and pi-meson exchanges are incorporated using a renormalizable gauge-theory model. A chiral transformation of the lagrangian is used to replace the pseudoscalar πN coupling with a pseudovector coupling, for which one-pion exchange is a reasonable first approximation. This transformation maintains the model's renormalizability so that corrections may be evaluated. Pion exchange has a small effect on the HF results of the Walecka model and brings HF results in closer in closer agreement with the mean-field theory. The diagrammatic techniques used here retain the mesonic degrees of freedom and are simple enough to be extended to more refined self-consistent approximations. (orig.)

Feynman rules for the Standard Model Effective Field Theory in R ξ -gauges

Science.gov (United States)

Dedes, A.; Materkowska, W.; Paraskevas, M.; Rosiek, J.; Suxho, K.

2017-06-01

We assume that New Physics effects are parametrized within the Standard Model Effective Field Theory (SMEFT) written in a complete basis of gauge invariant operators up to dimension 6, commonly referred to as "Warsaw basis". We discuss all steps necessary to obtain a consistent transition to the spontaneously broken theory and several other important aspects, including the BRST-invariance of the SMEFT action for linear R ξ -gauges. The final theory is expressed in a basis characterized by SM-like propagators for all physical and unphysical fields. The effect of the non-renormalizable operators appears explicitly in triple or higher multiplicity vertices. In this mass basis we derive the complete set of Feynman rules, without resorting to any simplifying assumptions such as baryon-, lepton-number or CP conservation. As it turns out, for most SMEFT vertices the expressions are reasonably short, with a noticeable exception of those involving 4, 5 and 6 gluons. We have also supplemented our set of Feynman rules, given in an appendix here, with a publicly available Mathematica code working with the FeynRules package and producing output which can be integrated with other symbolic algebra or numerical codes for automatic SMEFT amplitude calculations.

Fluxes, hierarchies, and metastable vacua in supersymmetric field theories

Energy Technology Data Exchange (ETDEWEB)

Bruemmer, F.

2008-02-06

This thesis concerns topics both in low-energy effective field theories from type IIB superstring flux compactifications and in four-dimensional, rigidly supersymmetric gauge theories. We introduce flux compactifications with so-called ''warped throat'' regions, which lead to large hierarchies of scales in the effective four-dimensional theory. The correspondence between a particular such throat and a five-dimensional Randall-Sundrum-like model is established. We shown how certain string-theoretic features of the compactification, such as moduli stabilization by fluxes or the presence of an unstabilized Kaehler modulus, are incorporated in the five-dimensional picture. The KKLT construction for metastable de Sitter vacua is reviewed, as well as some possible modifications involving spontaneous F-term supersymmetry breaking. For KKLT-like models with their hidden sector localized inside a throat, the mediation of supersymmetry breaking to the visible sector is investigated. We review the mechanism of mixed modulus-anomaly mediation, and show that there can be additional equally important gravity-mediated contributions. We finally turn to the ISS model of metastable dynamical supersymmetry breaking in four dimensions, and present a renormalizable extension which generates a large hierarchy naturally. We also recapitulate how the ISS model may be obtained from a type IIB superstring model. (orig.)

Fluxes, hierarchies, and metastable vacua in supersymmetric field theories

International Nuclear Information System (INIS)

Bruemmer, F.

2008-01-01

This thesis concerns topics both in low-energy effective field theories from type IIB superstring flux compactifications and in four-dimensional, rigidly supersymmetric gauge theories. We introduce flux compactifications with so-called ''warped throat'' regions, which lead to large hierarchies of scales in the effective four-dimensional theory. The correspondence between a particular such throat and a five-dimensional Randall-Sundrum-like model is established. We shown how certain string-theoretic features of the compactification, such as moduli stabilization by fluxes or the presence of an unstabilized Kaehler modulus, are incorporated in the five-dimensional picture. The KKLT construction for metastable de Sitter vacua is reviewed, as well as some possible modifications involving spontaneous F-term supersymmetry breaking. For KKLT-like models with their hidden sector localized inside a throat, the mediation of supersymmetry breaking to the visible sector is investigated. We review the mechanism of mixed modulus-anomaly mediation, and show that there can be additional equally important gravity-mediated contributions. We finally turn to the ISS model of metastable dynamical supersymmetry breaking in four dimensions, and present a renormalizable extension which generates a large hierarchy naturally. We also recapitulate how the ISS model may be obtained from a type IIB superstring model. (orig.)

Lattice gauge theories

International Nuclear Information System (INIS)

Hasenfratz, A.; Hasenfratz, P.

1985-01-01

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

Spontaneous symmetry breaking of the BRST symmetry in presence of the Gribov horizon: Renormalizability

International Nuclear Information System (INIS)

Capri, Marcio; Justo, Igor; Guimaraes, Marcelo; Sorella, Silvio; Dudal, David; Palhares, Leticia

2013-01-01

Full text: In recent years much attention has been devoted to the study of the issue of the Gribov copies and of its relevance for confinement in Yang-Mills theories. The existence of the Gribov copies is a general feature of the gauge-fixing quantization procedure, being related to the impossibility of finding a local gauge condition which picks up only one gauge configuration for each gauge orbit. As it has been shown by Gribov and Zwanziger, a partial solution of the Gribov problem in the Landau gauge can be achieved by restricting the domain of integration in the functional Euclidean integral to the first Gribov horizon. Among the various open aspects of the Gribov-Zwanziger framework, the issue of the BRST symmetry is a source of continuous investigations. In a recent work, we have been able to obtain an equivalent formulation of the Gribov-Zwanziger action which displays an exact BRST symmetry which turns out to be spontaneously broken by the restriction of the domain of integration to the Gribov horizon. In particular, the BRST operator retains the important property of being nilpotent. Moreover, it has also been shown that the Goldstone mode associated to the spontaneous breaking of the BRST symmetry is completely decoupled. The aim of the present work is that of fills up a gap not addressed in the previous work, namely, the renormalizability to all orders of the spontaneous symmetry breaking formulation of the Gribov-Zwanziger theory. As we shall see, the action obtained enjoys a large set of Ward identities which enables to prove that it is, in fact, multiplicatively renormalizable to all orders. (author)

Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

Science.gov (United States)

Lahoche, Vincent; Oriti, Daniele

2017-01-01

We study the renormalization of a general field theory on the homogeneous space (SU(2)/ ≤ft. U(1)\\right){{}× d} with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power counting for arbitrary d. For the case d  =  4, we prove perturbative renormalizability to all orders via multi-scale analysis, study both the renormalized and effective perturbation series, and establish the asymptotic freedom of the model. We also outline a general power counting for the homogeneous space {{≤ft(SO(D)/SO(D-1)\\right)}× d} , of direct interest for quantum gravity models in arbitrary dimension, and point out the obstructions to the direct generalization of our results to these cases.

Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many couplings

International Nuclear Information System (INIS)

Anselmi, Damiano

2003-01-01

I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary spacetime dimensions. I prove that when the spacetime manifold admits a metric of constant curvature, the propagator is not affected by terms with higher derivatives. More generally, certain Lagrangian terms are not turned on by renormalization, if they are absent at the tree level. This restricts the form of the action of a non-renormalizable theory, and has applications to quantum gravity. The new action contains infinitely many couplings, but not all of the ones that might have been expected. In quantum gravity, the metric of constant curvature is an extremal, but not a minimum, of the complete action. Nonetheless, it appears to be the right perturbative vacuum, at least when the curvature is negative, suggesting that the quantum vacuum has a negative asymptotically constant curvature. The results of this paper give also a set of rules for a more economical use of effective quantum field theories and suggest that it might be possible to give mathematical sense to theories with infinitely many couplings at high energies, to search for physical predictions

Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

Directory of Open Access Journals (Sweden)

George Zoupanos

2008-02-01

Full Text Available Finite Unified Theories (FUTs are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings and dimensionful (soft supersymmetry breaking terms sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold. We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized à la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere SN2. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M4 × S2, the scalars being interpreted as gauge fields on S2. Depending on the parameters of the model the low-energy gauge group can be SU(n, or broken further to SU(n1 × SU(n2 × U(1. Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to

Theory of charged vector mesons interacting with the electromagnetic field

International Nuclear Information System (INIS)

Lee, T.D.; Yang, C.N.

1983-01-01

It is shown that starting from the usual canonical formalism for the electromagnetic interaction of a charged vector meson with arbitrary magnetic moment one is led to a set of rules for Feynman diagrams, which appears to contain terms that are both infinite and noncovariant. These difficulties, however, can be circumvented by introducing a xi-limiting process which depends on a dimensionless positive parameter xi → 0. Furthermore, by using the mathematical artifice of a negative metric the theory becomes renormalizable (for xi > 0)

On the equivalence of massive qed with renormalizable and in unitary gauge

International Nuclear Information System (INIS)

Abdalla, E.

1978-03-01

In the framework of BPHZ renormalization procedure, we discuss the equivalence between 4-dimensional renormalizable massive quantum electrodynamics (Stueckelberg lagrangian), and massive QED in the unitary gauge

Renormalization of a distorted gauge: invariant theory

International Nuclear Information System (INIS)

Hsu, J.P.; Underwood, J.A.

1976-02-01

A new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry is considered. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (W-T) identities. Also, the theory is independent of the gauge parameter xi. An explicit renormalization at the oneloop level is completely carried out by exhibiting counter terms, defining the physical parameters and computing all renormalization constants to check the W-T identities

UV/IR mixing and the Goldstone theorem in noncommutative field theory

International Nuclear Information System (INIS)

Ruiz Ruiz, F.

2002-01-01

Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, λ 1 and λ 2 , associated to the two noncommutative extensions phi*starphistarphi* starphi and phistarphi*starphistarphi of the interaction term vertical bar phi vertical bar 4 on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all λ 1 and λ 2 compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if λ 2 =0, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter θ

Renormalizable models with broken symmetries

International Nuclear Information System (INIS)

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

1975-10-01

The results of the renormalized perturbation theory, in the absence of massless quanta, are summarized. The global symmetry breaking is studied and the associated currents are discussed in terms of the coupling with a classical Yang Mills field. Gauge theories are discussed; it is most likely that the natural set up should be the theory of fiber bundles and that making a choice of field coordinates makes the situation obscure. An attempt is made in view of clarifying the meaning of the Slavnov symmetry which characterizes gauge field theories [fr

Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations

International Nuclear Information System (INIS)

Brown, N.; Dorey, N.

1989-11-01

Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)

Collider tests of the Renormalizable Coloron Model

Energy Technology Data Exchange (ETDEWEB)

Bai, Yang; Dobrescu, Bogdan A.

2018-04-01

The coloron, a massive version of the gluon present in gauge extensions of QCD, has been searched for at the LHC as a dijet or top quark pair resonance. We point out that in the Renormalizable Coloron Model (ReCoM) with a minimal field content to break the gauge symmetry, a color-octet scalar and a singlet scalar are naturally lighter than the coloron because they are pseudo Nambu-Goldstone bosons. Consequently, the coloron may predominantly decay into scalar pairs, leading to novel signatures at the LHC. When the color-octet scalar is lighter than the singlet, or when the singlet mass is above roughly 1 TeV, the signatures consist of multi-jet resonances of multiplicity up to 12, including topologies with multi-prong jet substructure, slightly displaced vertices, and sometimes a top quark pair. When the singlet is the lightest ReCoM boson and lighter than about 1 TeV, its main decays ($W^+W^-$, $\\gamma Z$, $ZZ$) arise at three loops. The LHC signatures then involve two or four boosted electroweak bosons, often originating from highly displaced vertices, plus one or two pairs of prompt jets or top quarks.

Critical behavior and duality in extended Sine-Gordon theories

International Nuclear Information System (INIS)

Boyanovsky, D.; Holman, R.

1991-01-01

We study the critical properties of vectorial sine-Gordon theories based on the root system of simply-laced Lie algebras. We introduce the dual operators and study the renormalization aspects of these theories. These models are identified with vectorial Coulomb gas models of electric and magnetic charges and generalized Toda field theories. We prove that these theories are consistently renormalizable for simply-laced Lie algebras, but non-renormalizable in general in the non-simply-laced case. These models provide a description for the statistical mechanics of melting in the SU(3) case. They also provide a simplified model for strings compactified on root lattices. We compute the RG beta functions to quadratic order for general simply-laced algebras and find that in general there is a Weyl singlet, self-dual fixed point. This fixed point describes a critical theory with condensates of electric and magnetic charges corresponding to tachyonic and winding modes in string language. The different phases are related by Weyl and duality symmetry. The phase structure is conjectured in the general case, and analyzed in detail for SU(3) and SO(6). We compute Zamolodchikov's c-function to cubic order in the couplings in the general case and the conformal anomaly at the self-dual fixed point for SU(N). (orig.)

Electro-weak theory

International Nuclear Information System (INIS)

Deshpande, N.G.

1980-01-01

By electro-weak theory is meant the unified field theory that describes both weak and electro-magnetic interactions. The development of a unified electro-weak theory is certainly the most dramatic achievement in theoretical physics to occur in the second half of this century. It puts weak interactions on the same sound theoretical footing as quantum elecrodynamics. Many theorists have contributed to this development, which culminated in the works of Glashow, Weinberg and Salam, who were jointly awarded the 1979 Nobel Prize in physics. Some of the important ideas that contributed to this development are the theory of beta decay formulated by Fermi, Parity violation suggested by Lee and Yang, and incorporated into immensely successful V-A theory of weak interactions by Sudarshan and Marshak. At the same time ideas of gauge invariance were applied to weak interaction by Schwinger, Bludman and Glashow. Weinberg and Salam then went one step further and wrote a theory that is renormalizable, i.e., all higher order corrections are finite, no mean feat for a quantum field theory. The theory had to await the development of the quark model of hadrons for its completion. A description of the electro-weak theory is given

Constraint theory, singular lagrangians and multitemporal dynamics

International Nuclear Information System (INIS)

Lusanna, L.

1988-01-01

Singular Lagrangians and constraint theory permeate theoretical physics, as shown by the relevance of gauge theories, string models and general relativity. Their study used finite---dimensional models as a guide to develop the theory, but their main use was in classical field theory, due to the necessity of understanding their quantization. The covariant quantization of singular Lagrangians led to the BRST approach and to the theory of the effective action. On the other hand their phase---space formulation, culminated with the BFV approach for first class, second class and reducible constraints. It, in turn, gave new insights in the theory of singular Lagrangians and constraints and in their cohomological aspects. However the Hamiltonian approach to field theory is highly nontrivial, is open to criticism due to its problems with locality, geometry and manifest covariance and its canonical quantization has still to be developed, because there is no proof of the renormalizability of the Schroedinger representation of field theory. This paper discusses how, notwithstanding these developments, there is still a big amount of ambiguity at every level of the theory

Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus

International Nuclear Information System (INIS)

Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.

1983-01-01

The instanton contribution to the vacuum energy is supersymmetric Yang-Mills theories is considered. Using renormalizability of the theory the exact beta function for n-extended supersymmetry (n=1, 2, 4) is found. The coefficients of the beta function have a geometrical meaning - they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added the method allows one to fix the first two coefficients. A non-renormalization theorem which extends cancellation of vacuum loops to the case of the external instanton field is proved

On dynamics of 5D superconformal theories

International Nuclear Information System (INIS)

Smilga, A.V.

2006-02-01

5D superconformal theories involve vacuum valleys characterized in the simplest case by the vacuum expectation value of the real scalar field σ. If ≠ 0, conformal invariance is spontaneously broken and the theory is not renormalizable. In the conformally invariant sector = 0, the theory is intrinsically nonperturbative. We study classical and quantum dynamics of this theory in the limit when field dependence of the spatial coordinates is disregarded. The classical trajectories 'fall' on the singularity at σ = 0. The quantum spectrum involves ghost states with negative energies unbounded from below, but such states fail to form complete 16-plets as is dictated by the presence of four complex supercharges and should be rejected by that reason. Physical excited states come in supermultiplets and have all positive energies. We conjecture that the spectrum of the complete field theory Hamiltonian is nontrivial and has a similar nontrivial ghost-free structure and also speculate that the ghosts in higher-derivative supersymmetric field theories are exterminated by a similar mechanism. (author)

Radiation reaction for the classical relativistic spinning particle in scalar, tensor and linearized gravitational fields

International Nuclear Information System (INIS)

Barut, A.O.; Cruz, M.G.

1992-08-01

We use the method of analytic continuation of the equation of motion including the self-fields to evaluate the radiation reaction for a classical relativistic spinning point particle in interaction with scalar, tensor and linearized gravitational fields in flat spacetime. In the limit these equations reduce to those of spinless particles. We also show the renormalizability of these theories. (author). 10 refs

Mass generation within conformal invariant theories

International Nuclear Information System (INIS)

Flato, M.; Guenin, M.

1981-01-01

The massless Yang-Mills theory is strongly conformally invariant and renormalizable; however, when masses are introduced the theory becomes nonrenormalizable and weakly conformally invariant. Conditions which recover strong conformal invariance are discussed in the letter. (author)

Renormalization of gauge theories without cohomology

International Nuclear Information System (INIS)

Anselmi, Damiano

2013-01-01

We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

String-localized quantum fields

International Nuclear Information System (INIS)

Mund, Jens; Santos, Jose Amancio dos; Silva, Cristhiano Duarte; Oliveira, Erichardson de

2009-01-01

Full text. The principles of physics admit (unobservable) quantum fields which are localized not on points, but on strings in the sense of Mandelstam: a string emanates from a point in Minkowski space and extends to infinity in some space-like direction. This type of localization might permit the construction of new models, for various reasons: (a) in general, weaker localization implies better UV behaviour. Therefore, the class of renormalizable interactions in the string-localized has a chance to be larger than in the point-localized case; (b) for certain particle types, there are no point-localized (free) quantum fields - for example Anyons in d = 2 + 1, and Wigner's massless 'infinite spin' particles. For the latter, free string-localized quantum fields have been constructed; (c) in contrast to the point-localized case, string-localization admits covariant vector/tensor potentials for fotons and gravitons in a Hilbert space representation with positive energy. We shall present free string-localized quantum fields for various particle types, and some ideas about the perturbative construction of interacting string-localized fields. A central point will be an analogue of gauge theories, completely within a Hilbert space and without ghosts, trading gauge dependence with dependence on the direction of the localization string. In order to discuss renormalizability (item (a)), methods from microlocal analysis (wave front set and scaling degree) are needed. (author)

The theory of asymptotic behaviour

International Nuclear Information System (INIS)

Ward, B.F.L.; Purdue Univ., Lafayette, IN

1978-01-01

The Green's functions of renormalizable quantum field theory are shown to violate, in general, Euler's theorem on homogeneous functions, that is to say, to violate naive dimensional analysis. The respective violations are established by explicit calculation with Feynman diagrams. These violations, when incorporated into the renormalization group, then provide the basis for an entirely new approach to asymptotic behaviour in renormalizable field theory. Specifically, the violations add new delta-function sources to the usual partial differential equations of the group when these equations are written in terms of the external momenta of the respective Green's functions. The effect of these sources is illustrated by studying the real part, Re GAMMA 6 (lambda p), of the six-point 1PI vertex of the massless scalar field with quartic self-coupling - the simplest of ranormalizable situations. Here, lambda p is symbolic for the six-momenta of GAMMA 6 . Briefly, it is found that the usual theory of characteristics is unable to satisfy the boundary condition attendant to the respective dimensional-analysis-violating sources. Thus, the method of characteristics is completely abandonded in favour of the method of separation of variables. A complete solution which satisfies the inhomogeneous group equation and all boundary conditions is then explicitly constructed. This solution possesses Laurent expansions in the scale lambda of its momentum arguments for all real values of lambda 2 except lambda 2 = 0. For |lambda 2 |→ infinity and |lambda 2 |→ 0, the solution's leading term in its respective Laurent series is proportional to lambda -2 . The limits lambda 2 →0sub(+) and lambda 2 →0sup(-) of lambda 2 ReGAMMA 6 are both nonzero and unequal. The value of the solution at lambda 2 = 0 is not simply related to the value of either of these limits. The new approach would appear to be operationally established

Superstring theory

International Nuclear Information System (INIS)

Schwarz, J.H.

1985-01-01

Dual string theories, initially developed as phenomenological models of hadrons, now appear more promising as candidates for a unified theory of fundamental interactions. Type I superstring theory (SST I), is a ten-dimensional theory of interacting open and closed strings, with one supersymmetry, that is free from ghosts and tachyons. It requires that an SO(eta) or Sp(2eta) gauge group be used. A light-cone-gauge string action with space-time supersymmetry automatically incorporates the superstring restrictions and leads to the discovery of type II superstring theory (SST II). SST II is an interacting theory of closed strings only, with two D=10 supersymmetries, that is also free from ghosts and tachyons. By taking six of the spatial dimensions to form a compact space, it becomes possible to reconcile the models with our four-dimensional perception of spacetime and to define low-energy limits in which SST I reduces to N=4, D=4 super Yang-Mills theory and SST II reduces to N=8, D=4 supergravity theory. The superstring theories can be described by a light-cone-gauge action principle based on fields that are functionals of string coordinates. With this formalism any physical quantity should be calculable. There is some evidence that, unlike any conventional field theory, the superstring theories provide perturbatively renormalizable (SST I) or finite (SST II) unifications of gravity with other interactions

Angular momentum conservation law in light-front quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Chiu, Kelly Yu-Ju; Brodsky, Stanley J.; /SLAC /Stanford U.

2017-03-01

We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front formulation. We explicitly show that j 3 , the z -component of the angular momentum remains unchanged under Lorentz transformations generated by the light-front kinematical boost operators. The invariance of j 3 under Lorentz transformations is a feature unique to the front form. Applying the Lorentz invariance of the angular quantum number in the front form, we obtain a selection rule for the orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory.

Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus

International Nuclear Information System (INIS)

Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.

1983-01-01

The instanton contribution to the vacuum energy in supersymmetric Yang-Mills theories is considered. Using the renormalizability of the theory we find the exact beta function for n-extended supersymmetry (n=1, 2, 4). The coefficients of the beta function have a geometrical meaning: they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added our method allows one to fix the first two coefficients. We prove a non-renormalization theorem which extends the cancellation of vacuum loops to the case of the external instanton field. (orig.)

Study of the maximal Abelian gauge in SU(2) Euclidean Yang-Mills theory in the presence of the Gribov horizon

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

Relativistic quantum theory of composite systems

International Nuclear Information System (INIS)

Sogami, I.

1978-01-01

A relativistic quantum theory free from the difficulties of tachyons and ghosts is formulated to describe the scattering processes between composite systems of spinless quarks. To evade the complication brewed by introducing gluon fields or strings, valence quarks are effectively assumed to be in the relative motion of harmonic oscillation correlating with the motion of the composite system as a whole. A quark-antiquark system is represented by a bilocal field describing a sequence of mesons and every meson is identified with the composite system in a definite eigenstate of relative motion. The quantization is performed in the interaction picture, so that the microcausal condition is satisfied by local fields which result from the decomposition of bilocal fields. Imposing a weakened macrocausal condition on the whole motion of the extended system, a causal bilocal propagator is defined and a consistent time ordering among bilocal fields is defined. The invariant S-matrix is obtained and the graphical method for the calculation of its elements is developed in parallel with the conventional local field theory. For the (bilocal field) 3 interaction any malignant divergence does not appear excepting those in the renormalizable local field theory. The theory provides one promising and comprehensive phenomenology of hadrons which is suitable especially to describe the hard structure of hadrons. (author)

Unitary field theories

International Nuclear Information System (INIS)

Bergmann, P.G.

1980-01-01

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

The metric on field space, functional renormalization, and metric–torsion quantum gravity

International Nuclear Information System (INIS)

Reuter, Martin; Schollmeyer, Gregor M.

2016-01-01

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.

Nuclear Forces from Effective Field Theory

International Nuclear Information System (INIS)

Krebs, H.

2011-01-01

Chiral effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of the quantum chromodynamics. After a brief review on the current status in the development of the chiral nuclear forces I will focus on the role of the Δ-resonance contributions in the nuclear dynamics.We find improvement in the convergence of the chiral expansion of the nuclear forces if we explicitly take into account the Δ-resonance degrees of freedom. The overall results for two-nucleon forces with and without explicit Δ-resonance degrees of freedom are remarkably similar. We discussed the long- and shorter-range N 3 LO contributions to chiral three-nucleon forces. No additional free parameters appear at this order. There are five different topology classes which contribute to the forces. Three of them describe long-range contributions which constitute the first systematic corrections to the leading 2π exchange that appear at N 2 LO. Another two contributions are of a shorter range and include, additionally to an exchange of pions, also one short-range contact interaction and all corresponding 1/m corrections. The requirement of renormalizability leads to unique expressions for N 3 LO contributions to the three-nucleon force (except for 1/m-corrections). We presented the complete N 2 LO analysis of the nuclear forces with explicit Δ-isobar degrees of freedom. Although the overall results in the isospin-conserving case are very similar in the Δ-less and Δ-full theories, we found a much better convergence in all peripheral partial waves once Δ-resonance is explicitly taken into account. The leading CSB contributions to nuclear forces are proportional to nucleon- and Δ-mass splittings. There appear strong cancellations between the two contributions which at leading order yield weaker V III potentials. This effect is, however, entirely compensated at subleading order such that the results in the theories

String field theory

International Nuclear Information System (INIS)

Kaku, M.

1987-01-01

In this article, the authors summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. They also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group they call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). The geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory

Elementary methods for statistical systems, mean field, large-n, and duality

International Nuclear Information System (INIS)

Itzykson, C.

1983-01-01

Renormalizable field theories are singled out by such precise restraints that regularization schemes must be used to break these invariances. Statistical methods can be adapted to these problems where asymptotically free models fail. This lecture surveys approximation schemes developed in the context of statistical mechanics. The confluence point of statistical mechanics and field theory is the use of discretized path integrals, where continuous space time has been replaced by a regular lattice. Dynamic variables, a Boltzman weight factor, and boundary conditions are the ingredients. Mean field approximations --field equations, Random field transform, and gauge invariant systems--are surveyed. Under Large-N limits vector models are found to simplify tremendously. The reasons why matrix models drawn from SU (n) gauge theories do not simplify are discussed. In the epilogue, random curves versus random surfaces are offered as an example where global and local symmetries are not alike

String theory or field theory?

International Nuclear Information System (INIS)

Marshakov, Andrei V

2002-01-01

The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of string theory in the modern picture of the physical world. Even though quantum field theory describes a wide range of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments which are our concern in this review. (reviews of topical problems)

Geophysical Field Theory

International Nuclear Information System (INIS)

Eloranta, E.

2003-11-01

The geophysical field theory includes the basic principles of electromagnetism, continuum mechanics, and potential theory upon which the computational modelling of geophysical phenomena is based on. Vector analysis is the main mathematical tool in the field analyses. Electrostatics, stationary electric current, magnetostatics, and electrodynamics form a central part of electromagnetism in geophysical field theory. Potential theory concerns especially gravity, but also electrostatics and magnetostatics. Solid state mechanics and fluid mechanics are central parts in continuum mechanics. Also the theories of elastic waves and rock mechanics belong to geophysical solid state mechanics. The theories of geohydrology and mass transport form one central field theory in geophysical fluid mechanics. Also heat transfer is included in continuum mechanics. (orig.)

Quantum field theory

International Nuclear Information System (INIS)

Ryder, L.H.

1985-01-01

This introduction to the ideas and techniques of quantum field theory presents the material as simply as possible and is designed for graduate research students. After a brief survey of particle physics, the quantum theory of scalar and spinor fields and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a bridge survey of ''topological'' objects in field theory and assumes a knowledge of quantum mechanics and special relativity

Classical field theory

CERN Document Server

Franklin, Joel

2017-01-01

Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...

Anomalous ultraviolet divergences and renormalizability of the light-cone gauge

International Nuclear Information System (INIS)

Lee, H.C.; Milgram, M.S.

1985-01-01

The one-loop renormalizability of both the two-component (LC2) and four-component (LC4) formulations of the light-cone gauge is demonstrated by construction of the complete one-loop counter Lagrangians. The Mandelstam-Leibbrandt prescription is used to regularize the singular 1/p + factor. In LC4, the one-loop self-energy and three-vertex both have anomalous, unrenormalizable ultraviolet divergences, but the counterterms associated with these divergences cancel exactly, rendering the total counter Lagrangians for the two formulations identical, at least to O(g 3 )

Anomalous ultraviolet divergences and renormalizability of the light-cone gauge

Science.gov (United States)

Lee, H. C.; Milgram, M. S.

1985-11-01

The one-loop renormalizability of both the two-component (LC2) and four-component (LC4) formulations of the light-cone gauge is demonstrated by construction of the complete one-loop counter Lagrangians. The Mandelstam-Leibbrandt prescription is used to regularize the singular 1/p+ factor. In LC4, the one-loop self-energy and three-vertex both have anomalous, unrenormalizable ultraviolet divergences, but the counterterms associated with these divergences cancel exactly, rendering the total counter Lagrangians for the two formulations identical, at least to O(g3).

Renormalization problem in a class of nonrenormalizable theories

International Nuclear Information System (INIS)

Symanzik, K.

1975-08-01

A possible way to approach the simplest nonrenormalizable theory - phi 4 theory in more than four space-time dimensions - is described. The problems of extension to other nonrenormalizable theories are discussed and the conclusions reached so far are compared with the corresponding ones for renormalizable theories. For more details, Comm. Math. Phys. or DESY 75/12 should be consulted. (BJ) [de

Scalar field dark matter and the Higgs field

Directory of Open Access Journals (Sweden)

O. Bertolami

2016-08-01

Full Text Available We discuss the possibility that dark matter corresponds to an oscillating scalar field coupled to the Higgs boson. We argue that the initial field amplitude should generically be of the order of the Hubble parameter during inflation, as a result of its quasi-de Sitter fluctuations. This implies that such a field may account for the present dark matter abundance for masses in the range 10−6–10−4eV, if the tensor-to-scalar ratio is within the range of planned CMB experiments. We show that such mass values can naturally be obtained through either Planck-suppressed non-renormalizable interactions with the Higgs boson or, alternatively, through renormalizable interactions within the Randall–Sundrum scenario, where the dark matter scalar resides in the bulk of the warped extra-dimension and the Higgs is confined to the infrared brane.

String theory or field theory?

International Nuclear Information System (INIS)

Marshakov, A.V.

2002-01-01

The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are analyzed. This analysis helps better understand the role and place of experimental phenomena, it is emphasized that there are some insurmountable problems inherent in it - notably the impossibility to formulate the quantum theory of gravity on its basis - which prevent it from being a fundamental physical theory of the world of microscopic distances. It is this task, the creation of such a theory, which string theory, currently far from completion, is expected to solve. In spite of its somewhat vague current form, string theory has already led to a number of serious results and greatly contributed to progress in the understanding of quantum field theory. It is these developments, which are our concern in this review [ru

Unified field theory

International Nuclear Information System (INIS)

Prasad, R.

1975-01-01

Results of researches into Unified Field Theory over the past seven years are presented. The subject is dealt with in chapters entitled: the choice of affine connection, algebraic properties of the vector fields, field laws obtained from the affine connection based on the path integral method, application to quantum theory and cosmology, interpretation of physical theory in terms of geometry. (U.K.)

Finite discrete field theory

International Nuclear Information System (INIS)

Souza, Manoelito M. de

1997-01-01

We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)

Effective field theories

International Nuclear Information System (INIS)

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

1992-05-01

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

Continuum regularized Yang-Mills theory

International Nuclear Information System (INIS)

Sadun, L.A.

1987-01-01

Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

Field theory

CERN Multimedia

1999-11-08

In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.

Macroscopic influence on the spontaneous symmetry breaking in quantum field

International Nuclear Information System (INIS)

Kirzhnitz, D.A.

1977-01-01

Major results of investigations concerning macroscopic influence (heating, compression, external field and current) on elementary particle systems with spontaneous symmetry breaking are briefly reviewed. The study of this problem has been stimulated by recent progress in the unified renormalizable theory of elementary particles. Typically it appears that at some values of external parameters a phase transition with symmetry restoration takes place. There exists a profound and far going analogy with phase transition in many-body physics especially with superconductivity phenomenon. Some applications to cosmology are also considered

Field theory and strings

International Nuclear Information System (INIS)

Bonara, L.; Cotta-Ramusino, P.; Rinaldi, M.

1987-01-01

It is well-known that type I and heterotic superstring theories have a zero mass spectrum which correspond to the field content of N=1 supergravity theory coupled to supersymmetric Yang-Mills theory in 10-D. The authors study the field theory ''per se'', in the hope that simple consistency requirements will determine the theory completely once one knows the field content inherited from string theory. The simplest consistency requirements are: N=1 supersymmetry; and absence of chiral anomalies. This is what the authors discuss in this paper here leaving undetermined the question of the range of validity of the resulting field theory. As is known, a model of N=1 supergravity (SUGRA) coupled to supersymmetric Yang-Mills (SYM) theory was known in the form given by Chapline and Manton. The coupling of SUGRA to SYM was determined by the definition of the ''field strength'' 3-form H in this paper

Summation of all-loop UV divergences in maximally supersymmetric gauge theories

International Nuclear Information System (INIS)

Borlakov, A.T.; Kazakov, D.I.; Tolkachev, D.M.; Vlasenko, D.E.

2016-01-01

We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.

Summation of all-loop UV divergences in maximally supersymmetric gauge theories

Energy Technology Data Exchange (ETDEWEB)

Borlakov, A.T. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudny (Russian Federation); Kazakov, D.I. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna (Russian Federation); Alikhanov Institute for Theoretical and Experimental Physics,Moscow (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudny (Russian Federation); Tolkachev, D.M. [Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research,Dubna (Russian Federation); Stepanov Institute of Physics,Minsk (Belarus); Vlasenko, D.E. [Department of Physics, South Federal State University,Rostov-Don (Russian Federation)

2016-12-29

We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.

Algebraic conformal field theory

International Nuclear Information System (INIS)

Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

1991-11-01

Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

Generating functional for Donaldson invariants and operator algebra in topological D=4 Yang-Mills theory

International Nuclear Information System (INIS)

Johansen, A.A.

1992-01-01

It is shown, that under the certain constraints the generating functional for the Donaldson invariants in the D=4 topological Yang-Mills theory can be interpreted as a partition function for the renormalizable theory. 20 refs

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

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)

Studies in quantum field theory

International Nuclear Information System (INIS)

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

1982-01-01

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

The Global Approach to Quantum Field Theory

Energy Technology Data Exchange (ETDEWEB)

Fulling, S A [Texas A and M University (United States)

2006-05-21

temperature, black holes, and Euclideanization. Chapter 30, on black holes and Hawking radiation, will be very familiar to readers of DeWitt's influential review article. Chapter 28, on anomalies, makes a careful distinction (missing from many treatments) between 'critical' anomalies, which render equations of motion inconsistent in the (would-be) quantum theory, and harmless anomalies that merely invalidate predictions that would classically follow from certain symmetries. Examples of critical anomalies are the chiral anomaly of a spinor field coupled to a non-Abelian gauge field and the anomaly in the conservation law of the stress tensor of certain pathological theories. DeWitt's chapter calculates the trace and chiral anomalies in detail. The last two chapters of part VII treat the most important particular quantum field theories. Chapter 34 develops many of the textbook predictions of quantum eletrodynamics from DeWitt's starting point. Chapter 35 covers Yang-Mills fields and quantum gravity. The discussion of gravity is surprisingly brief, in view of DeWitt's lifelong preoccupation with that subject. He rejects renormalizable fourth-order modifications of four-dimensional gravity because he could not stomach unfriendly ghosts (states of negative norm or unboundedly negative energy) nor the technical difficulties of integrating such theories into the functional-integral formalism. Finally, there is part VIII, entitled 'Examples. Simple Exercises in the Use of the Global Formalism'. It consists of 25 short chapters numbered separately from those of the main text. The preface recommends reading these and the main text in parallel. Most valuable in my opinion is a string of successively more complicated fermionic models. Hidden in an appendix is a crucial motivational paragraph: Super Hilbert spaces are generalizations of ordinary Hilbert spaces, designed so as to enable one to consider quantum systems with supernumber

The Global Approach to Quantum Field Theory

International Nuclear Information System (INIS)

Fulling, S A

2006-01-01

Euclideanization. Chapter 30, on black holes and Hawking radiation, will be very familiar to readers of DeWitt's influential review article. Chapter 28, on anomalies, makes a careful distinction (missing from many treatments) between 'critical' anomalies, which render equations of motion inconsistent in the (would-be) quantum theory, and harmless anomalies that merely invalidate predictions that would classically follow from certain symmetries. Examples of critical anomalies are the chiral anomaly of a spinor field coupled to a non-Abelian gauge field and the anomaly in the conservation law of the stress tensor of certain pathological theories. DeWitt's chapter calculates the trace and chiral anomalies in detail. The last two chapters of part VII treat the most important particular quantum field theories. Chapter 34 develops many of the textbook predictions of quantum eletrodynamics from DeWitt's starting point. Chapter 35 covers Yang-Mills fields and quantum gravity. The discussion of gravity is surprisingly brief, in view of DeWitt's lifelong preoccupation with that subject. He rejects renormalizable fourth-order modifications of four-dimensional gravity because he could not stomach unfriendly ghosts (states of negative norm or unboundedly negative energy) nor the technical difficulties of integrating such theories into the functional-integral formalism. Finally, there is part VIII, entitled 'Examples. Simple Exercises in the Use of the Global Formalism'. It consists of 25 short chapters numbered separately from those of the main text. The preface recommends reading these and the main text in parallel. Most valuable in my opinion is a string of successively more complicated fermionic models. Hidden in an appendix is a crucial motivational paragraph: Super Hilbert spaces are generalizations of ordinary Hilbert spaces, designed so as to enable one to consider quantum systems with supernumber-valued parameters (e.g., a-type external sources) which, themselves, are introduced in

Engineering field theory

CERN Document Server

Baden Fuller, A J

2014-01-01

Engineering Field Theory focuses on the applications of field theory in gravitation, electrostatics, magnetism, electric current flow, conductive heat transfer, fluid flow, and seepage.The manuscript first ponders on electric flux, electrical materials, and flux function. Discussions focus on field intensity at the surface of a conductor, force on a charged surface, atomic properties, doublet and uniform field, flux tube and flux line, line charge and line sink, field of a surface charge, field intensity, flux density, permittivity, and Coulomb's law. The text then takes a look at gravitation

Phenomenological aspects of theories for baryon and lepton number violation

International Nuclear Information System (INIS)

Duerr, Michael

2013-01-01

The renormalizable couplings of the Standard Model are invariant under two accidental global symmetries, which correspond to conserved baryon and lepton numbers. In this thesis, we discuss possible roles of these symmetries in extension of the Standard Model. Two approaches are considered: explicit violation of lepton number by two units in the renormalizable couplings of the Lagrangian, and promotion of the global symmetries to local gauge symmetries that are spontaneously broken. The former approach directly leads to Majorana neutrino masses and neutrinoless double beta decay. We discuss the interplay of the contributions to this decay in a one-loop neutrino mass model, the colored seesaw mechanism. We find that, depending on the parameters of the model, both the light Majorana neutrino exchange and the contribution of the new colored particles may be dominant. Additionally, an experimental test is presented, which allows for a discrimination of neutrinoless double beta decay from unknown nuclear background using only one isotope. In the latter approach, fascinating implications originate from the attempt to write down an anomaly-free and spontaneously broken gauge theory for baryon and lepton numbers, such as an automatically stable dark matter candidate. When gauging the symmetries in a left-right symmetric setup, the same fields that allow for an anomaly-free theory generate neutrino masses via the type III seesaw mechanism.

Light-Front Quantization of Gauge Theories

Energy Technology Data Exchange (ETDEWEB)

Brodsky, Stanley J.

2003-03-25

Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.

Light-Front Quantization of Gauge Theories

Energy Technology Data Exchange (ETDEWEB)

Brodskey, Stanley

2002-12-01

Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.

Quantum field theory

CERN Document Server

Mandl, Franz

2010-01-01

Following on from the successful first (1984) and revised (1993) editions, this extended and revised text is designed as a short and simple introduction to quantum field theory for final year physics students and for postgraduate students beginning research in theoretical and experimental particle physics. The three main objectives of the book are to: Explain the basic physics and formalism of quantum field theory To make the reader proficient in theory calculations using Feynman diagrams To introduce the reader to gauge theories, which play a central role in elementary particle physic

Dual double field theory

Energy Technology Data Exchange (ETDEWEB)

Bergshoeff, Eric A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook, NY 11794-3636 (United States); Penas, Victor A. [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Riccioni, Fabio [INFN - Sezione di Roma, Dipartimento di Fisica, Università di Roma “La Sapienza”,Piazzale Aldo Moro 2, 00185 Roma (Italy)

2016-06-06

We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O(D,D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O(D,D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for “exotic' dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.

Nonlocal continuum field theories

CERN Document Server

2002-01-01

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

Morse theory interpretation of topological quantum field theories

International Nuclear Information System (INIS)

Labastida, J.M.F.

1989-01-01

Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: Topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained. (orig.)

Axiomatic conformal field theory

International Nuclear Information System (INIS)

Gaberdiel, M.R.; Goddard, P.

2000-01-01

A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, Moebius invariance rather than full conformal invariance is required but it is shown that every Moebius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. (orig.)

Gravity waves from the non-renormalizable electroweak vacua phase transition

Energy Technology Data Exchange (ETDEWEB)

Greenwood, Eric [Case Western Reserve Univ., Cleveland, OH (United States). Dept. of Physics; Vaudrevange, Pascal M. [Case Western Reserve Univ., Cleveland, OH (United States). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2010-11-15

It is currently believed that the Standard Model is an effective low energy theory which in principle may contain higher dimensional non-renormalizable operators. These operators may modify the standard model Higgs potential in many ways, one of which being the appearance of a second vacuum. For a wide range of parameters, this new vacuum becomes the true vacuum. It is then assumed that our universe is currently sitting in the false vacuum. Thus the usual second-order electroweak phase transition at early times will be followed by a second, first-order phase transition. In cosmology, a first-order phase transition is associated with the production of gravity waves. In this paper we present an analysis of the production of gravitational waves during such a second electroweak phase transition. We find that, for one certain range of parameters, the stochastic background of gravitational waves generated by bubble nucleation and collision have an amplitude which is estimated to be of order {omega}{sub GW}h{sup 2}{proportional_to}10{sup -11} at f=3 x 10{sup -4} Hz, which is within reach of the planned sensitivity of LISA. For another range of parameters, we find that the amplitude is estimated to be of order {omega}{sub GW}h{sup 2}{proportional_to} 0{sup -25} around f=10{sup 3} Hz, which is within reach of LIGO. Hence, it is possible to detect gravity waves from such a phase transition at two different detectors, with completely different amplitude and frequency ranges. (orig.)

Poincare and de Sitter gauge theories of gravity with propagating torsion

International Nuclear Information System (INIS)

Tseytlin, A.A.

1982-01-01

We consider a gauge approach to the gravitational theory based on the local Poincare P 10 de Sitter S 10 groups. The P 10 gauge rotations and translations take place in the tangent spaces to the space-time manifold. We interpret the independence of matter fields from the tangent vectors as the necessity to use a nonlinear realization of the P 10 or S 10 groups thus effectively breaking the full symmetry to the Lorentz group. The Lagrangian we choose is the S 10 Yang-Mills invariant with the space-time metric expressed in terms of the translational part of the S 10 nonlinear gauge field. Various consequences of the theory are discussed, including the correspondence with general relativity, the propagating spin-connection interactions, the analogy with the chiral Higgs mechanism, instantonlike solutions, a possibility of gravitational repulsion due to the noncompactness of the Lorentz group, etc. We also analyze the quantization of the theories with torsion with special emphasis on the presence of the nonlinear realization. We stress the possibility of obtaining a renormalizable theory if the metric is not quantized but is expressed in terms of a mean value of the quantized S 10 nonlinear gauge field

Renormalizable Non-Covariant Gauges and Coulomb Gauge Limit

CERN Document Server

Baulieu, L

1999-01-01

To study ``physical'' gauges such as the Coulomb, light-cone, axial or temporal gauge, we consider ``interpolating'' gauges which interpolate linearly between a covariant gauge, such as the Feynman or Landau gauge, and a physical gauge. Lorentz breaking by the gauge-fixing term of interpolating gauges is controlled by extending the BRST method to include not only the local gauge group, but also the global Lorentz group. We enumerate the possible divergences of interpolating gauges, and show that they are renormalizable, and we show that the expectation value of physical observables is the same as in a covariant gauge. In the second part of the article we study the Coulomb-gauge as the singular limit of the Landau-Coulomb interpolating gauge. We find that unrenormalized and renormalized correlation functions are finite in this limit. We also find that there are finite two-loop diagrams of ``unphysical'' particles that are not present in formal canonical quantization in the Coulomb gauge. We verify that in the ...

Hamiltonian Anomalies from Extended Field Theories

Science.gov (United States)

Monnier, Samuel

2015-09-01

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.

Large N field theories, string theory and gravity

Energy Technology Data Exchange (ETDEWEB)

Maldacena, J [Lyman Laboratory of Physics, Harvard University, Cambridge (United States)

2002-05-15

We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/ M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions. These lecture notes are based on the Review written by O. Aharony, S. Gubser, J. Maldacena, H. Ooguri and Y. Oz. (author)

Topics in quantum field theory

International Nuclear Information System (INIS)

Svaiter, N.F.

2006-11-01

This paper presents some important aspects on quantum field theory, covering the following aspects: the triumph and limitations of the quantum field theory; the field theory in curved spaces - Hawking and Unruh-Davies effects; the problem of divergent theory of the zero-point; the problem of the spinning detector and the Trocheries-Takeno vacuum; the field theory at finite temperature - symmetry breaking and phase transition; the problem of the summability of the perturbative series and the perturbative expansion for the strong coupling; quantized fields in presence of classical macroscopic structures; the Parisi-Wu stochastic quantization method

Theory of interacting quantum fields

International Nuclear Information System (INIS)

Rebenko, Alexei L.

2012-01-01

This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20 th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.

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

International Nuclear Information System (INIS)

Chung, Stephen-wei.

1993-01-01

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

Introduction to string field theory

International Nuclear Information System (INIS)

Horowitz, G.T.

1989-01-01

A light cone gauge superstring field theory is constructed. The BRST approach is described discussing generalizations to yield gauge invariant free superstring field theory and interacting theory for superstrings. The interaction term is explicitly expressed in terms of first quantized oscillators. A purily cubic action for superstring field theory is also derived. (author)

Further Development of HS Field Theory

Science.gov (United States)

Abdurrahman, Abdulmajeed; Faridani, Jacqueline; Gassem, Mahmoud

2006-04-01

We present a systematic treatment of the HS Field theory of the open bosonic string and discuss its relationship to other full string field theories of the open bosonic string such as Witten's theory and the CVS theory. In the development of the HS field theory we encounter infinite dimensional matrices arising from the change of representation between the two theories, i.e., the HS field theory and the full string field theory. We give a general procedure of how to invert these gigantic matrices. The inversion of these matrices involves the computation of many infinite sums. We give the values of these sums and state their generalizations arising from considering higher order vertices (i.e., more than three strings) in string field theory. Moreover, we give a general procedure, on how to evaluate the generalized sums, that can be extended to many generic sums of similar properties. We also discuss the conformal operator connecting the HS field theory to that of the CVS string field theory.

Naturality in conformal field theory

International Nuclear Information System (INIS)

Moore, G.; Seiberg, N.

1989-01-01

We discuss constraints on the operator product coefficients in diagonal and nondiagonal rational conformal field theories. Nondiagonal modular invariants always arise from automorphisms of the fusion rule algebra or from extensions of the chiral algebra. Moreover, when the chiral algebra has been maximally extended a strong form of the naturality principle of field theory can be proven for rational conformal field theory: operator product coefficients vanish if and only if the corresponding fusion rules vanish; that is, if and only if the vanishing can be understood in terms of a symmetry. We illustrate these ideas with several examples. We also generalize our ideas about rational conformal field theories to a larger class of theories: 'quasi-rational conformal field theories' and we explore some of their properties. (orig.)

The utility of quantum field theory

International Nuclear Information System (INIS)

Dine, Michael

2001-01-01

This talk surveys a broad range of applications of quantum field theory, as well as some recent developments. The stress is on the notion of effective field theories. Topics include implications of neutrino mass and a possible small value of sin(2β), supersymmetric extensions of the standard model, the use of field theory to understand fundamental issues in string theory (the problem of multiple ground states and the question: does string theory predict low energy supersymmetry), and the use of string theory to solve problems in field theory. Also considered are a new type of field theory, and indications from black hole physics and the cosmological constant problem that effective field theories may not completely describe theories of gravity. (author)

Theoretical physics. Field theory

International Nuclear Information System (INIS)

Landau, L.; Lifchitz, E.

2004-01-01

This book is the fifth French edition of the famous course written by Landau/Lifchitz and devoted to both the theory of electromagnetic fields and the gravity theory. The talk of the theory of electromagnetic fields is based on special relativity and relates to only the electrodynamics in vacuum and that of pointwise electric charges. On the basis of the fundamental notions of the principle of relativity and of relativistic mechanics, and by using variational principles, the authors develop the fundamental equations of the electromagnetic field, the wave equation and the processes of emission and propagation of light. The theory of gravitational fields, i.e. the general theory of relativity, is exposed in the last five chapters. The fundamentals of the tensor calculus and all that is related to it are progressively introduced just when needed (electromagnetic field tensor, energy-impulse tensor, or curve tensor...). The worldwide reputation of this book is generally allotted to clearness, to the simplicity and the rigorous logic of the demonstrations. (A.C.)

Quantum field theory

CERN Document Server

Sadovskii, Michael V

2013-01-01

This book discusses the main concepts of the Standard Model of elementary particles in a compact and straightforward way. The work illustrates the unity of modern theoretical physics by combining approaches and concepts of the quantum field theory and modern condensed matter theory. The inductive approach allows a deep understanding of ideas and methods used for solving problems in this field.

Experimental test of the renormalizability consequences of the standard electroweak theory

International Nuclear Information System (INIS)

Bardin, D.Yu.

1984-01-01

The present status of the one-loop radiative corrections calculations in the standard electroweak theory is discussed. The possibilities of experimental tests of the higher order predictions of the standard theory is analysed in view of recent data, inclu-ing CERN p anti pcolcider data on Msub(W) and Msub(Z) measurement. The perspectives of these tests in the near future experiments are discussed

Gauge field theories

International Nuclear Information System (INIS)

Leite Lopes, J.

1981-01-01

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

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

Quantum field theory of fluids.

Science.gov (United States)

Gripaios, Ben; Sutherland, Dave

2015-02-20

The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.

Modular groups in quantum field theory

International Nuclear Information System (INIS)

Borchers, H.-J.

2000-01-01

The author discusses the connection of Lagrangean quantum field theory, perturbation theory, the Lehmann-Symanzik-Zimmermann theory, Wightman's quantum field theory, the Euclidean quantum field theory, and the Araki-Haag-Kastler theory of local observables with modular groups. In this connection he considers the PCT-theorem, and the tensor product decomposition. (HSI)

Introduction to conformal field theory. With applications to string theory

International Nuclear Information System (INIS)

Blumenhagen, Ralph; Plauschinn, Erik

2009-01-01

Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields. (orig.)

Gauge field theories

International Nuclear Information System (INIS)

Pokorski, S.

1987-01-01

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

Grand partition function in field theory with applications to sine-Gordon field theory

International Nuclear Information System (INIS)

Samuel, S.

1978-01-01

Certain relativistic field theories are shown to be equivalent to the grand partition function of an interacting gas. Using the physical insight given by this analogy many field-theoretic results are obtained, particularly for the sine-Gordon field theory. The main results are enumerated in the summary to which the reader is referred

L_∞ algebras and field theory

International Nuclear Information System (INIS)

Hohm, Olaf; Zwiebach, Barton

2017-01-01

We review and develop the general properties of L_∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L_∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L_∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L_∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L_∞ algebra for the interacting theory. The analysis suggests that L_∞ algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

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.

Covariant Noncommutative Field Theory

Energy Technology Data Exchange (ETDEWEB)

Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

2008-07-02

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.

Covariant Noncommutative Field Theory

International Nuclear Information System (INIS)

Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

2008-01-01

The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced

Loop calculations for the non-commutative U*(1) gauge field model with oscillator term

International Nuclear Information System (INIS)

Blaschke, Daniel N.; Grosse, Harald; Kronberger, Erwin; Schweda, Manfred; Wohlgenannt, Michael

2010-01-01

Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U * (1) gauge field theory including an oscillator-like term in the action has been put forward in (Blaschke et al. in Europhys. Lett. 79:61002, 2007). The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed. (orig.)

[Studies in quantum field theory

International Nuclear Information System (INIS)

1990-01-01

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

Affine field theories

International Nuclear Information System (INIS)

Cadavid, A.C.

1989-01-01

The author constructs a non-Abelian field theory by gauging a Kac-Moody algebra, obtaining an infinite tower of interacting vector fields and associated ghosts, that obey slightly modified Feynman rules. She discusses the spontaneous symmetry breaking of such theory via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra. She proceeds to show that there is no obstacle in implementing the affine extension of supersymmetric Yang-Mills theories. The result is valid in four, six and ten space-time dimensions. Then the affine extension of supergravity is investigated. She discusses only the loop algebra since the affine extension of the super-Poincare algebra appears inconsistent. The construction of the affine supergravity theory is carried out by the group manifold method and leads to an action describing infinite towers of spin 2 and spin 3/2 fields that interact subject to the symmetries of the loop algebra. The equations of motion satisfy the usual consistency check. Finally, she postulates a theory in which both the vector and scalar fields lie in the loop algebra of SO(3). This theory has an expanded soliton sector, and corresponding to the original 't Hooft-Polyakov solitonic solutions she now finds an infinite family of exact, special solutions of the new equations. She also proposes a perturbation method for obtaining an arbitrary solution of those equations for each level of the affine index

The Nonlinear Field Space Theory

Energy Technology Data Exchange (ETDEWEB)

Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)

2016-08-10

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

The Nonlinear Field Space Theory

International Nuclear Information System (INIS)

Mielczarek, Jakub; Trześniewski, Tomasz

2016-01-01

In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.

WORKSHOP: Thermal field theory

Energy Technology Data Exchange (ETDEWEB)

Anon.

1989-04-15

The early history of the Universe is a crucial testing ground for theories of elementary particles. Speculative ideas about the constituents of matter and their interactions are reinforced if they are consistent with what we suppose happened near the beginning of time and discarded if they are not. The cosmological consequences of these theories are usually deduced using a general statistical approach called thermal field theory. Thus, 75 physicists from thirteen countries met in Cleveland, Ohio, last October for the first 'Workshop on Thermal Field Theories and their Applications'.

Braided quantum field theories and their symmetries

International Nuclear Information System (INIS)

Sasai, Yuya; Sasakura, Naoki

2007-01-01

Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided quantum field theories that are required for the relations to hold. As concrete examples, we apply our analysis to the Poincare symmetries of two examples of noncommutative field theories. One is the effective quantum field theory of three-dimensional quantum gravity coupled to spinless particles formulated by Freidel and Livine, and the other is noncommutative field theory on the Moyal plane. We also comment on quantum field theory in κ-Minkowski spacetime. (author)

Finite quantum field theories

International Nuclear Information System (INIS)

Lucha, W.; Neufeld, H.

1986-01-01

We investigate the relation between finiteness of a four-dimensional quantum field theory and global supersymmetry. To this end we consider the most general quantum field theory and analyse the finiteness conditions resulting from the requirement of the absence of divergent contributions to the renormalizations of the parameters of the theory. In addition to the gauge bosons, both fermions and scalar bosons turn out to be a necessary ingredient in a non-trivial finite gauge theory. In all cases discussed, the supersymmetric theory restricted by two well-known constraints on the dimensionless couplings proves to be the unique solution of the finiteness conditions. (Author)

Quantum Yang-Mills theory of Riemann surfaces and conformal field theory

International Nuclear Information System (INIS)

Killingback, T.P.

1989-01-01

It is shown that Yang-Mills theory on a smooth surface, when suitably quantized, is a topological quantum field theory. This topological gauge theory is intimately related to two-dimensional conformal field theory. It is conjectured that all conformal field theories may be obtained from Yang-Mills theory on smooth surfaces. (orig.)

Remarks on high energy stability and renormalizability of gravity theory

International Nuclear Information System (INIS)

Salam, A.; Strathdee, J.

1978-02-01

Arguing that high-energy (Froissart) boundedness of gravitational cross-sections may make it necessary to supplement Einstein's Lagrangian with terms containing R 2 and Rsup(μν)Rsub(μν), criteria are suggested which, if satisfied, could make the tensor ghost in such a theory innocuous

A superstring field theory for supergravity

Science.gov (United States)

Reid-Edwards, R. A.; Riccombeni, D. A.

2017-09-01

A covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.

Quantum symmetries in particle interactions

International Nuclear Information System (INIS)

Shirkov, D.V.

1983-01-01

The concept of a quantum symmetry is introduced as a symmetry in the formulation of which quantum representations and specific quantum notions are used essentially. Three quantum symmetry principles are discussed: the principle of renormalizability (possibly super-renormalizability), the principle of local gauge symmetry, and the principle of supersymmetry. It is shown that these principles play a deterministic role in the development of quantum field theory. Historically their use has led to ever stronger restrictions on the interaction mechanism of quantum fields

Quantum Field Theory A Modern Perspective

CERN Document Server

Parameswaran Nair, V

2005-01-01

Quantum field theory, which started with Paul Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair’s view of certain topics in field theory loosely knit together as it gr...

Noncommutative field theory

International Nuclear Information System (INIS)

Douglas, Michael R.; Nekrasov, Nikita A.

2001-01-01

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level

Aspects of affine Toda field theory

International Nuclear Information System (INIS)

Braden, H.W.; Corrigan, E.; Dorey, P.E.; Sasaki, R.

1990-05-01

The report is devoted to properties of the affine Toda field theory, the intention being to highlight a selection of curious properties that should be explicable in terms of the underlying group theory but for which in most cases there are no explanation. The motivation for exploring the ideas contained in this report came principally from the recent work of Zamolodchikov concerning the two dimensional Ising model at critical temperature perturbed by a magnetic field. Hollowood and Mansfield pointed out that since Toda field theory is conformal the perturbation considered by Zamolodchikov might well be best regarded as a perturbation of a Toda field theory. This work made it seem plausible that the theory sought by Zamolodchikov was actually affine E 8 Toda field theory. However, this connection required an imaginary value of the coupling constant. Investigations here concerning exact S-matrices use a perturbative approach based on real coupling and the results differ in various ways from those thought to correspond to perturbed conformal field theory. A further motivation is to explore the connection between conformal and perturbed conformal field theories in other contexts using similar ideas. (N.K.)

Towards weakly constrained double field theory

Directory of Open Access Journals (Sweden)

Kanghoon Lee

2016-08-01

Full Text Available We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.

Topics in low-dimensional field theory

International Nuclear Information System (INIS)

Crescimanno, M.J.

1991-01-01

Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density

Nonequilibrium quantum field theories

International Nuclear Information System (INIS)

Niemi, A.J.

1988-01-01

Combining the Feynman-Vernon influence functional formalism with the real-time formulation of finite-temperature quantum field theories we present a general approach to relativistic quantum field theories out of thermal equilibrium. We clarify the physical meaning of the additional fields encountered in the real-time formulation of quantum statistics and outline diagrammatic rules for perturbative nonequilibrium computations. We derive a generalization of Boltzmann's equation which gives a complete characterization of relativistic nonequilibrium phenomena. (orig.)

Hyperfunction quantum field theory

International Nuclear Information System (INIS)

Nagamachi, S.; Mugibayashi, N.

1976-01-01

The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not contain C infinitely functios with compact support. In spite of this defect the support concept of H-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory. (orig.) [de

Correspondence between quantum gauge theories without ghost fields and their covariantly quantized theories with ghost fields

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.)

The logarithmic conformal field theories

International Nuclear Information System (INIS)

Rahimi Tabar, M.R.; Aghamohammadi, A.; Khorrami, M.

1997-01-01

We study the correlation functions of logarithmic conformal field theories. First, assuming conformal invariance, we explicitly calculate two- and three-point functions. This calculation is done for the general case of more than one logarithmic field in a block, and more than one set of logarithmic fields. Then we show that one can regard the logarithmic field as a formal derivative of the ordinary field with respect to its conformal weight. This enables one to calculate any n-point function containing the logarithmic field in terms of ordinary n-point functions. Finally, we calculate the operator product expansion (OPE) coefficients of a logarithmic conformal field theory, and show that these can be obtained from the corresponding coefficients of ordinary conformal theory by a simple derivation. (orig.)

1. Vienna central european seminar on particle physics and quantum field theory. Advances in quantum field theory. Program

International Nuclear Information System (INIS)

Hueffel, H.

2004-01-01

The new seminar series 'Vienna central European seminar on particle physics and quantum field theory' has been created 2004 and is intended to provide interactions between leading researchers and junior physicists. This year 'Advances in quantum field theory' has been chosen as subject and is centred on field theoretic aspects of string dualities. The lectures mainly focus on these aspects of string dualities. Further lectures regarding supersymmetric gauge theories, quantum gravity and noncommutative field theory are presented. The vast field of research concerning string dualities justifies special attention to their effects on field theory. (author)

Photon-Graviton Interaction and CPH Theory

DEFF Research Database (Denmark)

Javadi, Hossein; Forouzbakhsh, Farshid; Daei Kasmaei, Hamed

2016-01-01

, and the weak interaction by the W and Z bosons. The hypothesis is that the gravitational interaction is likewise mediated by a – yet undiscovered – elementary particle, dubbed the graviton. In the classical limit, the theory would reduce to general relativity and conform to Newton's law of gravitation......-renormalizable). Since classical general relativity and quantum mechanics are incompatible at such energies, from a theoretical point of view the present situation is not tenable. Some proposed models of quantum gravity attempt to address these issues, but these are speculative theories. Does a new definition...

Bell-type quantum field theories

International Nuclear Information System (INIS)

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

2005-01-01

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

Renormalization in self-consistent approximation schemes at finite temperature I: theory

International Nuclear Information System (INIS)

Hees, H. van; Knoll, J.

2001-07-01

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)

BRST field theory of relativistic particles

International Nuclear Information System (INIS)

Holten, J.W. van

1992-01-01

A generalization of BRST field theory is presented, based on wave operators for the fields constructed out of, but different from the BRST operator. The authors discuss their quantization, gauge fixing and the derivation of propagators. It is shown, that the generalized theories are relevant to relativistic particle theories in the Brink-Di Vecchia-Howe-Polyakov (BDHP) formulation, and argue that the same phenomenon holds in string theories. In particular it is shown, that the naive BRST formulation of the BDHP theory leads to trivial quantum field theories with vanishing correlation functions. (author). 22 refs

On spin chains and field theories

International Nuclear Information System (INIS)

Roiban, Radu

2004-01-01

We point out that the existence of global symmetries in a field theory is not an essential ingredient in its relation with an integrable model. We describe an obvious construction which, given an integrable spin chain, yields a field theory whose 1-loop scale transformations are generated by the spin chain hamiltonian. We also identify a necessary condition for a given field theory to be related to an integrable spin chain. As an example, we describe an anisotropic and parity-breaking generalization of the XXZ Heisenberg spin chain and its associated field theory. The system has no nonabelian global symmetries and generally does not admit a supersymmetric extension without the introduction of more propagating bosonic fields. For the case of a 2-state chain we find the spectrum and the eigenstates. For certain values of its coupling constants the field theory associated to this general type of chain is the bosonic sector of the q-deformation of N = 4 SYM theory. (author)

Gauge field theory

International Nuclear Information System (INIS)

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

1981-01-01

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

Time independent mean-field theory

International Nuclear Information System (INIS)

Negele, J.W.

1980-02-01

The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures

Interpolating string field theories

International Nuclear Information System (INIS)

Zwiebach, B.

1992-01-01

This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles

Finite temperature field theory

CERN Document Server

Das, Ashok

1997-01-01

This book discusses all three formalisms used in the study of finite temperature field theory, namely the imaginary time formalism, the closed time formalism and thermofield dynamics. Applications of the formalisms are worked out in detail. Gauge field theories and symmetry restoration at finite temperature are among the practical examples discussed in depth. The question of gauge dependence of the effective potential and the Nielsen identities are explained. The nonrestoration of some symmetries at high temperature (such as supersymmetry) and theories on nonsimply connected space-times are al

Wavelet-Based Quantum Field Theory

Directory of Open Access Journals (Sweden)

Mikhail V. Altaisky

2007-11-01

Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.

Algebraic quantum field theory

International Nuclear Information System (INIS)

Foroutan, A.

1996-12-01

The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)

On the background independence of string field theory

International Nuclear Information System (INIS)

Sen, A.

1990-01-01

Given a solution Ψ cl of the classical equations of motion in either closed or open string field theory formulated around a given conformal field theory background, we can construct a new operator Q B in the corresponding two-dimensional field theory such that (Q B ) 2 =0. It is shown that in the limit when the background field Ψ cl is weak, Q B can be identified with the BRST charge of a new local conformal field theory. This indicates that the string field theories formulated around these two different conformal field theories are actually the same theory, and that these two conformal field theories may be regarded as different classical solutions of this string field theory. (orig.)

Supersymmetric extensions of K field theories

Science.gov (United States)

Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.

2012-02-01

We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.

Quantum field theory in gravitational background

International Nuclear Information System (INIS)

Narnhofer, H.

1986-01-01

The author suggests ignoring the influence of the quantum field on the gravitation as the first step to combine quantum field theory and gravitation theory, but to consider the gravitational field as fixed and thus study quantum field theory on a manifold. This subject evoked interest when thermal radiation of a black hole was predicted. The author concentrates on the free quantum field and can split the problem into two steps: the Weyl-algebra of the free field and the Wightman functional on the tangent space

Renormalization of supersymmetric models without using auxiliary fields

International Nuclear Information System (INIS)

Urbanek, P.

1986-01-01

Previously a linear representation of supersymmetry (Ss) was used in investigations of renormalizability. There auxiliary fields have been introduced in order that the Ss-algebra closes 'off-shell'. When the auxiliary fields are eliminated by their equations of motion, the Ss representation becomes nonlinear and Ss closes only 'on-shell'. Following O.Piguet and K.Sibold 1984 Ss is expressed through Ward identities which are formulated as functional variations of the generating functional of the Green functions. These functional operators form a closed algebra, a fact essential for the proof of renormalizability, which is given. It is not necessary to use a specific subtraction scheme in the Green functions. The procedure is applied to the Wess-Zumino model and the supersymmetric extension of the quantum electrodynamics. 15 refs. (qui)

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.)

Introduction to quantum field theory

CERN Document Server

Alvarez-Gaumé, Luís

1994-01-01

The purpose of this lecture is to review some elementary aspects of Quantum Field Theory. From the necessity to introduce quantum fields once quantum mechanics and special relativity are put together, to some of the basic practical computational tools in the subject, including the canonical quantization of simple field theories, the derivation of Feynman rules, computation of cross sections and decay rates, some introductory remarks on the treatment of unstable states and the possible realization of symmetries in a general field theory. The audience is required to have a working knowledge of quantum mechanics and special relativity and it would also be desirable to know the rudiments of relativistic quantum mechanics.

Conformal techniques in string theory and string field theory

International Nuclear Information System (INIS)

Giddings, S.B.

1987-01-01

The application of some conformal and Riemann surface techniques to string theory and string field theory is described. First a brief review of Riemann surface techniques and of the Polyakov approach to string theory is presented. This is followed by a discussion of some features of string field theory and of its Feynman rules. Specifically, it is shown that the Feynman diagrams for Witten's string field theory respect modular invariance, and in particular give a triangulation of moduli space. The Polyakov formalism is then used to derive the Feynman rules that should follow from this theory upon gauge-fixing. It should also be possible to apply this derivation to deduce the Feynman rules for other gauge-fixed string field theories. Following this, Riemann surface techniques are turned to the problem of proving the equivalence of the Polyakov and light-cone formalisms. It is first shown that the light-cone diagrams triangulate moduli space. Then the Polyakov measure is worked out for these diagrams, and shown to equal that deduced from the light-cone gauge fixed formalism. Also presented is a short description of the comparison of physical states in the two formalisms. The equivalence of the two formalisms in particular constitutes a proof of the unitarity of the Polyakov framework for the closed bosonic string

Mass corrections in string theory and lattice field theory

International Nuclear Information System (INIS)

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

2009-01-01

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

An introduction to gauge theories

International Nuclear Information System (INIS)

Iliopoulos, J.

1976-01-01

These lecture notes present an introduction to gauge theories: the systematics of Yang-Mills theories, spontaneous symmetry breaking, and Higgs mechanism. The treatment is simple, stressing the general principles rather than detailed calculations. We present the Weinberg-Salam model as an example of a renormalizable theory of weak and electromagnetic interactions of leptons, and we show that the extension of these ideas into the hadronic world requires the introduction of charm and colour. Finally, we try to include strong interactions into the scheme, guided by the experimental results of deep-inelastic lepton-nucleon scattering. We derive and solve the Callan-Symanzik equation, and we introduce the concepts of asymptotic freedom and quark confinement. (Author)

L{sub ∞} algebras and field theory

Energy Technology Data Exchange (ETDEWEB)

Hohm, Olaf [Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY (United States); Zwiebach, Barton [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA (United States)

2017-03-15

We review and develop the general properties of L{sub ∞} algebras focusing on the gauge structure of the associated field theories. Motivated by the L{sub ∞} homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L{sub ∞} structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L{sub ∞} algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L{sub ∞} algebra for the interacting theory. The analysis suggests that L{sub ∞} algebras provide a classification of perturbative gauge invariant classical field theories. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Mathematical aspects of quantum field theory

CERN Document Server

de Faria, Edson

2010-01-01

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Closed string field theory

International Nuclear Information System (INIS)

Strominger, A.

1987-01-01

A gauge invariant cubic action describing bosonic closed string field theory is constructed. The gauge symmetries include local spacetime diffeomorphisms. The conventional closed string spectrum and trilinear couplings are reproduced after spontaneous symmetry breaking. The action S is constructed from the usual ''open string'' field of ghost number minus one half. It is given by the associator of the string field product which is non-vanishing because of associativity anomalies. S does not describe open string propagation because open string states associate and can thereby be shifted away. A field theory of closed and open strings can be obtained by adding to S the cubic open string action. (orig.)

Fermion boson metamorphosis in field theory

International Nuclear Information System (INIS)

Ha, Y.K.

1982-01-01

In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered

N=1 field theory duality from M theory

International Nuclear Information System (INIS)

Schmaltz, M.; Sundrum, R.

1998-01-01

We investigate Seiberg close-quote s N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in type IIA string theory is given an elegant derivation from M theory. copyright 1998 The American Physical Society

Families and degenerations of conformal field theories

Energy Technology Data Exchange (ETDEWEB)

Roggenkamp, D.

2004-09-01

In this work, moduli spaces of conformal field theories are investigated. In the first part, moduli spaces corresponding to current-current deformation of conformal field theories are constructed explicitly. For WZW models, they are described in detail, and sigma model realizations of the deformed WZW models are presented. The second part is devoted to the study of boundaries of moduli spaces of conformal field theories. For this purpose a notion of convergence of families of conformal field theories is introduced, which admits certain degenerated conformal field theories to occur as limits. To such a degeneration of conformal field theories, a degeneration of metric spaces together with additional geometric structures can be associated, which give rise to a geometric interpretation. Boundaries of moduli spaces of toroidal conformal field theories, orbifolds thereof and WZW models are analyzed. Furthermore, also the limit of the discrete family of Virasoro minimal models is investigated. (orig.)

Dynamical Mean Field Approximation Applied to Quantum Field Theory

CERN Document Server

Akerlund, Oscar; Georges, Antoine; Werner, Philipp

2013-12-04

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

Field theory approach to gravitation

International Nuclear Information System (INIS)

Yilmaz, H.

1978-01-01

A number of authors considered the possibility of formulating a field-theory approach to gravitation with the claim that such an approach would uniquely lead to Einstein's theory of general relativity. In this article it is shown that the field theory approach is more generally applicable and uniqueness cannot be claimed. Theoretical and experimental reasons are given showing that the Einsteinian limit appears to be unviable

Asymptomatic freedom in renormalisable gravity and supergravity

International Nuclear Information System (INIS)

Fradkin, E.S.; Tseytlin, A.A.

1984-01-01

This chapter demonstrates that renormalizable supergravity, which is a superextension of renormalizable quantum gravity, can be the basis for a natural ''induced supergravity'' theory. A perturbatively operational unified theory is needed for a description of the early stages of the Universe, and renormalizable quantum gravity is well suited for unification with the renormalizable Grand Unified Models of matter. Topics considered include one-loop counter-terms and renormalization group (RG) equations for pure renormalizable gravity; the consequences of asymptotic freedom; the inclusion of matter; conformal supergravities; and renormalizable supergravity models. It is concluded that the presented lagrangian, which contains a locally superconformal extension of the Yang-Mills and massless spinor lagrangians and the conformal supergravity term, shows that conformal supergravity may play an important role in a fundamental theory

Dualities among one-time field theories with spin, emerging from a unifying two-time field theory

International Nuclear Information System (INIS)

Bars, Itzhak; Quelin, Guillaume

2008-01-01

The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS d-k xS k , and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure

Mathematical aspects of quantum field theories

CERN Document Server

Strobl, Thomas

2015-01-01

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...

Introduction to quantum field theory

International Nuclear Information System (INIS)

Kazakov, D.I.

1988-01-01

The lectures appear to be a continuation to the introduction to elementary principles of the quantum field theory. The work is aimed at constructing the formalism of standard particle interaction model. Efforts are made to exceed the limits of the standard model in the quantum field theory context. Grand unification models including strong and electrical weak interactions, supersymmetric generalizations of the standard model and grand unification theories and, finally, supergravitation theories including gravitation interaction to the universal scheme, are considered. 3 refs.; 19 figs.; 2 tabs

Vertex operator algebras and conformal field theory

International Nuclear Information System (INIS)

Huang, Y.Z.

1992-01-01

This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics

A landscape of field theories

Energy Technology Data Exchange (ETDEWEB)

Maxfield, Travis [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States); Robbins, Daniel [George P. and Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University,College Station, TX 77843-4242 (United States); Sethi, Savdeep [Enrico Fermi Institute, University of Chicago,Chicago, IL 60637 (United States)

2016-11-28

Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2,0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.

Operator algebras and conformal field theory

International Nuclear Information System (INIS)

Gabbiani, F.; Froehlich, J.

1993-01-01

We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III 1 factor. The conformal net determined by the algebras of local observables is proven to satisfy Haag duality. The representation of the Moebius group (and presumably of the entire Virasoro algebra) on the vacuum sector of a conformal field theory is uniquely determined by the Tomita-Takesaki modular operators associated with its vacuum state and its conformal net. We then develop the theory of Mebius covariant representations of a conformal net, using methods of Doplicher, Haag and Roberts. We apply our results to the representation theory of loop groups. Our analysis is motivated by the desire to find a 'background-independent' formulation of conformal field theories. (orig.)

Boundary effects on quantum field theories

International Nuclear Information System (INIS)

Lee, Tae Hoon

1991-01-01

Quantum field theory in the S 1 *R 3 space-time is simply described by the imaginary time formalism. We generalize Schwinger-DeWitt proper-time technique which is very useful in zero temperature field theories to this case. As an example we calculate the one-loop effective potential of the finite temperature scala field theory by this technique.(Author)

Generalized Field Theory and Kasner universe

International Nuclear Information System (INIS)

Klotz, A.H.

1986-01-01

It is shown that the only Kasner-like solution of the Generalized Field Theory field equations with a nonzero electromagnetic field corresponds to an empty field geometry of the space-time. In this case, the electromagnetic field tensors of the theory coincide as could be expected from general considerations. 6 refs. (author)

On finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1984-01-01

The properties that make massless versions of N = 4 super Yang-Mills theory and a class of N = 2 supersymmetric theories finite are: (I) a universal coupling for the gauge and matter interactions, (II) anomaly-free representations to which the bosonic and fermionic matter belong, and (III) no charge renormalisation, i.e. β(g) = 0. It was conjectured that field theories constructed out of N = 1 matter multiplets are also finite if they too share the above properties. Explicit calculations have verified these theories to be finite up to two loops. The implications of the finiteness conditions for N = 1 finite field theories with SU(M) gauge symmetry are discussed. (orig.)

Quantum Field Theory

CERN Document Server

Zeidler, Eberhard

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the different languages used by mathematicians and physicists. For students of mathematics it is shown that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which is beyond the usual curriculum in physics. It is the author's goal to present the state of the art of realizing Einstein's dream of a unified theory for the four fundamental forces in the universe (gravitational, electromagnetic, strong, and weak interaction). From the reviews: "… Quantum field theory is one of the great intellectual edifices in the history of human thought. … This volume differs from othe...

Microcontinuum field theories

CERN Document Server

Eringen, A Cemal

1999-01-01

Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. Material bodies are here viewed as collections of large numbers of deformable particles, much as each volume element of a fluid in statistical mechanics is viewed as consisting of a large number of small particles for which statistical laws are valid. Classical continuum theories are valid when the characteristic length associated with external forces or stimuli is much larger than any internal scale of the body under consideration. When the characteristic lengths are comparable, however, the response of the individual constituents becomes important, for example, in considering the fluid or elastic properties of blood, porous media, polymers, liquid crystals, slurries, and composite materials. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balanc...

Introduction to algebraic quantum field theory

International Nuclear Information System (INIS)

Horuzhy, S.S.

1990-01-01

This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

Quaternionic quantum field theory

International Nuclear Information System (INIS)

Adler, S.L.

1986-01-01

In this paper the author describes a new kind of quantum mechanics or quantum field theory based on quaternions. Quaternionic quantum mechanics has a Schrodinger equation, a Dirac transformation theory, and a functional integral. Quaternionic quantum mechanics does not seem to have (except in the complex quantum mechanics specialization): A correspondence principle, and beyond this a commuting tensor product, asymptotic states, an S-matrix, a canonical formalism, coherent states or a Euclidean continuation. A new kind of quantum mechanics exists. There are many interesting formal questions to study, which should enable one to decide whether quaternionic quantum field theory is relevant for particle physics

Solution of equation for imaginary part of forward scattering amplitude for theories with lambdaphisup(n) interaction

International Nuclear Information System (INIS)

Arbuzov, B.A.; D'yakonov, V.Yu.; Rochev, V.E.

1975-01-01

Solution of equations for imaginary part of forward scattering amplitude in ladder approximation for theories with lambdaphisup(n),n(>=)4 interaction have been obtained. Two types of diagrams have been considered for lambdaphisup(n) renormalizable theory. It is shown, that the leading singularity is the branch point, which gives the power asymptotics with accuracy up to logarithms. The unrenormalizable theory with n(>=)5 lead to exponentially rising asymptotics

A philosophical approach to quantum field theory

CERN Document Server

Öttinger, Hans Christian

2015-01-01

This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.

Toward finite quantum field theories

International Nuclear Information System (INIS)

Rajpoot, S.; Taylor, J.G.

1986-01-01

The properties that make the N=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule Σsub(s=0.1/2)(-1)sup(2s+1)(2s+1)M 2 sub(s)=O. Finite N=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting of N=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finite N=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that an N=1 finite SU(5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments. (author)

Superspace conformal field theory

Energy Technology Data Exchange (ETDEWEB)

Quella, Thomas [Koeln Univ. (Germany). Inst. fuer Theoretische Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-07-15

Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

Superspace conformal field theory

International Nuclear Information System (INIS)

Quella, Thomas

2013-07-01

Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

Mean-field theory and solitonic matter

International Nuclear Information System (INIS)

Cohen, T.D.

1989-01-01

Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)

Lectures on matrix field theory

CERN Document Server

Ydri, Badis

2017-01-01

These lecture notes provide a systematic introduction to matrix models of quantum field theories with non-commutative and fuzzy geometries. The book initially focuses on the matrix formulation of non-commutative and fuzzy spaces, followed by a description of the non-perturbative treatment of the corresponding field theories. As an example, the phase structure of non-commutative phi-four theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to non-commutative gauge theories, while two appendices round out the text. Primarily written as a self-study guide for postgraduate students – with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications – these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of non-commutative field theory with an emphasis on matrix models and fuzzy geometries.

Non-perturbative field theory/field theory on a lattice

International Nuclear Information System (INIS)

Ambjorn, J.

1988-01-01

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

The birth of asymptotic freedom

International Nuclear Information System (INIS)

Hooft, G. 't

1985-01-01

An account is given of the authors' personal perception of the historical developments that accumulated into the present understanding of the renormalization group behavior of renormalizable quantum field theories. (orig.)

Cutkosky rules for superstring field theory

International Nuclear Information System (INIS)

Pius, Roji; Sen, Ashoke

2016-01-01

Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.

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

Effective Field Theory on Manifolds with Boundary

Science.gov (United States)

Albert, Benjamin I.

In the monograph Renormalization and Effective Field Theory, Costello made two major advances in rigorous quantum field theory. Firstly, he gave an inductive position space renormalization procedure for constructing an effective field theory that is based on heat kernel regularization of the propagator. Secondly, he gave a rigorous formulation of quantum gauge theory within effective field theory that makes use of the BV formalism. In this work, we extend Costello's renormalization procedure to a class of manifolds with boundary and make preliminary steps towards extending his formulation of gauge theory to manifolds with boundary. In addition, we reorganize the presentation of the preexisting material, filling in details and strengthening the results.

Z/NZ conformal field theories

International Nuclear Information System (INIS)

Degiovanni, P.

1990-01-01

We compute the modular properties of the possible genus-one characters of some Rational Conformal Field Theories starting from their fusion rules. We show that the possible choices of S matrices are indexed by some automorphisms of the fusion algebra. We also classify the modular invariant partition functions of these theories. This gives the complete list of modular invariant partition functions of Rational Conformal Field Theories with respect to the A N (1) level one algebra. (orig.)

On the development of non-commutative translation-invariant quantum gauge field models

International Nuclear Information System (INIS)

Sedmik, R.I.P.

2009-01-01

Aiming to understand the most fundamental principles of nature one has to approach the highest possible energy scales corresponding to the smallest possible distances - the Planck scale. Historically, three different theoretical fields have been developed to treat the problems appearing in this endeavor: string theory, quantum gravity, and non-commutative (NC) quantum field theory (QFT). The latter was originally motivated by the conjecture that the introduction of uncertainty relations between space-time coordinates introduces a natural energy cutoff, which should render the resulting computations well defined and finite. Despite failing to fulfill this expectation, NC physics is a challenging field of research, which has proved to be a fruitful source for new ideas and methods. Mathematically, non-commutativity is implemented by the so called Weyl quantization, giving rise to a modified product - the Groenewold-Moyal product. It realizes an operator ordering, and allows to work within the well established framework of QFT on non-commutative spaces. The main obstacle of NCQFT is the appearance of singularities being shifted from high to low energies. This effect, being referred to as 'uV/IR mixing', is a direct consequence of the deformation of the product, and inhibits or complicates the direct application of well approved renormalization schemes. In order to remedy this problem, several approaches have been worked out during the past decade which, unfortunately, all have shortcomings such as the breaking of translation invariance or an inappropriate alternation of degrees of freedom. Thence, the resulting theories are either being rendered 'unphysical', or considered a priori to be toy models. Nonetheless, these efforts have helped to analyze the mechanisms leading to uV/IR mixing and finally led to the insight that renormalizability can only be achieved by respecting the inherent connection of long and short distances (scales) of NCQFT in the construction of

Development of a (4-ε)-dimensional theory for the density of states of a disordered system near the Anderson transition

International Nuclear Information System (INIS)

Suslov, Igor' M

1998-01-01

The calculation of the density of states for the Schroedinger equation with a Gaussian random potential is equivalent to the problem of a second-order transition with a 'wrong' sign for the coefficient of the quartic term in the Ginzburg-Landau Hamiltonian. The special role of the dimension d = 4 for such a Hamiltonian can be seen from different viewpoints but is fundamentally determined by the renormalizability of the theory. The construction of an ε expansion in direct analogy with the phase-transition theory gives rise to the problem of a 'spurious' pole. To solve this problem, a proper treatment of the factorial divergency of the perturbation series is necessary. Simplifications arising in high dimensions can be used for the development of a (4-ε)-dimensional theory, but this requires successive consideration of four types of theories: a nonrenormalizable theories for d > 4, nonrenormalizable and renormalizable theories in the logarithmic situation (d = 4), and a super-renormalizable theories for d < 4. An approximation is found for each type of theory giving asymptotically exact results. In the (4-ε)-dimensional theory, the terms of leading order in 1/ε are only retained for N∼1 (N is the order of the perturbation theory) while all degrees of 1/ε are essential for large N in view of the fast growth of their coefficients. The latter are calculated in the leading order in N from the Callan-Symanzik equation with the results of Lipatov method used as boundary conditions. The qualitative effect is the same in all four cases and consists in a shifting of the phase transition point in the complex plane. This results in the elimination of the 'spurious' pole and in regularity of the density of states for all energies. A discussion is given of the calculation of high orders of perturbation theory and a perspective of the ε expansion for the problem of conductivity near the Anderson transition. (reviews of topical problems)

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

Remarks on the formal symmetries of the asymptotic fields

International Nuclear Information System (INIS)

Ragiadakos, C.

1976-01-01

Based on the formal validity of the Lagrangian expression of the S-matrix, the internal unitary symmetries and the Dirac electromagnetic interactions are derived as the unique ones among the renormalizable interactions. The same arguments are not compatible with gauge theories while in some special cases they are in contradiction with some physical results [fr

Group field theory with noncommutative metric variables.

Science.gov (United States)

Baratin, Aristide; Oriti, Daniele

2010-11-26

We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

Perturbation theory and coupling constant analyticity in two-dimensional field theories

International Nuclear Information System (INIS)

Simon, B.

1973-01-01

Conjectural material and results over a year old are presented in the discussion of perturbation theory and coupling constant analyticity in two-dimensional field theories. General properties of perturbation series are discussed rather than questions of field theory. The question is interesting for two reasons: First, one would like to understand why perturbation theory is such a good guide (to show that perturbation theory determines the theory in some way). Secondly, one hopes to prove that some or all of the theories are nontrivial. (U.S.)

Semiclassical methods in field theories

International Nuclear Information System (INIS)

Ventura, I.

1978-10-01

A new scheme is proposed for semi-classical quantization in field theory - the expansion about the charge (EAC) - which is developed within the canonical formalism. This method is suitable for quantizing theories that are invariant under global gauge transformations. It is used in the treatment of the non relativistic logarithmic theory that was proposed by Bialynicki-Birula and Mycielski - a theory we can formulate in any number of spatial dimensions. The non linear Schroedinger equation is also quantized by means of the EAC. The classical logarithmic theories - both, the non relativistic and the relativistic one - are studied in detail. It is shown that the Bohr-Sommerfeld quantization rule(BSQR) in field theory is, in many cases, equivalent to charge quantization. This rule is then applied to the massive Thirring Model and the logarithmic theories. The BSQR can be see as a simplified and non local version of the EAC [pt

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.)

Algebraic quantum field theory, perturbation theory, and the loop expansion

International Nuclear Information System (INIS)

Duetsch, M.; Fredenhagen, K.

2001-01-01

The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to arbitrary small subregions of Minkowski space. We also give an algebraic formulation of the loop expansion by introducing a projective system A (n) of observables ''up to n loops'', where A (0) is the Poisson algebra of the classical field theory. Finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of Green's functions. (orig.)

Singularity theory and N = 2 superconformal field theories

International Nuclear Information System (INIS)

Warner, N.P.

1989-01-01

The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs

On the vacuum states for non-commutative gauge theory TH1"-->

Science.gov (United States)

de Goursac, A.; Wallet, J.-C.; Wulkenhaar, R.

2008-07-01

Candidates for renormalizable gauge theory models on Moyal spaces constructed recently have non-trivial vacua. We show that these models support vacuum states that are invariant under both global rotations and symplectic isomorphisms which form a global symmetry group for the action. We compute the explicit expression in position space for these vacuum configurations in two and four dimensions.

Higher-derivative boson field theories and constrained second-order theories

Energy Technology Data Exchange (ETDEWEB)

Urries, F.J. de [Departamento de Fisica, Universidad de Alcala de Henares, Madrid (Spain) and IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (Spain)]. E-mail: fernando.urries@uah.es; Julve, J. [IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (Spain)]. E-mail: julve@imaff.cfmac.csic.es; Sanchez, E.J. [IMAFF, Consejo Superior de Investigaciones Cientificas, Madrid (ES) and Departamento de Matematica, Universidad Europea, Madrid (Spain)]. E-mail: ejesus.sanchez@mat.ind.uem.es

2001-10-26

As an alternative to the covariant Ostrogradski method, we show that higher-derivative (HD) relativistic Lagrangian field theories can be reduced to second differential order by writing them directly as covariant two-derivative theories involving Lagrange multipliers and new fields. Despite the intrinsic non-covariance of the Dirac procedure used to deal with the constraints, the explicit Lorentz invariance is recovered at the end. We develop this new setting on the basis of a simple scalar model and then its applications to generalized electrodynamics and HD gravity are worked out. For a wide class of field theories this method is better suited than Ostrogradski's for a generalization to 2n-derivative theories. (author)

Wilson lines in quantum field theory

Energy Technology Data Exchange (ETDEWEB)

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

2014-07-01

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

Wilson lines in quantum field theory

International Nuclear Information System (INIS)

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

2014-01-01

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

Geometry of lattice field theory

International Nuclear Information System (INIS)

Honan, T.J.

1986-01-01

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

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

Introduction to classical and quantum field theory

International Nuclear Information System (INIS)

Ng, Tai-Kai

2009-01-01

This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into three parts, the first part covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part introduces more advanced concepts and techniques. Part III discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing, 'real' physics problems. Throughout there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers. (orig.)

Field theory and the Standard Model

Energy Technology Data Exchange (ETDEWEB)

Dudas, E [Orsay, LPT (France)

2014-07-01

This brief introduction to Quantum Field Theory and the Standard Model contains the basic building blocks of perturbation theory in quantum field theory, an elementary introduction to gauge theories and the basic classical and quantum features of the electroweak sector of the Standard Model. Some details are given for the theoretical bias concerning the Higgs mass limits, as well as on obscure features of the Standard Model which motivate new physics constructions.

Effective theories of single field inflation when heavy fields matter

CERN Document Server

Achucarro, Ana; Hardeman, Sjoerd; Palma, Gonzalo A; Patil, Subodh P

2012-01-01

We compute the low energy effective field theory (EFT) expansion for single-field inflationary models that descend from a parent theory containing multiple other scalar fields. By assuming that all other degrees of freedom in the parent theory are sufficiently massive relative to the inflaton, it is possible to derive an EFT valid to arbitrary order in perturbations, provided certain generalized adiabaticity conditions are respected. These conditions permit a consistent low energy EFT description even when the inflaton deviates off its adiabatic minimum along its slowly rolling trajectory. By generalizing the formalism that identifies the adiabatic mode with the Goldstone boson of this spontaneously broken time translational symmetry prior to the integration of the heavy fields, we show that this invariance of the parent theory dictates the entire non-perturbative structure of the descendent EFT. The couplings of this theory can be written entirely in terms of the reduced speed of sound of adiabatic perturbat...

Euler-Poincare reduction for discrete field theories

International Nuclear Information System (INIS)

Vankerschaver, Joris

2007-01-01

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

Perturbative analysis of non-Abelian Aharonov-Bohm scattering

International Nuclear Information System (INIS)

Bak, D.; Bergman, O.

1995-01-01

We perform a perturbative analysis of the non-Abelian Aharonov-Bohm problem to one loop in the framework of a local field theory, and show the necessity of contact interactions for renormalizability of perturbation theory. Moreover at critical values of the contact interaction strength the theory is finite and preserves classical conformal invariance

Unified field theory

International Nuclear Information System (INIS)

Vollendorf, F.

1976-01-01

A theory is developed in which the gravitational as well as the electromagnetic field is described in a purely geometrical manner. In the case of a static central symmetric field Newton's law of gravitation and Schwarzschild's line element are derived by means of an action principle. The same principle leads to Fermat's law which defines the world lines of photons. (orig.) [de

Austerity and geometric structure of field theories

International Nuclear Information System (INIS)

Kheyfets, A.

1986-01-01

The relation between the austerity idea and the geometric structure of the three basic field theories - electrodynamics, Yang-Mills theory, and general relativity - is studied. One of the most significant manifestations of the austerity idea in field theories is thought to be expressed by the boundary of a boundary principle (BBP). The BBP says that almost all content of the field theories can be deduced from the topological identity of delta dot produced with delta = 0 used twice, at the 1-2-3-dimensional level (providing the homogeneous field equations), and at the 2-3-4-dimensional level (providing the conservation laws for the source currents). There are some difficulties in this line of thought due to the apparent lack of universality in application of the BBP to the three basic modern field theories above. This dissertation: (a) analyzes the difficulties by means of algebraic topology, integration theory, and modern differential geometry based on the concepts of principal bundles and Ehresmann connections: (b) extends the BBP to the unified Kaluza-Klein theory; (c) reformulates the inhomogeneous field equations and the BBP in terms of E. Cartan moment of rotation, in the way universal for the three theories and compatible with the original austerity idea; and (d) underlines the important role of the soldering structure on spacetime, and indicates that the future development of the austerity idea would involve the generalized theories

On background-independent open-string field theory

International Nuclear Information System (INIS)

Witten, E.

1992-01-01

A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical ''space of all open-string world-sheet theories.'' It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant open-string world-sheet theories and that, when expanding around a classical solution, the infinitesimal gauge transformations are generated by the world-sheet BRST operator

An introduction to conformal field theory

International Nuclear Information System (INIS)

Gaberdiel, Matthias R.; Fitzwilliam College, Cambridge

2000-01-01

A comprehensive introduction to two-dimensional conformal field theory is given. The structure of the meromorphic subtheory is described in detail, and a number of examples are presented explicitly. Standard constructions such as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Zhu's algebra in classifying highest weight representations is elucidated. The fusion product of two representations and the corresponding fusion rules are defined, and Verlinde's formula is explained. Finally, higher correlation functions are considered, and the polynomial relations of Moore and Seiberg and the quantum group structure of chiral conformal field theory are discussed. The treatment is relatively general and also allows for a description of less well known classes of theories such as logarithmic conformal field theories. (author)

Factorization algebras in quantum field theory

CERN Document Server

Costello, Kevin

2017-01-01

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.

Metric quantum field theory: A preliminary look

International Nuclear Information System (INIS)

Watson, W.N.

1988-01-01

Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature? This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics

The classical theory of fields electromagnetism

CERN Document Server

Helrich, Carl S

2012-01-01

The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...

An introduction to effective field theory

International Nuclear Information System (INIS)

Donoghue, John F.

1999-01-01

In these lectures I describe the main ideas of effective field theory. These are first illustrated using QED and the linear sigma model as examples. Calculational techniques using both Feynman diagrams and dispersion relations are introduced. Within QCD, chiral perturbation theory is a complete effective field theory, and I give a guide to some calculations in the literature which illustrates key ideas. (author)

Quantum Field Theory in (0 + 1) Dimensions

Science.gov (United States)

Boozer, A. D.

2007-01-01

We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…

Gravitational effects in field gravitation theory

International Nuclear Information System (INIS)

Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.; Vlasov, A.A.

1979-01-01

The possibilities to describe various gravitation effects of field gravitation theory (FGT) are considered. Past-Newtonian approximation of the FGT has been constructed and on the basis of this approximation it has been shown that the field theory allows one to describe the whole set of experimental facts. The comparison of post-Newtonian parameters in FGT with those in the Einstein's theory makes it clear that these two; theories are undistinguishable from the viewpoint of any experiments, realized with post-Newtonian accuracy. Gravitational field of an island type source with spherically symmetrical distribution of matter and unstationary homogeneous model of Universe, which allows to describe the effect of cosmological red shift, are considered

Knots, topology and quantum field theories

International Nuclear Information System (INIS)

Lusanna, L.

1989-01-01

The title of the workshop, Knots, Topology and Quantum Field Theory, accurate reflected the topics discussed. There have been important developments in mathematical and quantum field theory in the past few years, which had a large impact on physicist thinking. It is historically unusual and pleasing that these developments are taking place as a result of an intense interaction between mathematical physicists and mathematician. On the one hand, topological concepts and methods are playing an increasingly important lead to novel mathematical concepts: for instance, the study of quantum groups open a new chapter in the deformation theory of Lie algebras. These developments at present will lead to new insights into the theory of elementary particles and their interactions. In essence, the talks dealt with three, broadly defined areas of theoretical physics. One was topological quantum field theories, the other the problem of quantum groups and the third one certain aspects of more traditional field theories, such as, for instance, quantum gravity. These topics, however, are interrelated and the general theme of the workshop defies rigid classification; this was evident from the cross references to be found in almo all the talks

An introduction to conformal field theory in two dimensions and string theory

International Nuclear Information System (INIS)

Wadia, S.R.

1989-01-01

This paper provides information on The S-Matrix; Elements of conformally invariant field theory in 2-dim.; The Virasoro gauge conditions; Some representations of the Virasoro algebra; The S-matrix of the Bosonic string theory; Super conformal field theory; Superstring; superstring spectrum and GSO projection; The (β,γ) ghost system; BRST formulation; and String propagation in background fields

Path integral quantization of parametrized field theory

International Nuclear Information System (INIS)

Varadarajan, Madhavan

2004-01-01

Free scalar field theory on a flat spacetime can be cast into a generally covariant form known as parametrized field theory in which the action is a functional of the scalar field as well as the embedding variables which describe arbitrary, in general curved, foliations of the flat spacetime. We construct the path integral quantization of parametrized field theory in order to analyze issues at the interface of quantum field theory and general covariance in a path integral context. We show that the measure in the Lorentzian path integral is nontrivial and is the analog of the Fradkin-Vilkovisky measure for quantum gravity. We construct Euclidean functional integrals in the generally covariant setting of parametrized field theory using key ideas of Schleich and show that our constructions imply the existence of nonstandard 'Wick rotations' of the standard free scalar field two-point function. We develop a framework to study the problem of time through computations of scalar field two-point functions. We illustrate our ideas through explicit computation for a time independent (1+1)-dimensional foliation. Although the problem of time seems to be absent in this simple example, the general case is still open. We discuss our results in the contexts of the path integral formulation of quantum gravity and the canonical quantization of parametrized field theory

Nonlocal quantum field theory

International Nuclear Information System (INIS)

Efimov, G.V.

1976-01-01

The basic ideas for creating the theory of nonlocal interactions of a scalar one-component field are presented. Lagrangian describing a non-interacting field is the ordinary one so that non-interacting particles are described by standard methods of the Fock space. Form factors introduced have been chosen from a class of analytic functionals and quantized. Conditions of microcausality have been considered in detail. The convergence of all integrals corresponding to the arbitrary Feynman diagrams in spinor electrodynamics is guaranteed in the frame of the rules formulated. It is noted in conclusion that the spinor electrodynamics with nonlocal interaction contains no ultraviolet divergencies and satisfies all the requirements of the quantum field theory; in this sense it is mathematically more consistent than its local version

Two-dimensional topological field theories coupled to four-dimensional BF theory

International Nuclear Information System (INIS)

Montesinos, Merced; Perez, Alejandro

2008-01-01

Four-dimensional BF theory admits a natural coupling to extended sources supported on two-dimensional surfaces or string world sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two-dimensional world sheet. We show how two-dimensional Yang-Mills degrees of freedom can be added on the world sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two-dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background-independent quantum field theory where local degrees of freedom at low energies arise from global topological (world sheet) degrees of freedom at the fundamental level

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

A novel string field theory solving string theory by liberating left and right movers

International Nuclear Information System (INIS)

Nielsen, Holger B.; Ninomiya, Masao

2014-01-01

We put forward ideas to a novel string field theory based on making some “objects” that essentially describe “liberated” left- and right- mover fields X L μ (τ+σ) and X R μ (τ−σ) on the string. Our novel string field theory is completely definitely different from any other string theory in as far as a “null set” of information in the string field theory Fock space has been removed relatively, to the usual string field theories. So our theory is definitely new. The main progress is that we manage to make our novel string field theory provide the correct mass square spectrum for the string. We finally suggest how to obtain the Veneziano amplitude in our model

Hidden gravity in open-string field theory

International Nuclear Information System (INIS)

Siegel, W.

1994-01-01

We clarify the nature of the graviton as a bound state in open-string field theory: The flat metric in the action appears as the vacuum value of an open string field. The bound state appears as a composite field in the free field theory

Field theory of relativistic strings: I. Trees

International Nuclear Information System (INIS)

Kaku, M.; Kikkawa, K.

1985-01-01

The authors present an entirely new kind of field theory, a field theory quantized not at space-time points, but quantized along an extended set of multilocal points on a string. This represents a significant departure from the usual quantum field theory, whose free theory represents a definite set of elementary particles, because the field theory on relativistic strings can accommodate an infinite set of linearly rising Regge trajectories. In this paper, the authors (1) present canonical quantization and the Green's function of the free string, (2) introduce three-string interactions, (3) resolve the question of multiple counting, (4) complete the counting arguments for all N-point trees, and (5) introduce four-string interactions which yield a Yang-Mills structure when the zero-slope limit is taken

Conformal field theories and tensor categories. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics

2014-08-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Conformal field theories and tensor categories. Proceedings

International Nuclear Information System (INIS)

Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph

2014-01-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Neural fields theory and applications

CERN Document Server

Graben, Peter; Potthast, Roland; Wright, James

2014-01-01

With this book, the editors present the first comprehensive collection in neural field studies, authored by leading scientists in the field - among them are two of the founding-fathers of neural field theory. Up to now, research results in the field have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. Starting with a tutorial for novices in neural field studies, the book comprises chapters on emergent patterns, their phase transitions and evolution, on stochastic approaches, cortical development, cognition, robotics and computation, large-scale numerical simulations, the coupling of neural fields to the electroencephalogram and phase transitions in anesthesia. The intended readership are students and scientists in applied mathematics, theoretical physics, theoretical biology, and computational neuroscience. Neural field theory and its applications have a long-standing tradition in the mathematical and computational ...

Twistor-theoretic approach to topological field theories

International Nuclear Information System (INIS)

Ito, Kei.

1991-12-01

The two-dimensional topological field theory which describes a four-dimensional self-dual space-time (gravitational instanton) as a target space, which we constructed before, is shown to be deeply connected with Penrose's 'twistor theory'. The relations are presented in detail. Thus our theory offers a 'twistor theoretic' approach to topological field theories. (author)

The S-matrix of superstring field theory

International Nuclear Information System (INIS)

Konopka, Sebastian

2015-01-01

We show that the classical S-matrix calculated from the recently proposed superstring field theories give the correct perturbative S-matrix. In the proof we exploit the fact that the vertices are obtained by a field redefinition in the large Hilbert space. The result extends to include the NS-NS subsector of type II superstring field theory and the recently found equations of motions for the Ramond fields. In addition, our proof implies that the S-matrix obtained from Berkovits’ WZW-like string field theory then agrees with the perturbative S-matrix to all orders.

A non-linear field theory

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs

Symmetry non-restoration at high temperature and supersymmetry

CERN Document Server

Dvali, Gia; Dvali, Gia

1996-01-01

We analyse the high temperature behaviour of softly broken supersymmetric theories taking into account the role played by effective non-renormalizable terms generated by the decoupling of superheavy degrees of freedom or the Planck scale physics. It turns out that discrete or continuous symmetries, spontaneously broken at intermediate scales, may never be restored, at least up to temperatures of the cutoff scale. There are a few interesting differences from the usual non-restoration in non-supersymmetric theories case where one needs at least two Higgs fields and non-restoration takes place for a range of parameters only. We show that with non-renormalizable interactions taken into account the non-restoration can occur for any nonzero range of parameters even for a single Higgs field. We show that such theories in general solve the cosmological domain wall problem, since the thermal production of the dangerous domain walls is enormously suppressed.

Statistical mechanics and field theory

International Nuclear Information System (INIS)

Samuel, S.A.

1979-05-01

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

Conformal field theories and critical phenomena

International Nuclear Information System (INIS)

Xu, Bowei

1993-01-01

In this article we present a brief review of the conformal symmetry and the two dimensional conformal quantum field theories. As concrete applications of the conformal theories to the critical phenomena in statistical systems, we calculate the value of central charge and the anomalous scale dimensions of the Z 2 symmetric quantum chain with boundary condition. The results are compatible with the prediction of the conformal field theories

Local algebras in Euclidean quantum field theory

International Nuclear Information System (INIS)

Guerra, Francesco.

1975-06-01

The general structure of the local observable algebras of Euclidean quantum field theory is described, considering the very simple examples of the free scalar field, the vector meson field, and the electromagnetic field. The role of Markov properties, and the relations between Euclidean theory and Hamiltonian theory in Minkowski space-time are especially emphasized. No conflict appears between covariance (in the Euclidean sense) and locality (in the Markov sense) on one hand and positive definiteness of the metric on the other hand [fr

Using field theory in hadron physics

International Nuclear Information System (INIS)

Abarbanel, H.D.I.

1978-03-01

Topics are covered on the connection of field theory and hadron physics. The renormalization group and infrared and ultraviolet limits of field theory, in particular quantum chromodynamics, spontaneous mass generation, color confinement, instantons, and the vacuum state in quantum chromodynamics are treated. 21 references

Finite-temperature field theory

International Nuclear Information System (INIS)

Kapusta, J.I.; Landshoff, P.V.

1989-01-01

Particle number is not conserved in relativistic theories although both lepton and baryon number are. Therefore when discussing the thermodynamics of a quantum field theory one uses the grand canonical formalism. The entropy S is maximised, keeping fixed the ensemble averages E and N of energy and lepton number. Two lagrange multipliers are introduced. (author)

Effective field theory for NN interactions

International Nuclear Information System (INIS)

Tran Duy Khuong; Vo Hanh Phuc

2003-01-01

The effective field theory of NN interactions is formulated and the power counting appropriate to this case is reviewed. It is more subtle than in most effective field theories since in the limit that the S-wave NN scattering lengths go to infinity. It is governed by nontrivial fixed point. The leading two body terms in the effective field theory for nucleon self interactions are scale invariant and invariant under Wigner SU(4) spin-isospin symmetry in this limit. Higher body terms with no derivatives (i.e. three and four body terms) are automatically invariant under Wigner symmetry. (author)

Four-dimensional boson field theory. II. Existence

International Nuclear Information System (INIS)

Baker, G.A. Jr.

1986-01-01

The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high-temperature expansions of the corresponding continuous-spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free

Moduli spaces of unitary conformal field theories

International Nuclear Information System (INIS)

Wendland, K.

2000-08-01

We investigate various features of moduli spaces of unitary conformal field theories. A geometric characterization of rational toroidal conformal field theories in arbitrary dimensions is presented and discussed in relation to singular tori and those with complex multiplication. We study the moduli space M 2 of unitary two-dimensional conformal field theories with central charge c = 2. All the 26 non-exceptional non-isolated irreducible components of M 2 are constructed that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly. All multicritical points and lines are determined, such that all but three of these 26 components are directly or indirectly connected to the space of toroidal theories in M 2 . Relating our results to those by Dixon, Ginsparg, Harvey on the classification of c = 3/2 superconformal field theories, we give geometric interpretations to all non-isolated orbifolds discussed by them and correct their statements on multicritical points within the moduli space of c = 3/2 superconformal field theories. In the main part of this work, we investigate the moduli space M of N = (4, 4) superconformal field theories with central charge c = 6. After a slight emendation of its global description we give generic partition functions for models contained in M. We explicitly determine the locations of various known models in the component of M associated to K3 surfaces

Effective quantum field theories

International Nuclear Information System (INIS)

Georgi, H.M.

1989-01-01

Certain dimensional parameters play a crucial role in the understanding of weak and strong interactions based on SU(2) x U(1) and SU(3) symmetry group theories and of grand unified theories (GUT's) based on SU(5). These parameters are the confinement scale of quantum chromodynamics and the breaking scales of SU(2) x U(1) and SU(5). The concepts of effective quantum field theories and renormalisability are discussed with reference to the economics and ethics of research. (U.K.)

Quantum Field Theory in a Semiotic Perspective

CERN Document Server

Günter Dosch, Hans; Sieroka, Norman

2005-01-01

Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincaré, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly ac...

Quantum field theory for the gifted amateur

CERN Document Server

Lancaster, Tom

2014-01-01

Quantum field theory is arguably the most far-reaching and beautiful physical theory ever constructed, with aspects more stringently tested and verified to greater precision than any other theory in physics. Unfortunately, the subject has gained a notorious reputation for difficulty, with forbidding looking mathematics and a peculiar diagrammatic language described in an array of unforgiving, weighty textbooks aimed firmly at aspiring professionals. However, quantum field theory is too important, too beautiful, and too engaging to be restricted to the professionals. This book on quantum field theory is designed to be different. It is written by experimental physicists and aims to provide the interested amateur with a bridge from undergraduate physics to quantum field theory. The imagined reader is a gifted amateur, possessing a curious and adaptable mind, looking to be told an entertaining and intellectually stimulating story, but who will not feel patronised if a few mathematical niceties are spelled out in ...

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.

Statistical predictions from anarchic field theory landscapes

International Nuclear Information System (INIS)

Balasubramanian, Vijay; Boer, Jan de; Naqvi, Asad

2010-01-01

Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness constraints. We argue that appropriately 'coarse-grained' aspects of the randomly chosen field theory in such landscapes, such as the fraction of gauge groups with ranks in a given range, can be statistically predictable. To illustrate our point we show how the uniform measures on simple classes of N=1 quiver gauge theories localize in the vicinity of theories with certain typical structures. Generically, this approach would predict a high energy theory with very many gauge factors, with the high rank factors largely decoupled from the low rank factors if we require asymptotic freedom for the latter.

Vacuum instability in scalar field theories

International Nuclear Information System (INIS)

McKane, A.J.

1978-09-01

Scalar field theories with an interaction of the form gphisup(N) have no stable vacuum state for some range of values of their coupling constant, g. This thesis reports calculations of vacuum instability in such theories. Using the idea that the tunnelling out of the vacuum state is described by the instanton solutions of the theory, the imaginary part of the vertex functions is calculated for the massless theory in the one-loop approximation, near the dimension dsub(c) = 2N/N-2, where the theory is just renormalisable. The calculation differs from previous treatments in that dimensional regularisation is used to control the ultra-violet divergences of the theory. In this way previous analytic calculations in conformally invariant field theories are extended to the case where the theory is almost conformally invariant, since it is now defined in dsub(c) - epsilon dimensions (epsilon > 0). (author)

Thermo field dynamics: a quantum field theory at finite temperature

International Nuclear Information System (INIS)

Mancini, F.; Marinaro, M.; Matsumoto, H.

1988-01-01

A brief review of the theory of thermo field dynamics (TFD) is presented. TFD is introduced and developed by Umezawa and his coworkers at finite temperature. The most significant concept in TFD is that of a thermal vacuum which satisfies some conditions denoted as thermal state conditions. The TFD permits to reformulate theories at finite temperature. There is no need in an additional principle to determine particle distributions at T ≠ 0. Temperature and other macroscopic parameters are introduced in the definition of the vacuum state. All operator formalisms used in quantum field theory at T=0 are preserved, although the field degrees of freedom are doubled. 8 refs

Quantum field theory in a semiotic perspective

International Nuclear Information System (INIS)

Dosch, H.G.

2005-01-01

Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)

Quantum field theory in a semiotic perspective

Energy Technology Data Exchange (ETDEWEB)

Dosch, H.G. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Mueller, V.F. [Technische Univ. Kaiserslautern (Germany). Fachbereich Physik; Sieroka, N. [Zurich Univ. (Switzerland)

2005-07-01

Viewing physical theories as symbolic constructions came to the fore in the middle of the nineteenth century with the emancipation of the classical theory of the electromagnetic field from mechanics; most notably this happened through the work of Helmholtz, Hertz, Poincare, and later Weyl. The epistemological problems that nourished this development are today highlighted within quantum field theory. The present essay starts off with a concise and non-technical outline of the firmly based aspects of relativistic quantum field theory, i.e. the very successful description of subnuclear phenomena. The particular methods, by which these different aspects have to be accessed, then get described as distinct facets of quantum field theory. The authors show how these different facets vary with respect to the relation between quantum fields and associated particles. Thus, by emphasising the respective role of various basic concepts involved, the authors claim that only a very general epistemic approach can properly account for this diversity - an account they trace back to the philosophical writings of the aforementioned physicists and mathematicians. Finally, what they call their semiotic perspective on quantum field theory gets related to recent discussions within the philosophy of science and turns out to act as a counterbalance to, for instance, structural realism. (orig.)

Light-front quantization of field theory

Energy Technology Data Exchange (ETDEWEB)

Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

1996-07-01

Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.

Light-front quantization of field theory

International Nuclear Information System (INIS)

Srivastava, Prem P.

1996-07-01

Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs

Quantum field theory of point particles and strings

CERN Document Server

Hatfield, Brian

1992-01-01

The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string.

Flat holography: aspects of the dual field theory

Energy Technology Data Exchange (ETDEWEB)

Bagchi, Arjun [Indian Institute of Technology Kanpur,Kalyanpur, Kanpur 208016 (India); Center for Theoretical Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Basu, Rudranil [Saha Institute of Nuclear Physics,Block AF, Sector 1, Bidhannagar, Kolkata 700068 (India); Kakkar, Ashish [Indian Institute of Science Education and Research,Dr Homi Bhabha Road, Pashan, Pune 411008 (India); Mehra, Aditya [Indian Institute of Technology Kanpur,Kalyanpur, Kanpur 208016 (India); Indian Institute of Science Education and Research,Dr Homi Bhabha Road, Pashan, Pune 411008 (India)

2016-12-29

Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk – 2d boundary case and then focus on the 4d bulk – 3d boundary example, where the symmetry in question is the infinite dimensional BMS{sub 4} algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D=4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.

Correlated effective field theory in transition metal compounds

International Nuclear Information System (INIS)

Mukhopadhyay, Subhasis; Chatterjee, Ibha

2004-01-01

Mean field theory is good enough to study the physical properties at higher temperatures and in higher dimensions. It explains the critical phenomena in a restricted sense. Near the critical temperatures, when fluctuations become important, it may not give the correct results. Similarly in low dimensions, the correlations become important and the mean field theory seems to be inadequate to explain the physical phenomena. At low-temperatures too, the quantum correlations become important and these effects are to be treated in an appropriate way. In 1974, Prof. M.E. Lines of Bell Laboratories, developed a theory which goes beyond the mean field theory and is known as the correlated effective field (CEF) theory. It takes into account the fluctuations in a semiempirical way. Lines and his collaborators used this theory to explain the short-range correlations and their anisotropy in the paramagnetic phase. Later Suzuki et al., Chatterjee and Desai, Mukhopadhyay and Chatterjee applied this theory to the magnetically ordered phase and a tremendous success of the theory has been found in real systems. The success of the CEF theory is discussed in this review. In order to highlight the success of this theory, earlier effective field theories and their improvements over mean field theories e.g., Bethe-Peierls-Weiss method, reaction field approximation, etc., are also discussed in this review for completeness. The beauty of the CEF theory is that it is mean field-like, but captures the essential physics of real systems to a great extent. However, this is a weak correlated theory and as a result is inappropriate for the metallic phase when strong correlations become important. In recent times, transition metal oxides become important due to the discovery of the high-temperature superconductivity and the colossal magnetoresistance phenomena. These oxides seem to be Mott insulators and undergo an insulator to metal transition by applying magnetic field, pressure and by changing

The Global Approach to Quantum Field Theory

International Nuclear Information System (INIS)

Folacci, Antoine; Jensen, Bruce

2003-01-01

Thanks to its impressive success in the second half of the 20th century, both in high-energy physics and in critical phenomena, quantum field theory has enjoyed an abundant literature. We therefore greet yet another book on this subject with caution: what can a monograph on quantum field theory bring now that is new, either conceptually or pedagogically? But when it is written by a physicist such as Bryce DeWitt, who has made his own contribution to the collection of field theory books with The Global Approach to Quantum Field Theory, all suspicion is naturally abandoned. DeWitt has made a formidable contribution to various areas of physics: general relativity, the interpretation of quantum mechanics, and most of all the quantization of non-Abelian gauge theories and quantum gravity. In addition, his pedagogical publications, especially the Les Houches schools of 1963 and 1983, have had a great impact on quantum field theory. We must begin by alerting the potential readers of this book that it cannot be compared to any other book in the field. This uniqueness applies to both the scientific content and the way the ideas are presented. For DeWitt, a central concept of field theory is that of 'space of histories'. For a field varphi i defined on a given spacetime M, the set of all varphi i (x) for all x in all charts of M defines its history. It is the space Phi of all possible histories (dynamically allowed or not) of the fields defined on M which is called the 'pace of histories' by DeWitt. If only bosonic fields are considered, the space of histories is an infinite-dimensional manifold and if fermionic fields are also present, it must be viewed as an infinite-dimensional supermanifold. The fields can then be regarded as coordinates on these structures, and the geometrical notions of differentiation, metric, connections, measure, as well as the geodesics which can be defined on it, are of fundamental importance in the development of the formalism of quantum field

Pilot-wave approaches to quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Struyve, Ward, E-mail: Ward.Struyve@fys.kuleuven.be [Institute of Theoretical Physics, K.U.Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium); Institute of Philosophy, K.U.Leuven, Kardinaal Mercierplein 2, B-3000 Leuven (Belgium)

2011-07-08

The purpose of this paper is to present an overview of recent work on pilot-wave approaches to quantum field theory. In such approaches, systems are not only described by their wave function, as in standard quantum theory, but also by some additional variables. In the non-relativistic pilot-wave theory of deBroglie and Bohm those variables are particle positions. In the context of quantum field theory, there are two natural choices, namely particle positions and fields. The incorporation of those variables makes it possible to provide an objective description of nature in which rather ambiguous notions such as 'measurement' and 'observer' play no fundamental role. As such, the theory is free of the conceptual difficulties, such as the measurement problem, that plague standard quantum theory.

Dual field theories of quantum computation

International Nuclear Information System (INIS)

Vanchurin, Vitaly

2016-01-01

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

Fractional Quantum Field Theory: From Lattice to Continuum

Directory of Open Access Journals (Sweden)

Vasily E. Tarasov

2014-01-01

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

Quark confinement and the short-range component of general affine gauge gravity

International Nuclear Information System (INIS)

Sijacki, D.

1982-01-01

Within the framework of a gauge field theory based on the general affine space-time symmetry, we propose a certain purely quadratic gauge field lagrangian. In the large-scale region it yields an Einstein-Cartan-like gravity with Newton's constand generated spontaneously, while in the particle domain it yields a renormalizable theory with a confining potential applying to quarks and not to leptons. (orig.)

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

OpenAIRE

Raab, Andreas

2013-01-01

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

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

Calculations in perturbative string field theory

International Nuclear Information System (INIS)

Thorn, C.B.

1987-01-01

The author discusses methods for evaluating the Feynman diagrams of string field theory, with particular emphasis on Witten's version of open string field theory. It is explained in some detail how the rules states by Giddings and Martinec for relating a given diagram to a Polyakov path integral emerge from the Feynman rules

Introduction to conformal field theory and string theory

International Nuclear Information System (INIS)

Dixon, L.J.

1989-12-01

These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs

Quantum field theory in a nutshell

CERN Document Server

Zee, A

2010-01-01

Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading

A Yang-Mills structure for string field theory

International Nuclear Information System (INIS)

Tsousheung Tsun

1990-01-01

String theorists believe that one way to achieve a fully quantized theory of string is through string field theory. The other way is to study conformal field theory on Riemann surfaces of different genera, which is the subject of many of the talks at this Conference. In a way, string field theory is the more conservative approach, since it aims just to replace the spacetime points of conventional quantum field theory by string, which are extended objects. However, from this point of view string theory has one rather unsatisfactory aspect, in the sense that although it has been very well developed and minutely studied, we are still rather unclear about its basic structure. We can contrast this to both general relativity, which is based on the geometry of spacetime, and to gauge theory, which is about the structure of various natural bundles over spacetime. And yet string theory is supposed to embody both these two essentially geometric theories. To paraphrase Witten, in string theory we seem to have to work backwards to get at the still unknown basic structure. Some joint work with Chan Hong-Mo is reported in an attempt to gain some understanding in that general direction. It seems that one could in some sense consider string field theory as a generalized Yang-Mills theory. This idea is explored. (author)

Renormalization in quantum Brans-Dicke gravity

OpenAIRE

Haba, Z.

2002-01-01

In the Brans-Dicke model we treat the scalar field exactly and expand the gravitational field in a power series. A comparison with 2D sigma models and \\phi^{4} perturbation theory in four dimensions suggests that the perturbation series in 4D Brans-Dicke model is renormalizable.

Growing up with field theory

International Nuclear Information System (INIS)

Vajskopf, V.F.

1982-01-01

The article deals with the history of the development of quantum electrodynamics since the date of publishing the work by P.A.M. Dirac ''The Quantum Theory of the Emission and Absorption of Radiation''. Classic ''before-Dirac'' electrodynamics related with the names of Maxwell, Lorenz, Hertz, is outlined. Work of Bohr and Rosenfeld is shown to clarify the physical sense of quantized field and to reveal the existence of uncertainties between the strengths of different fields. The article points to the significance of the article ''Quantum theory of radiation'' by E. Fermi which clearly describes the Dirac theory of radiation, relativistic wave equation and fundamentals of quantum electrodynamics. Shown is work on elimination of troubles related with the existence of states with negative kinetic energy or with negative mass. Hypothesis on the Dirac filled-in vacuum led to understanding of the existence of antiparticles and two unknown till then fundamental processes - pair production and annihilation. Ways of fighting against the infinite quantities in quantum electrodynamics are considered. Renormalization of the theory overcame all the infinities and gave a pattern for calculation of any processes of electron interactions with electromagnetic field to any desired accuracy

Two problems in thermal field theory

Indian Academy of Sciences (India)

In this talk, I review recent progress made in two areas of thermal field theory. In par- ticular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate. Keywords. Thermal field theory; quark-gluon plasma. PACS Nos 11.10.Wx; 12.38.

Magnetic fields, special relativity and potential theory elementary electromagnetic theory

CERN Document Server

Chirgwin, B H; Kilmister, C W

1972-01-01

Magnetic Fields, Special Relativity and Potential Theory is an introduction to electromagnetism, special relativity, and potential theory, with emphasis on the magnetic field of steady currents (magnetostatics). Topics covered range from the origin of the magnetic field and the magnetostatic scalar potential to magnetization, electromagnetic induction and magnetic energy, and the displacement current and Maxwell's equations. This volume is comprised of five chapters and begins with an overview of magnetostatics, followed by a chapter on the methods of solving potential problems drawn from elec

The space-time operator product expansion in string theory duals of field theories

International Nuclear Information System (INIS)

Aharony, Ofer; Komargodski, Zohar

2008-01-01

We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting ('single-trace') terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the space-time OPE limit. The worldsheet OPE generically contains only non-physical operators, but all the non-physical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of space-time correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories

An introduction to gauge theories

International Nuclear Information System (INIS)

Iliopoulos, J.

1977-01-01

The CERN-JINR School of Physics is meant to give young experimental physicists an introduction to the theoretical aspects of recent advances in elementary particle physics. This paper presents an introduction to gauge theories: the systematics of Yang-Mills theories, spontaneous symmetry breaking, and Higgs mechanism. The treatment is simple, stressing the general principles rather than detailed calculations. The author presents the Weinberg-Salam model as an example of a renormalizable theory of weak and electromagnetic interactions of leptons, and it is shown that the extension of these ideas into the hadronic world requires the introduction of charm and colour. Finally, an attempt is made to include strong interactions into the scheme, guided by the experimental results of deep-inelastic lepton-nucleon scattering. The Callan-Symanzik equation, and the concepts of asymptotic freedom and quark confinement are introduced. (Auth.)

Topological quantum field theory and four manifolds

CERN Document Server

Marino, Marcos

2005-01-01

The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten’s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the ...

Analytic aspects of rational conformal field theories

International Nuclear Information System (INIS)

Kiritsis, E.B.; Lawrence Berkeley Lab., CA

1990-01-01

The problem of deriving linear differential equations for correlation functions of Rational Conformal Field Theories is considered. Techniques from the theory of fuchsian differential equations are used to show that knowledge of the central charge, dimensions of primary fields and fusion rules are enough to fix the differential equations for one- and two-point functions on the tours. Any other correlation function can be calculated along similar lines. The results settle the issue of 'exact solution' of rational conformal field theories. (orig.)

A Field Theory with Curvature and Anticurvature

Directory of Open Access Journals (Sweden)

M. I. Wanas

2014-01-01

Full Text Available The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

Gauge field theories an introduction with applications

CERN Document Server

Guidry, Mike

1991-01-01

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

On single-time reduction in quantum field theory

International Nuclear Information System (INIS)

Arkhipov, A.A.

1984-01-01

It is shown, how the causality and spectrality properties in qUantum field theory may help one to carry out a single-time reduction of the Bethe-Salpeter wave fUnction. The single-time reduction technique is not based on any concrete model of the quantum field theory. Axiomatic formulations underline the quantum field theory