Suppes, Patrick
1972-01-01
This clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.
Takeuti, Gaisi
1973-01-01
This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The in...
Towards Axiomatic Foundations for Defuzzification Theory
Thiele, Helmut
1998-01-01
The starting point of the paper presented are the well-known defuzzification procedures on the one hand and approaches to axiomatize the concept of defuzzification, on the other hand. We present a new attempt to build up an axiomatic foundation for defuzzification theory using the theory of groups and the theory of partially ordered sets, and in particular, the theory of GALOIS connections.
A synthetic axiomatization of Map Theory
DEFF Research Database (Denmark)
Berline, Chantal; Grue, Klaus Ebbe
2016-01-01
theorems of ZFC set theory including the axiom of foundation are provable in Map Theory, and if one omits Hilbert's epsilon operator from Map Theory then one is left with a computer programming language. Map Theory fulfills Church's original aim of lambda calculus. Map Theory is suited for reasoning about......”. The class of wellfounded maps in Map Theory corresponds to the universe of sets in ZFC. The first axiomatization MT 0 of Map Theory had axioms which populated the class of wellfounded maps, much like the power set axiom along with others populate the universe of ZFC. The new axiomatization MT of Map Theory......Abstract This paper presents a substantially simplified axiomatization of Map Theory and proves the consistency of this axiomatization (called MT) in ZFC under the assumption that there exists an inaccessible ordinal. Map Theory axiomatizes lambda calculus plus Hilbert's epsilon operator. All...
Introduction to axiomatic set theory
Takeuti, Gaisi
1971-01-01
In 1963, the first author introduced a course in set theory at the Uni versity of Illinois whose main objectives were to cover G6del's work on the consistency of the axiom of choice (AC) and the generalized con tinuum hypothesis (GCH), and Cohen's work on the independence of AC and the GCH. Notes taken in 1963 by the second author were the taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are highlighted, and second, the student who wishes to master the sub ject is compelled to develop the details on his own. However, an in structor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text. We have chosen instead a development that is quite detailed and complete. F...
Finite groups in Axiomatic Index Number Theory
Marco Fattore
2006-01-01
In this paper we adopt Group Theory to investigate the symmetry and invariance properties of price index numbers. An alternative treatment is given to the study of the reversibilty axioms, that clarifies their meaning and allows for a conceptual unification of this topic, within the framework of Axiomatic Index Number Theory.
Axiomatics of Galileo-invariant quantum field theory
International Nuclear Information System (INIS)
The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms
S-matrix theory of nuclear forces
Energy Technology Data Exchange (ETDEWEB)
Vinh Mau, R.
1984-09-01
The use of the S-matrix theory for deriving the nucleon-nucleon interaction is reviewed. Fits to recent NN data are described. Applications to nuclear structure properties and nucleon-nucleus reactions are also discussed, and the results compared with data. 20 references.
Improving the requirements process in Axiomatic Design Theory
DEFF Research Database (Denmark)
Thompson, Mary Kathryn
2013-01-01
This paper introduces a model to integrate the traditional requirements process into Axiomatic Design Theory and proposes a method to structure the requirements process. The method includes a requirements classification system to ensure that all requirements information can be included in the Axi......This paper introduces a model to integrate the traditional requirements process into Axiomatic Design Theory and proposes a method to structure the requirements process. The method includes a requirements classification system to ensure that all requirements information can be included...... in the Axiomatic Design process, a stakeholder classification system to reduce the chances of excluding one or more key stakeholders, and a table to visualize the mapping between the stakeholders and their requirements....
Axiomatic quantum field theory in curved spacetime
Hollands, S
2008-01-01
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and t...
Axiomatic, Parameterized, Off-Shell Quantum Field Theory
Seidewitz, Ed
2016-01-01
Axiomatic QFT attempts to provide a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of axiomatic QFT, showing they are consistent. Nevertheless, even after more than 50 years, there is still no known non-trivial theory of quantum fields with interactions in four-dimensional Minkowski spacetime that meets the same axioms. This paper provides a similar axiomatic basis for parameterized QFT, in which an invariant, fifth path parameter is added to the usual four spacetime position arguments of quantum fields. Dynamic evolution is in terms of the path parameter rather than the frame-dependent time coordinate. Further, the states of the theory are allowed to be off shell. Particles are therefore fundamentally "virtual" during interaction but, in the appropriate non-interacting, large-time limit, they dynamically tend towards "physical", on-shell states. Unlike traditional QFT, it...
On the S-matrix renormalization in effective theories
Semenov-Tian-Shansky, K; Vereshagin, V
2005-01-01
This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal -- needed to fix the S-matrix, and non-minimal -- for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that in theories with the amplitudes which asymptotic behavior is governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixi...
Axiomatic Theory of Algorithms: Computability and Decidability in Algorithmic Classes
Burgin, Mark
2004-01-01
Axiomatic approach has demonstrated its power in mathematics. The main goal of this preprint is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer science. Here the main modes of computer functioning and program execution are described, formalized, and studied in an axiomatic context. The emphasis is on three principal modes: computation, decision, and acceptation. Now the prevalent mode for computers...
Dependency through Axiomatic Approach On Rough Set Theory
Directory of Open Access Journals (Sweden)
Nilaratna Kalia
2010-03-01
Full Text Available The idea of rough set consist the approximation of a set by pair of sets called the lower and the upper approximation of the set. In fact, these approximations are interior and closer operations in acertain topology generated by available data about elements of theset. The rough set is based on knowledge of an agent about somereality and his ability to discern some phenomenon processes etc.Thus this approach is based on the ability to classify data obtainedfrom observation, measurement, etc. In this paper we define thedependency of knowledge through the axiomatic approach instead ofthe traditional (Pawlak method of rough set.
A unifying approach to axiomatic non-expected utility theories: correction and comment
C.S. Hong; L.G. Epstein; P. Wakker
1993-01-01
Chew and Epstein attempted to provide a unifying axiomatic framework for a number of generalizations of expected utility theory. Wakker pointed out that Theorem A, on which the central unifying proposition is based, is false. In this note, we apply Segal's result to prove that Theorem 2 is neverthel
Quark Physics without Quarks: A Review of Recent Developments in S-Matrix Theory.
Capra, Fritjof
1979-01-01
Reviews the developments in S-matrix theory over the past five years which have made it possible to derive results characteristic of quark models without any need to postulate the existence of physical quarks. In the new approach, the quark patterns emerge as a consequence of combining the general S-matrix principles with the concept of order.…
Axiomatics of classical electrodynamics and its relation to gauge field theory
Gronwald, F; Nitsch, J; Gronwald, Frank; Hehl, Friedrich W.
2005-01-01
We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The {\\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.
An alternative S-matrix for N = 6 Chern-Simons theory?
International Nuclear Information System (INIS)
We have recently proposed an S-matrix for the planar limit of the N = 6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena which leads to the all-loop Bethe ansatz equations conjectured by Gromov and Vieira. An unusual feature of this proposal is that the scattering of A and B particles is reflectionless. We consider here an alternative S-matrix, for which A-B scattering is not reflectionless. We argue that this S-matrix does not lead to the Bethe ansatz equations which are consistent with perturbative computations.
There is no axiomatic system for the quantum theory
Nagata, Koji
2007-01-01
Recently, [arXiv:0810.3134] is accepted and published. We derive an inequality with two settings as tests for the existence of the Bloch sphere in a spin-1/2 system. The probability theory of measurement outcome within the formalism of von Neumann projective measurement violates the inequality. Namely, we have to give up the existence of the Bloch sphere. Or, we have to give up the probability theory of measurement outcome within the formalism of von Neumann projective measurement. Hence it t...
Axiomatization of the AGM theory of belief revision in a temporal logic
Bonanno, Giacomo
2006-01-01
It is natural to think of belief revision as the interaction of belief and information over time. Thus branching-time temporal logic seems a natural setting for a theory of belief revision. We propose two extensions of a modal logic that, besides the ""next-time"" temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic pro...
Integration of axiomatic design and theory of inventive problem solving for conceptual design
Institute of Scientific and Technical Information of China (English)
TIAN Qi-hua; XIAO Ren-bin; ZHONG Yi-fang; DU Yi-xian; YANG Hong-mei
2009-01-01
Axiomatic design (AD) and theory of inventive problem solving (TRIZ) are widely used in conceptual design. Both of them have limitations, however. We presented an integrated model of these two methods to increase the efficiency and quality of the problem solving process for conceptual design. AD is used for systematically defining and structuring a problem into a hierarchy. Sometimes, the design matrix is coupled in AD which indicates the functional requirements are coupled. TRIZ separation principles can be used to separate non-independent design parameters, which provide innovative solutions at each hierarchical level. We applied the integrated model to the heating and drying equipment of bitumen reproduction device. The result verifies that the integrated model can work very well in conceptual design.
Application of axiomatic formal theory to the Abraham-Minkowski controversy
Crenshaw, Michael
Continuum electrodynamics is an axiomatic formal theory whose axioms are the macroscopic Maxwell equations. We demonstrate that valid theorems of the formal theory are inconsistent with conservation laws and with special relativity because continuum electrodynamics allows transformations of the Maxwell equations that constitute an improper tensor transformation that changes the conservation properties, the relativity properties, and the space-time embedding of the coupled equations of motion. The inconsistencies are resolved by a reformulation of physical principles in a flat non-Minkowski material spacetime in which the timelike coordinate corresponds to ct/n. Applying Lagrangian field theory, we derive equations of motion for the macroscopic electric and magnetic fields in a simple dielectric medium. We construct a new formal theory of continuum electrodynamics and we derive a tensor energy-momentum continuity theorem that trivially resolves the century-old Abraham-Minkowski momentum controversy. We derive the theory of special relativity in a dielectric, including the material Lorentz factor and the material Lorentz transformation. We derive the momentum of a polariton in the context of material special relativity to confirm the resolution of the Abraham-Minkowski debate.
Could a Weak Coupling Massless SU(5) Theory Underly the Standard Model S-Matrix?
White, Alan R
2010-01-01
The unitary Critical Pomeron connects to a unique massless left-handed SU(5) theory that, remarkably, might provide an unconventional underlying unification for the Standard Model. Multi-regge theory suggests the existence of a {\\it bound-state high-energy S-Matrix} that replicates Standard Model states and interactions via massless fermion anomaly dynamics. Configurations of anomalous wee gauge boson reggeons play a vacuum-like role. All particles, including neutrinos, are bound-states with dynamical masses (there is no Higgs field) that are formed (in part) by anomaly poles. The contributing zero-momentum chirality transitions break the SU(5) symmetry to vector SU(3)xU(1) in the S-Matrix. The high-energy interactions are vector reggeon exchanges accompanied by wee boson sums (odd-signature for the strong interaction and even-signature for the electroweak interaction) that strongly enhance couplings. The very small SU(5) coupling, ~ 1/120, should be reflected in small (Majorana) neutrino masses. A color sext...
N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
Ahn, Changrim
2008-01-01
We propose the exact S-matrix for the planar limit of the N=6 super Chern-Simons theory recently proposed by Aharony, Bergman, Jafferis, and Maldacena for the AdS_4/CFT_3 correspondence. Assuming SU(2|2) symmetry, factorizability and certain crossing-unitarity relations, we find the S-matrix including the dressing phase. We use this S-matrix to formulate the asymptotic Bethe ansatz. Our result for the Bethe-Yang equations and corresponding Bethe ansatz equations confirms the all-loop Bethe ansatz equations recently conjectured by Gromov and Vieira.
S-Matrix Theory of ionization of molecules in intense laser fields
International Nuclear Information System (INIS)
We illustrate the application of the so-called Intense-Field Many-Body S-Matrix Theory (IMST) for molecular systems in strong laser fields. First, we investigate the phenomena of 'enhanced ionization' for diatomic and polyatomic molecules. For the simple one- and two-electron molecules, H2+ and H2, the results of our calculations show the phenomena and are in good agreement with those of numerical simulations. We further predict the appearance of this phenomena for the more complex polyatomic molecule benzene (C6H6). Finally, we analyze the recently measured ionization yields of di- and polyatomic molecules in intense Ti:sapphire laser pulses as a function of the laser intensity
Flores, J C
2016-03-01
This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan's laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes.
Complex structures for an S-matrix of Klein-Gordon theory on AdS spacetimes
Dohse, Max
2015-01-01
While the standard construction of the S-matrix fails on Anti-de Sitter (AdS) spacetime, a generalized S-matrix makes sense, based on the hypercylinder geometry induced by the boundary of AdS. In contrast to quantum field theory in Minkowski spacetime, there is not yet a standard way to resolve the quantization ambiguities arising in its construction. These ambiguities are conveniently encoded in the choice of a complex structure. We explore in this paper the space of complex structures for real scalar Klein-Gordon theory based on a number of criteria. These are: invariance under AdS isometries, induction of a positive definite inner product, compatibility with the standard S-matrix picture and recovery of standard structures in Minkowski spacetime under a limit of vanishing curvature. While there is no complex structure that satisfies all demands, we emphasize two interesting candidates that satisfy most: In one case we have to give up part of the isometry invariance, in the other case the induced inner prod...
Strong-field S -matrix theory with final-state Coulomb interaction in all orders
Faisal, F. H. M.
2016-09-01
During the last several decades the so-called Keldysh-Faisal-Reiss or strong-field approximation (SFA) has been highly useful for the analysis of atomic and molecular processes in intense laser fields. However, it is well known that SFA does not account for the final-state Coulomb interaction which is, however, unavoidable for the ubiquitous ionization process. In this Rapid Communication we solve this long-standing problem and give a complete strong-field S -matrix expansion that accounts for the final-state Coulomb interaction in all orders, explicitly.
Axiomatic differential geometry II-2 - differential forms
Nishimura, Hirokazu
2013-01-01
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.
Axiomatic Differential Geometry Ⅱ-2: Differential Forms
Nishimura, Hirokazu
2013-01-01
We refurbish our axiomatics of differential geometry introduced in [arXiv 1203.3911]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of Pure and Applied Mathematics, 64 (2010), 85-102] to our present axiomatic framework.
Strong-Field S-Matrix Theory With Coulomb-Volkov Final State in All Orders
Faisal, F H M
2016-01-01
Despite its long standing usefulness for the analysis of various processes in intense laser fields, it is well-known that the so-called strong-field KFR or SFA ansatz does not account for the final-state Coulomb interaction. Due to its importance for the ubiquitous ionisation process, numerous heuristic attempts have been made during the last several decades to account for the final state Coulomb interaction with in the SFA. Also to this end an ad hoc model with the so-called Coulomb-Volkov final state was introduced a long time ago. However, till now, no systematic strong-field S-matrix expansion using the Coulomb-Volkov final state could be found. Here we solve this long standing problem by determining the Coulomb-Volkov Hamiltonian, identifying the rest-interaction in the final state, and explicitly constructng the Coulomb-Volkov propagator (or Green's function). We employ them to derive the complete S-matrix series for the ionisation amplitude governed by the Coulomb-Volkov final state in all orders. The ...
Naive Axiomatic Mengenlehre for Experiments
DePauli-Schimanovich, Werner
2008-01-01
The main goal of "Naive Axiomatic Mengenlehre" (NAM) is to find a more or less adequately explicit criterion that precisely formalizes the intuitive notion of a "normal set". NAM is mainly a construction procedure for building several formal systems NAMix, each of which can turn out to be an adequate codification of the contentual naive set theory. ("i" is a natural number which enumerates the used "normality" condition, and "x" is a letter which points to the variants of the used axioms.) Parallel to NAM, the Naive Axiomatic Class Theory NACT is constructed as a system of systems too.
Lee, C W
2002-01-01
The multichannel quantum defect theory (MQDT) is reformulated into the form of the configuration mixing (CM) method using the geometrical construction of the S matrix developed for the system involving two open and one closed channels. The reformulation is done by the phase renormalization method of Giusti-Suzor and Fano. The rather unconventional short-range reactance matrix K whose diagonal elements are not zero is obtained though the Lu-Fano plot becomes symmetrical. The reformulation of MQDT yields the partial cross section formulas analogous to Fano's resonance formula, which has not easily been available in other's work.
International Nuclear Information System (INIS)
The multichannel quantum defect theory (MQDT) is reformulated into the form of the configuration mixing (CM) method using the geometrical construction of the S matrix developed for the system involving two open and one closed channels. The reformulation is done by the phase renormalization method of Giusti-Suzor and Fano. The rather unconventional short-range reactance matrix K whose diagonal elements are not zero is obtained though the Lu-Fano plot becomes symmetrical. The reformulation of MQDT yields the partial cross section formulas analogous to Fano's resonance formula, which has not easily been available in other's work
Hilbert's axiomatic method and Carnap's general axiomatics.
Stöltzner, Michael
2015-10-01
This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' 'material' talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics. PMID:26386526
Thermofield Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix
Leineker, Marcelo; de Queiroz, Amilcar R.; Ademir E. Santana; Siqueira, Chrystian de Assis
2010-01-01
Poincare invariant quantum field theories can be formulated on non-commutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincare group is suitably twisted. In the present work we present a twisted Poincare invariant quantum field theory at finite temperature. For that we use the formalism of Thermofield Dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a non trivial step, since the separation in ...
Thermofield Dynamics for Twisted POINCARÉ-INVARIANT Field Theories:. Wick Theorem and S-Matrix
Leineker, Marcelo; Queiroz, Amilcar R.; Santana, Ademir E.; de Assis Siqueira, Chrystian
Poincaré invariant quantum field theories can be formulated on noncommutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincaré group is suitably twisted. In the present work we present a twisted Poincaré invariant quantum field theory at finite temperature. For that we use the formalism of thermofield dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a nontrivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.
Thermofied Dynamics for Twisted Poincare-Invariant Field Theories: Wick Theorem and S-matrix
Leineker, Marcelo; Santana, Ademir E; Siqueira, Chrystian de Assis
2010-01-01
Poincare invariant quantum field theories can be formulated on non-commutative planes if the statistics of fields is twisted. This is equivalent to state that the coproduct on the Poincare group is suitably twisted. In the present work we present a twisted Poincare invariant quantum field theory at finite temperature. For that we use the formalism of Thermofield Dynamics (TFD). This TFD formalism is extend to incorporate interacting fields. This is a non trivial step, since the separation in positive and negative frequency terms is no longer valid in TFD. In particular, we prove the validity of Wick's theorem for twisted scalar quantum field at finite temperature.
On triviality of S-matrix in conformal higher spin theory
Beccaria, M; Tseytlin, A A
2016-01-01
We consider the conformal higher spin (CHS) theory in d=4 that contains the s=1 Maxwell vector, s=2 Weyl graviton and their higher spin s=3,4,... counterparts with higher-derivative \\box^s kinetic terms. The interacting action for such theory can be found as the coefficient of the logarithmically divergent part in the induced action for sources coupled to higher spin currents in a free complex scalar field model. We explicitly determine some cubic and quartic interaction vertices in the CHS action from scalar loop integrals. We then compute the simplest tree-level 4-particle scattering amplitudes 11 -> 11, 22 -> 22 and 11 -> 22 and find that after summing up all the intermediate CHS exchanges they vanish. This generalises the vanishing of the scattering amplitude for external conformal scalars interacting via the exchange of all CHS fields found earlier in arXiv:1512.08896. This vanishing should generalise to all scattering amplitudes in the CHS theory and as in the conformal scalar scattering case should be ...
Naive Axiomatic Class Theory: A Solution for the Antinomies of Naive Mengenlehre
DePauli-Schimanovich, Werner
2008-01-01
Since the axioms in (Consi-CoS) are not recursively enumerable, NACT* is no axiom system in the classical sense . Therefore we construct a series of partial systems which form a recursive axiom system too. Starting with the "dichotomic" systems NACT# and its variant NACT#4, we are going on to the "disjunctive" systems NACT+ and NACT+4, and eventually to NACT+Strat. After that we discuss the medium classes of these systems. Finally we present the inconsistent NSA-systems based on Not-SelfApplicability and explain their help for computational set theory.
On a third S-matrix in the theory of quantized fields on curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Gottschalk, H. [Bonn Univ. (Germany). Physikalisches Inst.; Hack, T. [Bonn Univ. (Germany). Inst. fuer Angewandte Mathematik
2007-01-15
Wightman functions for interacting quantum fields on curved space times are calculated via the perturbation theory of the Yang-Feldman equations, where the incoming field is a free field in a quasifree representation. We show that these Wightman functions that are obtained as a sum over extended Feynman graphs fulfill the basic axioms of hermiticity, invariance, spectrality (on stationary spacetimes), perturbative positivity and locality (the latter property is shown up to second order in the loop expansion). In the case of non-stationary spacetimes, the outgoing field in general is in a non-quasifree representation of the CCR. This makes it necessary to develop a method to calculate the unitary transformation between a non quasifree representation and a quasifree one. This is carried out using *-calculus on the dual of the Borchers algebra with a combinatorial co-product. Given that preferred quasifree representations for early and late times exist, we thus obtain a complete scattering description using three S-matrices: The first is determined by vacuum expectation values between incoming and outgoing fields. The second is a unitary transformation between the non-quasifree representation for the ''out''-fields and the quasifree representation for the ''in''-field. The last one is the Bogoliubov transformation between the preferred representation at early times (i.e. the ''in''-field representation) and the preferred representation at late times. (orig.)
Naive Axiomatic Mengenlehre for Experiments
DePauli-Schimanovich, Werner
2008-01-01
The main goal of "Naive Axiomatic Mengenlehre" (NAM) is to find a more or less adequately explicit criterion that precisely formalizes the intuitive notion of a "normal set". NAM is mainly a construction procedure for building several formal systems NAMix, each of which can turn out to be an adequate codification of the contentual naive set theory. ("i" is a natural number which enumerates the used "normality" condition, and "x" is a letter which points to the variants of the used axioms.) Pa...
International Nuclear Information System (INIS)
Theories of modern physics predict that antimatter having rest mass will be attracted by the earth's gravitational field, but the actual coupling of antimatter with gravitation has not been established experimentally. The purpose of the present research was to identify laws of physics that would govern the universe if antimatter having rest mass would be repulsed by the earth's gravitational field. As a result, a formalized axiomatic system was developed together with interpretation rules for the terms of the language: the intention is that every theorem of the system yields a true statement about physical reality. Seven non-logical axioms of this axiomatic system form the elementary process theory (EPT): this is then a scheme of elementary principles describing the dynamics of individual processes taking place at supersmall scale. It is demonstrated how gravitational repulsion functions in the universe of the EPT, and some observed particles and processes have been formalized in the framework of the EPT. Incompatibility of quantum mechanics (QM) and General Relativity (GR) with the EPT is proven mathematically; to demonstrate applicability to real world problems to which neither QM nor GR applies, the EPT has been applied to a theory of the Planck era of the universe. The main conclusions are that a completely formalized framework for physics has been developed supporting the existence of gravitational repulsion and that the present results give rise to a potentially progressive research program. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
International Nuclear Information System (INIS)
Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense
International Nuclear Information System (INIS)
We propose a mathematical adequate formulation of the causality principle: the concept of event order includes in it the primordial concept of causality, based on the chrono-geometric division of the multitude of temporal and spatial events. The mathematical basis of our conception comes from the idea of the removal of divergences occurring in the quantum field theory through the unambiguous definition of the generalized functions product. The expression of the causal Feynman's function must be understood according to the distribution theory. The causality principle, generalized in this way, together with conservation laws of the energy-impulse and with the demand of Lorentz invariance, allow us to define T-product and its mathematical expression for the causality Green function by transition to the limit ε0→0. (author)
On string theory on AdS3×S3×T4 with mixed 3-form flux: Tree-level S-matrix
International Nuclear Information System (INIS)
We consider superstring theory on AdS3×S3×T4 supported by a combination of RR and NSNS 3-form fluxes (with parameter of the NSNS 3-form q). This theory interpolates between the pure RR flux model (q=0) whose spectrum is expected to be described by a (thermodynamic) Bethe ansatz and the pure NSNS flux model (q=1) which is described by the supersymmetric extension of the SL(2,R)×SU(2) WZW model. As a first step towards the solution of this integrable theory for generic value of q we compute the corresponding tree-level S-matrix for massive BMN-type excitations. We find that this S-matrix has a surprisingly simple dependence on q: the diagonal amplitudes have exactly the same structure as in the q=0 case but with the BMN dispersion relation e2=p2+1 replaced by the one with shifted momentum and mass, e2=(p±q)2+1−q2. The off-diagonal amplitudes are then determined from the classical Yang–Baxter equation. We also construct the Pohlmeyer-reduced model corresponding to this superstring theory and find that it depends on q only through the rescaled mass parameter, μ→√(1−q2)μ, implying that its relativistic S-matrix is q-independent
Axiomatizing GSOS with Predicates
Aceto, Luca; Goriac, Eugen-Ioan; Ingolfsdottir, Anna; 10.4204/EPTCS.62.1
2011-01-01
In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.
Matsumoto, Takuma; Ogata, Kazuyuki; Yahiro, Masanobu
2009-01-01
We present a practical way of smoothing discrete breakup S-matrix elements calculated by the continuum-discretized coupled-channel method (CDCC). This method makes the smoothing procedure much easier. The reliability of the smoothing method is confirmed for the three-body breakup reactions, 58Ni(d,pn) at 80 MeV and 12C(6He,4He2n) at 229.8 MeV.
Massive S-matrix of AdS{sub 3}×S{sup 3}×T{sup 4} superstring theory with mixed 3-form flux
Energy Technology Data Exchange (ETDEWEB)
Hoare, B., E-mail: ben.hoare@physik.hu-berlin.de [Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin (Germany); Tseytlin, A.A., E-mail: tseytlin@imperial.ac.uk [The Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)
2013-08-11
The type IIB supergravity AdS{sub 3}×S{sup 3}×T{sup 4} background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5–D1 and NS5–NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In (arXiv:1303.1447) we have found the tree-level S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q=0 case in (arXiv:1303.5995)
Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3-form flux
Hoare, B.; Tseytlin, A. A.
2013-08-01
The type IIB supergravity AdS3×S3×T4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the tree-level S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q=0 case in arXiv:1303.5995. This is a consequence of the fact that parity symmetry is broken with the introduction of the NSNS flux. However, charge conjugation composed with parity is still a symmetry.
Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
Hoare, B
2013-01-01
The type IIB supergravity AdS_3 x S^3 x T^4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the tree-level S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q=0 case in arXiv:1303.5995.
On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
Hoare, B
2013-01-01
We consider superstring theory on AdS_3 x S^3 x T^4 supported by a combination of RR and NSNS 3-form fluxes (with parameter of the NSNS 3-form q). This theory interpolates between the pure RR flux model (q=0) whose spectrum is expected to be described by a Bethe ansatz and the pure NSNS flux model (q=1) which is described by the supersymmetric extension of the SL(2,R) x SU(2) WZW model. As a first step towards the solution of this integrable theory for generic value of q we compute the corresponding tree-level S-matrix for massive BMN-type excitations. We find that this S-matrix has a surprisingly simple dependence on q: the diagonal amplitudes have exactly the same structure as in the q=0 case but with the BMN dispersion relation e^2 = p^2 + 1 replaced by the one with shifted momentum and mass, e^2 = (p + q)^2 + 1 - q^2. The off-diagonal amplitudes are then determined from the classical Yang-Baxter equation. We also construct the Pohlmeyer reduced model corresponding to this superstring theory and find that ...
Equity considerations in health care: An axiomatic bargaining approach
Cuadras, Xavier; Pinto, Jos?? Luis; Abell??n, Jos?? M??
2000-01-01
The general issues of equity and efficiency are placed at the center of the analysis of resource allocation problems in health care. We examine them using axiomatic bargaining theory. We study different solutions that have been proposed and relate them to previous literature on health care allocation. In particular, we focus on the solutions based on axiomatic bargaining with claims and suggest that they may be particularly appealing as distributive criteria in hea...
Energy Technology Data Exchange (ETDEWEB)
Griffin, J. J.; Lichtner, P. C.; Dworzecka, M.; Kan, K. K.
1979-01-01
The restrictions implied for the time dependent many-body reaction theory by the (TDHF) single determinantal assumption are explored by constructive analysis. A restructured TD-S-HF reaction theory is modelled, not after the initial-value form of the Schroedinger reaction theory, but after the (fully equivalent) S-matrix form, under the conditions that only self-consistent TDHF solutions occur in the theory, every wave function obeys the fundamental statistical interpretation of quantum mechanics, and the theory reduces to the exact Schroedinger theory for exact solutions which are single determinantal. All of these conditions can be accomodated provided that the theory is interpreted on a time-averaged basis, i.e., physical constants of the Schroedinger theory which are time-dependent in the TDHF theory, are interpreted in TD-S-HF in terms of their time averaged values. The resulting reaction theory, although formulated heuristically, prescribes a well defined and unambiguous calculational program which, although somewhat more demanding technically than the conventional initial-value TDHF method, is nevertheless more consonant with first principles, structurally and mechanistically. For its physical predictions do not depend upon the precise location of the distant measuring apparatus, and are in no way influenced by the spurious cross channel correlations which arise whenever the description of many reaction channels is imposed upon one single-determinantal solution. For nuclear structure physics, the TDHF-eigenfunctions provide the first plausible description of exact eigenstates in the time-dependent framework; moreover, they are unencumbered by any restriction to small amplitudes. 14 references.
Al- Khwarizmi and axiomatic foundation of algebra
International Nuclear Information System (INIS)
This paper intends to investigate the axiomatic foundations of algebra, as they were presented in the book of algebra of al-Khwarizmi (9 th century), and as they were developed in many subsequent Arabic works. The paper gives also a description of algebra evolution towards a discipline independent ofgeometry and arithmetic: the two disciplines whosemarriage had led to its birth.By an in depth reading of some details in the text of al Khwarizmi , we concluded that this mathematician intended to lay down the axiomatic foundations of that new discipline. His resort to arithmetical and geometrical means was a way of making his theory more accessible. He used them to justify the axioms: those that were not explicitly introduced per se, and those that were remained implicit. The paper also relies on some unedited writingsof al-Khwarizmi's successors, which could shedlight on the ways they used to consolidate the foundations of algebra and improve its methods. (author)
Peli, G; Masuch, M
1997-01-01
As a part of a larger effort to apply formal logic to organization science, we axiomatize the theory of propagation strategies (life history strategies) of Organization Ecology. We provide an axiomatic system in first-order logic that derives the theory's predictions as theorems from a set of underl
White, Alan R
2007-01-01
The Critical Pomeron solution of high-energy unitarity leads to a unique underlying massless field theory that might be the origin of the Standard Model. A color sextet quark sector - producing both electroweak symmetry breaking and dark matter - is added to QCD to saturate asymptotic freedom. The sextet sector is then embedded uniquely in ``QUD'' - an anomaly free, just asymptotically free, massless SU(5) theory with elementary lepton and triplet quark sectors very close to the Standard Model. A multi-regge bound-state S-Matrix is constructed using infra-red divergent scaling reggeon interactions that couple via massless fermion chiral anomalies. Within the QCD sub-sector there is an ``anomalous wee gluon'' critical phenomenon that produces a spectrum with confinement and chiral symmetry breaking. The exponentiation of left-handed gauge boson divergences implies that the full set of composite interactions and the low-mass spectrum of QUD could be just those of the Standard Model. All particles, including neu...
String theory in AdS_3 x S^3 x T^4 with mixed flux: semiclassical and 1-loop phase in the S-matrix
Stepanchuk, A
2014-01-01
We present a semiclassical derivation of the tree-level and 1-loop dressing phases in the massive sector of string theory on AdS_3 x S^3 x T^4 supplemented by R-R and NS-NS 3-form fluxes. In analogy with the AdS_5 x S^5 case, we use the dressing method to obtain scattering solutions for dyonic giant magnons which allows us to determine the semiclassical bound-state S-matrix and its 1-loop correction. We also find that the 1-loop correction to the dyonic giant magnon energy vanishes. Looking at the relation between the bound-state picture and elementary magnons in terms of the fusion procedure we deduce the elementary dressing phases. In both the semiclassical and 1-loop cases we find agreement with recent proposals from finite-gap equations and unitarity cut methods. Further, we find consistency with the finite-gap picture by determining the resolvent for the dyonic giant magnon from the semiclassical bosonic scattering data.
Stepanchuk, A.
2015-05-01
We present a semiclassical derivation of the tree-level and 1-loop dressing phases in the massive sector of string theory on Ad{{S}3}× {{S}3}× {{T}4} supplemented by Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz 3-form fluxes. In analogy with the Ad{{S}5}× {{S}5} case, we use the dressing method to obtain scattering solutions for dyonic giant magnons which allows us to determine the semiclassical bound-state S-matrix and its 1-loop correction. We also find that the 1-loop correction to the dyonic giant magnon energy vanishes. Looking at the relation between the bound-state picture and elementary magnons in terms of the fusion procedure we deduce the elementary dressing phases. In both the semiclassical and 1-loop cases we find agreement with recent proposals from finite-gap equations and unitarity cut methods. Further, we find consistency with the finite-gap picture by determining the resolvent for the dyonic giant magnon from the semiclassical bosonic scattering data.
CERN. Geneva
2016-01-01
In this talk I will describe recent work aiming to reinvigorate the 50 year old S-matrix program, which aims to constrain scattering of massive particles non-perturbatively. I will begin by considering quantum fields in anti-de Sitter space and show that one can extract information about the S-matrix by considering correlators in conformally invariant theories. The latter can be studied with "bootstrap" techniques, which allow us to constrain the S-matrix. In particular, in 1+1D one obtains bounds which are saturated by known integrable models. I will also show that it is also possible to directly constrain the S-matrix, without using the CFT crutch, by using crossing symmetry and unitarity. This alternative method is simpler and gives results in agreement with the previous approach. Both techniques are generalizable to higher dimensions.
Axiomatizing first order consequences in dependence logic
Kontinen, Juha; Väänänen, Jouko
2012-01-01
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the respective Completeness Theorem.
Axiomatizations of Pareto Equilibria in Multicriteria Games
Voorneveld, M.; Vermeulen, D.; Borm, P.E.M.
1997-01-01
We focus on axiomatizations of the Pareto equilibrium concept in multicriteria games based on consistency.Axiomatizations of the Nash equilibrium concept by Peleg and Tijs (1996) and Peleg, Potters, and Tijs (1996) have immediate generalizations.The axiomatization of Norde et al.(1996) cannot be generalized without the use of an additional axiom.
Axiomatization of Special Relativity in First Order Logic
Luo, Yi-Chen; Chen, Lei; He, Wan-Ting; Ma, Yong-Ge; Zhang, Xin-Yu
2016-07-01
The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecRel for special relativity proposed recently by Andréka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional space-time perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecRel+. Then we introduce an axiom of mass (AxMass) and take four-momentum conservation as an axiom (AxCFM) in SpecRel+. It turns out that the twin paradox and energy-mass relation can be derived from SpecRel+ logically. Hence, as an extension of SpecRel, SpecRel+ is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity. Supported by the National Science Foundation of China under Grant Nos. 11235003 and 11475023, National Social Sciences Foundation of China under Grant No. 14BZX078 and the Research Fund for the Doctoral Program of Higher Education of China, and the Undergraduate Training Program of Beijing
Baryoniums - the S-matrix approach
International Nuclear Information System (INIS)
In this series of lectures the question of how the baryoniums are related to charmoniums and strangoniums is discussed and it is pointed out that in the S-matrix framework, they all follow from the same pair of hypotheses, duality and no exotics. Invoking no underlying quark structure, except that inherent in the assumption of no exotics, it is shown that there are no mesons outside the singlet and octet representation of SU(3) and no baryons outside the singlet, octet and decaplet. In other words all mesons occur within the quantum number of a q-antiq system and all baryons within those of qqq. This seems to be an experimental fact, which has no natural explanation within the S-matrix framework except that it is the minimal non-zero solution to the duality constraints. The approach in the past has been to take it as an experimental input and build up a phenomenological S-matrix framework. Lately it has been realised that the answer may come from the colour dynamics of quarks. If true this would provide an important link between the fundamental but invisible field theory of quarks and gluons and the phenomenological but visible S-matrix theory overlying it. The subject is discussed under the headings; strangonium and charmonium, baryonium, spectroscopy, baryonium resonances, FESR constraint, baryonium exchange, phenomenological estimate of ω - baryonium mixing at t = 0, and models of ω - baryonium mixing. (UK)
THE AESTHETIC AXIOMATIC: DECONSTRUCTION
Directory of Open Access Journals (Sweden)
IRINA VASKES SANTCHES
2007-08-01
Full Text Available Resumen: El presente trabajo contribuye al debate sobre la actualidad estética, abordando diferentes enfoques del polémico concepto de deconstrucción, introducido por Jacques Derrida. Esta categoría es de referencia casi obligatoriacuando se habla sobre teoría estética contemporánea, forma parte de su nuevo aparato conceptual y expresa bien la nueva realidad que no tiene análogos históricos en lo que antes llamaban arte, estética y cultura. La elaboracióndel concepto de deconstrucción, el análisis de cómo funciona esa nueva forma del pensamiento crítico, y el método creativo de la interpretación y de la producción del texto artístico, nos permite entrar en el código de muchas obras artísticas actuales donde el espacio entre arte y teoría del arte es cada vez más incierto, especialmente en las diversas formas de arte conceptual o “performance art”.Abstract: Tackling polemic concept of deconstruction, introduced by Jacqes Derrida, from different approaches this article contributes to the debate on aesthetic current issues. This category is of almost obligatory reference when discussing about contemporary aesthetic theory. Deconstruction belongs to its new conceptual apparatus, and expresses well new reality that does not have historical analogy with what before was called art, aesthetics and culture. The elaboration of the concept of deconstruction, and the analysis of how this new form of strategical “procedure” of interpretation and production of the text (as textual reading is functioning allow us to enter the code of many current art works where the space between art and theory of the art is more and more uncertain, specially in the diverse forms of conceptual art or “performance art“.
The gravitational S-matrix: Erice lectures
Giddings, Steven B
2011-01-01
These lectures discuss an S-matrix approach to quantum gravity, and its relation to more local spacetime approaches. Prominent among the problems of quantum gravity are those of unitarity and observables. In a unitary theory with solutions approximating Minkowski space, the S-matrix (or, in four dimensions, related inclusive probabilities) should be sharply formulated and physical. Features of its perturbative description are reviewed. A successful quantum gravity theory should in particular address the questions posed by the ultrahigh-energy regime. Some control can be gained in this regime by varying the impact parameter as well as the collision energy. However, with decreasing impact parameter gravity becomes strong, first eikonalizing, and then entering the regime where in the classical approximation black holes form. Here one confronts what may be the most profound problem of quantum gravity, that of providing unitary amplitudes, as seen through the information problem of black hole evaporation. Existing...
Ultrametric fixed points in reduced axiomatic systems
Turinici, Mihai
2015-01-01
The Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] is used to get a proof, in the reduced axiomatic system (ZF-AC+DC), of a fixed point result [in the complete axiomatic system (ZF)] over Cantor complete ultrametric spaces due to Petalas and Vidalis [Proc. Amer. Math. Soc., 118 (1993), 819-821].
Axiomatic design in large systems complex products, buildings and manufacturing systems
Suh, Nam
2016-01-01
This book provides a synthesis of recent developments in Axiomatic Design theory and its application in large complex systems. Introductory chapters provide concise tutorial materials for graduate students and new practitioners, presenting the fundamentals of Axiomatic Design and relating its key concepts to those of model-based systems engineering. A mathematical exposition of design axioms is also provided. The main body of the book, which represents a concentrated treatment of several applications, is divided into three parts covering work on: complex products; buildings; and manufacturing systems. The book shows how design work in these areas can benefit from the scientific and systematic underpinning provided by Axiomatic Design, and in so doing effectively combines the state of the art in design research with practice. All contributions were written by an international group of leading proponents of Axiomatic Design. The book concludes with a call to action motivating further research into the engineeri...
Alternative Axiomatic Characterizations of the Grey Shapley Value
Directory of Open Access Journals (Sweden)
Sirma Zeynep Alparslan Gok
2014-05-01
Full Text Available The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends.
Unitarity and the Holographic S-Matrix
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A.Liam; /Stanford U., Phys. Dept.; Kaplan, Jared; /SLAC
2012-08-28
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators O{sub 1} and O{sub 2} to extract the contribution of an individual primary O{sub {Delta},{ell}} in their OPE. This provides a method for isolating the contribution of specific conformal blocks which we use to prove an important relation between certain conformal block coefficients and anomalous dimensions. These techniques make essential use of the simplifications that occur when CFT correlators are expressed in terms of a Mellin amplitude.
Unitarity and the holographic S-Matrix
Fitzpatrick, A. Liam; Kaplan, Jared
2012-10-01
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators {{{O}}_1} and {{{O}}_2} to extract the contribution of an individual primary {{{O}}_{{\\varDelta, ell }}} in their OPE. This provides a method for isolating the contribution of specific conformal blocks which we use to prove an important relation between certain conformal block coefficients and anomalous dimensions. These techniques make essential use of the simplifications that occur when CFT correlators are expressed in terms of a Mellin amplitude.
Unitarity and the Holographic S-Matrix
Fitzpatrick, A Liam
2011-01-01
The bulk S-Matrix can be given a non-perturbative definition in terms of the flat space limit of AdS/CFT. We show that the unitarity of the S-Matrix, ie the optical theorem, can be derived by studying the behavior of the OPE and the conformal block decomposition in the flat space limit. When applied to perturbation theory in AdS, this gives a holographic derivation of the cutting rules for Feynman diagrams. To demonstrate these facts we introduce some new techniques for the analysis of conformal field theories. Chief among these is a method for conglomerating local primary operators to extract the contribution of an individual primary in their OPE. This provides a method for isolating the contribution of specific conformal blocks which we use to prove an important relation between certain conformal block coefficients and anomalous dimensions. These techniques make essential use of the simplifications that occur when CFT correlators are expressed in terms of a Mellin amplitude.
Axiomatic Theories of Truth on Intuitionistic Logic%直觉主义逻辑上的公理化真理论
Institute of Scientific and Technical Information of China (English)
李娜; 李晟
2015-01-01
In this paper, we investigate the disquotation scheme and the compositional axioms of truth based on the intuitionistic logic and Heyting arithmetic HA. Three intuitionistic typed theories of truth, that is, IDT, ICT and SICT, will be obtained and their basic properties will be discussed. The main results of this paper are the standard interpretation of arithmetic is suitable for all of them, IDT and SICT are both theories of truth meet adequacy conditions, and IDT is conservative over HA, but SICT not.%本文在直觉主义逻辑和海廷算术HA的基础上，重新考察了去引号模式和组合真公理，得到了三种直觉主义的类型真理论：IDT、ICT和SICT，并探讨了它们的一些基本性质。本文证明了三者都满足对算术的标准解释，并且IDT和SICT是实质上充分的真理论，而ICT不是。在保守性方面，本文证明了IDT是HA的算术保守扩充理论，而SICT是非保守扩充。
Axiomatic Design of Micro Quartz Rate Sensor
Institute of Scientific and Technical Information of China (English)
SHI Yang-he; ZHANG Hong-hai; LIU Sheng
2007-01-01
Quartz rate sensors (QRS) made out of one single piece of quartz crystal are inertial devices which can be used for general rate control, stabilization, automotive and aerospace/defense markets,etc. The mechanical design of the QRS has been investigated based on axiomatic design. The axiomatic design matrix of the mechanical structure of Coriolis Vibratory Gyroscopes (CVG) has been proposed. The mechanical function of QRS is divided into three Function Requirements ( FR ) , i. e. , FR1 is the drive mode, FR2 is the sense mode, FR3 is a coupled connection where the Coriolis force can couple the two modes with a term proportional to the rotational rate. A new QRS which is easy to be fabricated has been put forward. Furthermore, the new QRS indicated that the axiomatic design is a help to functional design of products.
Ragnar Frisch's Axiomatic Approach in Econometrics
BJERKHOLT, Olav; DUPONT, Ariane
2007-01-01
Ragnar Frisch's concept of econometrics was broader in scope than the more restricted connotation it has today as a sub-discipline of economics, it may be more properly rendered as a reconstruction of economics along principles inspired and drawn from natural sciences. In this reconstruction an axiomatic approach played a key role. In his 1926 essay, Sur un problème d'économie pure, Frisch set out what may have been the first axiomatic approach towards modelling consumer behaviour. Frisch's a...
An Axiomatic Representation of System Dynamics
Baianu, I
2004-01-01
An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.
Axiomatization for 1-level universal AND operator
Institute of Scientific and Technical Information of China (English)
MA Ying-cang; HE Hua-can
2008-01-01
The aim of this article is the partial axiomatization for 1-level universal logic. A propositional calculus formal deductive system UL-h∈(0,1] based on 1-level universal AND operator of universal logic is built up. The corresponding algebra L∏G- is introduced. The soundness and the completeness of system UL-h∈(0,1] are proved.
Axiomatic Characterizations of IVF Rough Approximation Operators
Directory of Open Access Journals (Sweden)
Guangji Yu
2014-01-01
Full Text Available This paper is devoted to the study of axiomatic characterizations of IVF rough approximation operators. IVF approximation spaces are investigated. The fact that different IVF operators satisfy some axioms to guarantee the existence of different types of IVF relations which produce the same operators is proved and then IVF rough approximation operators are characterized by axioms.
SELF-ORGANIZED SEMANTIC FEATURE EVOLUTION FOR AXIOMATIC DESIGN
Institute of Scientific and Technical Information of China (English)
HAO He; FENG Yixiong; TAN Jianrong; XUE Yang
2008-01-01
Aiming at the problem existing in the computer aided design process that how to express the design intents with high-level engineering terminologies, a mechanical product self-organized semantic feature evolution technology for axiomatic design is proposed, so that the constraint relations between mechanical parts could be expressed in a semantic form which is more suitable for designers. By describing the evolution rules for semantic constraint information, the abstract expression of design semantics in mechanical product evolution process is realized and the constraint relations between parts are mapped to the geometric level from the semantic level; With semantic feature relation graph, the abstract semantic description, the semantic relative structure and the semantic constraint information are linked together; And the methods of semantic feature self-organized evolution are classified. Finally, combining a design example of domestic high-speed elevator, how to apply the theory to practical product development is illustrated and this method and its validity is described and verified. According to the study results, the designers are able to represent the design intents at an advanced semantic level in a more intuitional and natural way and the automation, recursion and visualization for mechanical product axiomatic design are also realized.
Axiomatic Definition of Entropy for Nonequilibrium States
Beretta, Gian Paolo
2008-01-01
In introductory courses and textbooks on elementary thermodynamics, entropy is often presented as a property defined only for equilibrium states, and its axiomatic definition is almost invariably given in terms of a heat to temperature ratio, the traditional Clausius definition. Teaching thermodynamics to undergraduate and graduate students from all over the globe, we have sensed a need for more clarity, unambiguity, generality and logical consistency in the exposition of thermodynamics, incl...
Axiomatic Definition of Entropy for Nonequilibrium States
Directory of Open Access Journals (Sweden)
Gian Paolo Beretta
2008-06-01
Full Text Available In introductory courses and textbooks on elementary thermodynamics, entropy is often presented as a property defined only for equilibrium states, and its axiomatic definition is almost invariably given in terms of a heat to temperature ratio, the traditional Clausius definition. Teaching thermodynamics to undergraduate and graduate students from all over the globe, we have sensed a need for more clarity, unambiguity, generality and logical consistency in the exposition of thermodynamics, including the general definition of entropy, than provided by traditional approaches. Continuing the effort pioneered by Keenan and Hatsopoulos in 1965, we proposed in 1991 a novel axiomatic approach which eliminates the ambiguities, logical circularities and inconsistencies of the traditional approach still adopted in many new books. One of the new and important aspects of our exposition is the simple, non-mathematical axiomatic definition of entropy which naturally extends the traditional Clausius definition to all states, including non-equilibrium states (for which temperature is not defined. And it does so without any recourse to statistical mechanical reasoning. We have successfully presented the foundations of thermodynamics in undergraduate and graduate courses for the past thirty years. Our approach, including the definition of entropy for non-equilibrium states, is developed with full proofs in the treatise E. P. Gyftopoulos and G. P. Beretta, Thermodynamics. Foundations and Applications, Dover Edition, 2005 (First edition, Macmillan, 1991 [1]. The slight variation we present here illustrates and emphasizes the essential elements and the minimal logical sequence to get as quickly as possible to our general axiomatic definition of entropy valid for nonequilibrium states no matter how “far” from thermodynamic equilibrium.
John von Neumann on Mathematical and Axiomatic Physics
Rédei, Miklós
The aim of this paper is to recall and analyse von Neumann's position on mathematical and axiomatic physics. It will be argued that von Neumann demanded much less mathematical rigor in physics than commonly thought and that he followed an opportunistically interpreted soft axiomatic method in physics. The notion of opportunistic soft axiomatization is illustrated by recalling his work on the mathematical foundations of quantum mechanics.
Ragnar Frisch’s Axiomatic Approach to Econometrics
BJERKHOLT, Olav
2012-01-01
Ragnar Frisch's concept of econometrics was broader in scope than the more restricted connotation it has today as a sub-discipline of economics, it may be more properly rendered as a reconstruction of economics along principles inspired and drawn from natural sciences. In this reconstruction an axiomatic approach played a key role. The general aim of Frisch's axiomatic approach was to argue in favour of using axiomatics as a basis for theorizing in economics and the modelling of individual be...
The Black Hole S-Matrix from Quantum Mechanics
Betzios, Panagiotis; Papadoulaki, Olga
2016-01-01
We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory \\& $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\\textemdash of waves scattering off inverted harmonic oscillator potentials\\textemdash that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.
Axiomatizations and factorizations of Sugeno utility functions
Couceiro, Miguel
2011-01-01
In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions. Moreover, we address and solve the problem of factorizing a Sugeno utility function as a composition of a Sugeno integral with local utility functions, if such a factorization exists.
The S-matrix Bootstrap II: Two Dimensional Amplitudes
Paulos, Miguel F; Toledo, Jonathan; van Rees, Balt C; Vieira, Pedro
2016-01-01
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with a fixed mass spectrum. In special cases we identify interesting integrable theories saturating these bounds. Our analytic bounds match precisely with numerical bounds obtained in a companion paper where we consider massive QFT in an AdS box and study boundary correlators using the technology of the conformal bootstrap.
Classical space–times from the S-matrix
Energy Technology Data Exchange (ETDEWEB)
Neill, Duff [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Rothstein, Ira Z. [Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213 (United States)
2013-12-11
We show that classical space–times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space–time as a series in G{sub N}. At no point of the derivation is any use made of the Einstein–Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space–time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space–times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang–Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently then the more traditional Feynman diagram approach.
Wang, Shiping; Zhu, Qingxin; Zhu, William; Min, Fan
2012-01-01
Covering is an important type of data structure while covering-based rough sets provide an efficient and systematic theory to deal with covering data. In this paper, we use boolean matrices to represent and axiomatize three types of covering approximation operators. First, we define two types of characteristic matrices of a covering which are essentially square boolean ones, and their properties are studied. Through the characteristic matrices, three important types of covering approximation ...
Classical Space-Times from the S Matrix
Neill, Duff
2013-01-01
We show that classical space-times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space-time as a series in $G_N$. At no point of the derivation is any use made of the Einstein-Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space-time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space-times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang-Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity thre...
The place of probability in Hilbert's axiomatization of physics, ca. 1900-1928
Verburgt, Lukas M.
2016-02-01
Although it has become a common place to refer to the 'sixth problem' of Hilbert's (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert's project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a 'vague' mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the 'sixth problem' of 1900.
Renormalization group coefficients and the S-matrix
Caron-Huot, Simon
2016-01-01
We show how to use on-shell unitarity methods to calculate renormalisation group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phase-space integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by pi. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.
Axiomatic nonextensive statistics at NICA energies
Tawfik, Abdel Nasser
2016-01-01
We discuss the possibility of implementing axiomatic nonextensive statistics, where it is conjectured that the phase-space volume determines the (non)extensive entropy, on the particle production at NICA energies. Both Boltzmann-Gibbs and Tsallis statistics are very special cases of this generic (non)extensivity. We conclude that the lattice thermodynamics is {\\it ab initio} extensive and additive and thus the nonextensive approaches including Tsallis statistics categorically are not matching with them, while the particle production, for instance the particle ratios at various center-of-mass energies, is likely a nonextensive process but certainly not of Tsallis type. The resulting freezeout parameters, the temperature and the chemical potentials, are approximately compatible with the ones deduced from Boltzmann-Gibbs statistics.
An axiomatic approach to Maxwell's equations
Heras, José A
2016-01-01
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem provides an integral representation for each function. A corollary of this theorem yields Maxwell's equations with magnetic monopoles. It is pointed out that the causality principle and the conservation of electric and magnetic charges are the most fundamental physical axioms underlying these equations. Another application of the corollary yields Maxwell's equations in material media. The theorem is also formulated in the Minkowski space-time and applied to obtain the covariant form of Maxwell's equations with magnetic monopoles and the covariant form of Maxwell's equations in material media. The approach makes use of the infinite-space Green function of the wave equation and is therefore suitable for an advanced course in electrodynamics.
Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
Hoare, Ben; Miramontes, J Luis
2013-01-01
The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a q-deformation that relates it to the S-matrix of a generalization of the sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring. Whilst this is a fascinating development the resulting S-matrix is not explicitly unitary. The problem has been known for a long time in the context of S-matrices related to quantum groups. A braiding relation often called "unitarity" actually only corresponds to quantum field theory unitarity when the S-matrix is Hermitian analytic and quantum group S-matrices manifestly violate this. On the other hand, overall consistency of the S-matrix under the bootstrap requires that the deformation parameter is a root of unity and consequently one is forced to perform the "vertex" to IRF, or SOS, transformation on the states to truncate the spectrum consistently. In the IRF formulation unitarity is now manifest and the string S-matrix and the S-matrix of the generalised sine-Gordon theory are...
Analyticity and the Holographic S-Matrix
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A.Liam; /Stanford U., Phys. Dept.; Kaplan, Jared; /SLAC
2012-04-03
We derive a simple relation between the Mellin amplitude for AdS/CFT correlation functions and the bulk S-Matrix in the flat spacetime limit, proving a conjecture of Penedones. As a consequence of the Operator Product Expansion, the Mellin amplitude for any unitary CFT must be a meromorphic function with simple poles on the real axis. This provides a powerful and suggestive handle on the locality vis-a-vis analyticity properties of the S-Matrix. We begin to explore analyticity by showing how the familiar poles and branch cuts of scattering amplitudes arise from the holographic description. For this purpose we compute examples of Mellin amplitudes corresponding to 1-loop and 2-loop Witten diagrams in AdS. We also examine the flat spacetime limit of conformal blocks, implicitly relating the S-Matrix program to the Bootstrap program for CFTs. We use this connection to show how the existence of small black holes in AdS leads to a universal prediction for the conformal block decomposition of the dual CFT.
Final design of a spacer grid using axiomatic design
Energy Technology Data Exchange (ETDEWEB)
Park, Gyung-Jin; Lee, Hyun-Ah; Kim, Chong-Ki [Hanyang Univ., Seoul (Korea, Republic of); Song, Gi-Nam [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2007-03-15
The spacer grid set is a component in the nuclear fuel assembly. The set supports the fuel rod safely. The spacer grid set must have enough strength to sustain external loads such as earthquake. The fretting wear occurs between the spring of the fuel rod and the spacer grid due to the flow-induced vibration after the fuel rod is inserted to the spacer grid set. Design of the spring is carried out by using the independence axiom in axiomatic design to solve the two problems. The spacer grid is divided into two parts for sustaining the impact load and reducing fretting wear based on the function requirements. The design for the impact load is performed through non-linear analysis and the homology theory is adopted to reduce fretting wear achieved for shape optimization. The objective function to be minimized ids the maximum stress and constraints are defined to increase the contact area between the fuel rod and the spring using the homology theory. In the design results, the contact area becomes large and it is conformed by nonlinear static analysis. The final design shows that larger impact loads can be sustained compared to the current model.
Symmetries of the Bosonic String S-Matrix
Moore, G
1993-01-01
The bracket operation on mutually local BRST classes may be combined with Lorentz invariance and analyticity to write an infinite set of finite difference relations on string scattering amplitudes. When combined with some simple physical criteria these relations uniquely determine the genus zero string $S$-matrix for $N\\leq 26$-particle scattering in $\\IR^{25,1}$ in terms of a single parameter, $\\kappa$, the string coupling. We propose that the high-energy limit of the relations are the Ward identities for the high-energy symmetries of string theory.
Energy Technology Data Exchange (ETDEWEB)
Bousso, Raphael
2005-01-25
We study conditions for the existence of asymptotic observables in cosmology. With the exception of de Sitter space, the thermal properties of accelerating universes permit arbitrarily long observations, and guarantee the production of accessible states of arbitrarily large entropy. This suggests that some asymptotic observables may exist, despite the presence of an event horizon. Comparison with decelerating universes shows surprising similarities: Neither type suffers from the limitations encountered in de Sitter space, such as thermalization and boundedness of entropy. However, we argue that no realistic cosmology permits the global observations associated with an S-matrix.
Particles as S-matrix poles: hadron democracy
International Nuclear Information System (INIS)
The connection between two theoretical ideas of the 1950s is traced in this article, namely that hadrons are nonfundamental, ''composite'' particles and that all physically observable particles correspond to singularities of an analytic scattering matrix. The S matrix theory developed by Werner Heisenberg in the early forties now incorporated the concepts of unitarity, invariance, analyticity and causality. The meson-exchange force meant that poles must be present in nucleon-nuclear and pion-nucleon scattering as predicted by dispersion relations. Experimental work in accessible regions determined pole residues. Pole residue became associated with force strength and pole position with particle mass. In 1959, the author discovered the so-called ''bootstrap'' theory the rho meson as a force generates a rho particle. By the end of the 1950s it was clear that all hadrons had equal status, each being bound states of other hadrons, sustained by hadron exchange forces and that hadrons are self-generated by an S-matrix bootstrap mechanism that determines all their properties. (UK)
Semiclassical S-matrix for black holes
Bezrukov, Fedor; Levkov, Dmitry; Sibiryakov, Sergey
2015-12-01
We propose a semiclassical method to calculate S -matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(- B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp( B) as the number of black hole states. The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordström black hole. Our semiclassical method opens a new systematic approach to the gravitational S -matrix in the non-perturbative regime.
Semiclassical S-matrix for black holes
Bezrukov, Fedor; Sibiryakov, Sergey
2015-01-01
We propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(-B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states. The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordstrom black hole. Our semiclassical method opens a new systematic approach to the gravitational S-matrix in the non-perturbative regime.
New Representations of the Perturbative S-Matrix
Baadsgaard, Christian; Bourjaily, Jacob L; Caron-Huot, Simon; Damgaard, Poul H; Feng, Bo
2015-01-01
We propose a new framework to represent the perturbative S-matrix which is well-defined for all quantum field theories of massless particles, constructed from tree-level amplitudes and integrable term-by-term. This representation is derived from the Feynman expansion through a series of partial fraction identities, discarding terms that vanish upon integration. Loop integrands are expressed in terms of "Q-cuts" that involve both off-shell and on-shell loop-momenta, defined with a precise contour prescription that can be evaluated by ordinary methods. This framework implies recent results found in the scattering equation formalism at one-loop, and it has a natural extension to all orders---even non-planar theories without well-defined forward limits or good ultraviolet behavior.
Directory of Open Access Journals (Sweden)
Christopher G. Jesudason
2003-07-01
Full Text Available Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988, 143(1, 65-70]. Since the traditional formulations are central to science, a brief analysis of some of these newer theories along traditional lines is attempted, based on well-attested axioms which have formed the basis of equilibrium thermodynamics. It is deduced that the Clausius analysis leading to the law of increasing entropy does not follow from the given axioms but it can be proved that for irreversible transitions, the total entropy change of the system and thermal reservoirs (the "Universe" is not negative, even for the case when the reservoirs are not at the same temperature as the system during heat transfer. On the basis of two new simple theorems and three corollaries derived for the correlation between irreversible and reversible pathways and the traditional axiomatics, it is shown that a sequence of reversible states can never be used to describe a corresponding sequence of irreversible states for at least closed systems, thereby restricting the principle of local equilibrium. It is further shown that some of the newer irreversible entropy forms given exhibit some paradoxical properties relative to the standard axiomatics. It is deduced that any reconciliation between the traditional approach and novel theories lie in creating a well defined set of axioms to which all theoretical developments should attempt to be based on unless proven not be useful, in which case there should be consensus in removing such axioms from theory. Clausius' theory of equivalent transformations do not contradict the traditional understanding of heat- work efficiency. It is concluded that the intuitively derived assumptions over the last two
Causality and dispersion relations and the role of the S-matrix in the ongoing research
Schroer, Bert
2011-01-01
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but differen...
Applying axiomatic design methodology in developing modified libertation products
Directory of Open Access Journals (Sweden)
Bibiana Margarita Vallejo Díaz
2010-04-01
Full Text Available Some conceptual elements regarding the axiomatic design method were applied to a specific case-study regarding developing modified liberation compressed product (CLM-UN, for use in the agricultural sector as pH regulating agent in solil. The study was orientated towards defining functional requeriments, design parameters and process variables for manufacturing the product. Independence and information were evaluated, supporting axiomatic design as an alternative for integral product and process design (as a rational and systemic exercise, facilitating producing products having the quality which future users expect from them.
Classical-limit S-matrix for heavy ion scattering. [S matrix
Energy Technology Data Exchange (ETDEWEB)
Donangelo, R.J.
1977-01-01
An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, and therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed.
An Axiomatic, Unified Representation of Biosystems and Quantum Dynamics
Baianu, I
2004-01-01
An axiomatic representation of system dynamics is introduced in terms of categories, functors, organismal supercategories, limits and colimits of diagrams. Specific examples are considered in Complex Systems Biology, such as ribosome biogenesis and Hormonal Control in human subjects. "Fuzzy" Relational Structures are also proposed for flexible representations of biological system dynamics and organization.
A Complete Axiomatization for Prefix Iteration in Branching Bisimulation
Fokkink, W.J.
2008-01-01
This paper studies the interaction of prefix iteration μ*x with the silent step τ in the setting of branching bisimulation. That is, we present a finite equational axiomatization for Basic Process Algebra with deadlock, empty process and the silent step, extended with prefix iteration, and prove tha
On the Axiomatic Characterization of "Who is a J?"
Dimitrov, D.A.; Sung, S.C.
2003-01-01
Recent work by Kasher and Rubinstein (1997) considers the problem of group identification from a social choice perspective.These authors provide an axiomatic characterization of a liberal aggregator whereby the group consist of those and only those individuals each of which views oneself a member of
Paired Comparisons Analysis : An Axiomatic Approach to Rankings in Tournaments
Gonzalez-Diaz, J.; Hendrickx, R.L.P.; Lohmann, E.R.M.A.
2011-01-01
In this paper we present an axiomatic analysis of several ranking methods for tournaments. We find that two of them exhibit a very good behaviour with respect to the set of properties under consideration. One of them is the maximum likelihood ranking, the most common method in statistics and psychol
Paired comparisons analysis: an axiomatic approach to ranking methods
Gonzalez-Diaz, J.; Hendrickx, Ruud; Lohmann, E.R.M.A.
2014-01-01
In this paper we present an axiomatic analysis of several ranking methods for general tournaments. We find that the ranking method obtained by applying maximum likelihood to the (Zermelo-)Bradley-Terry model, the most common method in statistics and psychology, is one of the ranking methods that per
Directory of Open Access Journals (Sweden)
Aleksandar Perović
2008-01-01
Full Text Available During the last two decades, Group for intelligent systems at Mathematicalfaculty in Belgrade has developed several theorem provers for different kind of formalsystems. Lately, we have turned our attention to fuzzy logic and development of thecorresponding theorem prover. The first step is to find the suitable axiomatization, i.e., theformalization of fuzzy logic that is sound, complete and decidable. It is well known thatthere are fuzzy logics (such as Product logic that require infinitary axiomatization in orderto tame the non-compactness phenomena. Though such logics are strongly complete (everyconsistent set of formulas is satisfiable, the only possible decidability result is thesatisfiability of a formula. Therefore, we have adapted the method of Fagin, Halpern andMegiddo for polynomial weight formulas in order to interpret the Lukasiewicz and theProduct logic into the first order theory of the reals.
The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
Mitev, Vladimir; Tsuboi, Zengo
2012-01-01
The S-matrix of the AdS5 x S5 string theory is a tensor product of two centrally extended su(2|2) S-matrices, each of which is related to the R-matrix of the Hubbard model. The R-matrix of the Hubbard model was first found by Shastry, who ingeniously exploited the fact that, for zero coupling, the Hubbard model can be decomposed into two XX models. In this article, we review and clarify this construction from the AdS/CFT perspective and investigate the implications this has for the AdS5 x S5 S-matrix.
Essays on Econometrics and Decision Theory
Montiel Olea, Jose Luis
2013-01-01
This dissertation presents three essays. The first essay, coauthored with Tomasz Strzalecki, is a classical exercise in axiomatic decision theory. We propose a simple and novel axiomatization of quasi-hyperbolic discounting, a tractable model of present bias preferences that has found many applications in economics. Our axiomatization imposes consistency restrictions directly on the intertemporal tradeoffs faced by the decision maker, without relying on auxiliary calibration devices such as l...
Causality and dispersion relations and the role of the S-matrix in the ongoing research
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert, E-mail: schroer@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Univ. , Berlin (Germany). Inst. fur Theoretische Physik
2011-07-01
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their seri- ous shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach. (author)
Causality and dispersion relations and the role of the S-matrix in the ongoing research
International Nuclear Information System (INIS)
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their seri- ous shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach. (author)
A sound and complete axiomatization for Dynamic Topological Logic
Duque, David Fernández
2012-01-01
Dynamic Topological Logic (DTL) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a complete axiomatization for the full language of DTL over the class of all dynamical systems has proven to be quite elusive. Here we propose to enrich the language to include a polyadic topological modality, originally introduced by Dawar and Otto in a different context. We then provide a sound axiomatization for DTL over this extended language, and prove that it is complete. The polyadic modality is used in an essential way in our proof.
A note on the axiomatization of the Nash equilibrium correspondence
Forgó, Ferenc
2015-01-01
A new axiomatization of the Nash equilibrium correspondence for n-person games based on independence of irrelevant strategies is given. Using a flexible general model, it is proved that the Nash equilibrium correspondence is the only solution to satisfy the axioms of non-emptiness, weak one-person rationality, independence of irrelevant strategies and converse independence of irrelevant strategies on the class of subgames of a fixed finite n-person game which admit at least one Nash equili...
Geometrical exposition of structural axiomatic economics (I): Fundamentals
Kakarot-Handtke, Egmont
2012-01-01
Behavioral assumptions are not solid enough to be eligible as first principles of theoretical economics. Hence all endeavors to lay the formal foundation on a new site and at a deeper level actually need no further vindication. Part (I) of the structural axiomatic analysis submits three nonbehavioral axioms as groundwork and applies them to the simplest possible case of the pure consumption economy. The geometrical analysis makes the interrelations between income, profit and employment under ...
Feasible elimination procedures in social choice : an axiomatic characterization
Peleg, B.; Peters, H.J.M.
2016-01-01
Feasible elimination procedures (Peleg, 1978) play a central role in constructing social choice functions which have the following property: in the associated game form, for any preference profile there exists a strong Nash equilibrium resulting in the sincere outcome. In this paper we provide an axiomatic characterization of the social choice correspondence resulting from applying feasible elimination procedures. The axioms are anonymity, Maskin monotonicity, and independent blocking.
An Axiomatic Basis for Quantum Mechanics
Cassinelli, Gianni; Lahti, Pekka
2016-10-01
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in this derivation are the co-ordinatization of generalized geometries and a theorem of Solér which characterizes Hilbert spaces among the orthomodular spaces. A generalized Wigner theorem is applied to reduce some of the assumptions of Solér's theorem to the theory of symmetry in quantum mechanics. Since this reduction is only partial we also point out the remaining open questions.
Gravitational spin Hamiltonians from the S matrix
Vaidya, Varun
2014-01-01
We utilize generalized unitarity and recursion relations combined with effective field theory(EFT) techniques to compute spin dependent interaction terms for inspiralling binary systems in the post newtonian(PN) approximation. Using these methods offers great computational advantage over traditional techniques involving feynman diagrams, especially at higher orders in the PN expansion. As a specific example, we reproduce the spin-orbit interaction up to 2.5 PN order as also the leading order ...
A Simple Axiomatization of Nonadditive Expected Utility
R.K. Sarin (Rakesh); P.P. Wakker (Peter)
1992-01-01
textabstractThis paper provides an extension of Savage's subjective expected utility theory for decisions under uncertainty. It includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive. The
Inclusive fitness maximization: An axiomatic approach.
Okasha, Samir; Weymark, John A; Bossert, Walter
2014-06-01
Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual׳s 'as if preferences' (binary choices) for the case in which phenotypic effects are additive. Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it.
Inclusive fitness maximization: An axiomatic approach.
Okasha, Samir; Weymark, John A; Bossert, Walter
2014-06-01
Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual׳s 'as if preferences' (binary choices) for the case in which phenotypic effects are additive. Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it. PMID:24530825
Gravitational spin Hamiltonians from the S matrix
Vaidya, Varun
2014-01-01
We utilize generalized unitarity and recursion relations combined with effective field theory(EFT) techniques to compute spin dependent interaction terms for inspiralling binary systems in the post newtonian(PN) approximation. Using these methods offers great computational advantage over traditional techniques involving feynman diagrams, especially at higher orders in the PN expansion. As a specific example, we reproduce the spin-orbit interaction up to 2.5 PN order as also the leading order $S^2$(3PN) hamiltonian for an arbitrary massive object. We also obtain the unknown $S^3$(3.5PN) spin hamiltonian for an arbitrary massive object in terms of its low frequency linear response to gravitational perturbations, which was till now known only for a black hole. Furthermore, we derive the missing $S^4$ Hamiltonian at leading order(4PN) for an arbitrary massive object and establish that a minimal coupling of a massive elementary particle to gravity leads to a black hole structure. Finally, the Kerr metric is obtain...
Arkani-Hamed, Nima; Cheung, Clifford; Kaplan, Jared
2009-01-01
The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity scattering amplitudes suggest the existence of a "weak-weak" dual formulation in which these structures are made manifest at the expense of manifest locality. We suggest that this dual description lives in (2,2) signature and is naturally formulated in twistor space. We recast the BCFW recursion relations in an on-shell form that begs to be transformed into twistor space. Our twistor transformation is inspired by Witten's, but differs in treating twistor and dual twistor variables more equally. In these variables the three and four-point amplitudes are amazingly simple; the BCFW relations are represented by diagrammatic rules that precisely define the "twistor diagrams" of Andrew Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees; they reveal striking connections between amplitudes and suggest a new form for them in momentum space. We also obtain a twistorial formulation of gravity. All tree amplitudes can b...
Asymptotic states and the definition of the S-matrix in quantum gravity
International Nuclear Information System (INIS)
Viewing gravitational energy–momentum pGμ as equal by observation, but different in essence from inertial energy–momentum pIμ naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space M4. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit—mapping the gravitational energy–momentum onto the inertial energy–momentum to account for their observed equality—is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeomorphisms. The so-defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy–momentum. Finally, generalized Lehmann–Symanzik–Zimmermann reduction formulae for scalar, Dirac and gauge fields are established which allow us to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in Wiesendanger (2011 arXiv:1103.1012) any transition amplitude can in principle be computed consistently to any order in perturbative quantum gravity. (paper)
The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
Borsato, Riccardo; Sfondrini, Alessandro; Stefanski, Bogdan
2014-01-01
We derive the non-perturbative worldsheet S matrix for fundamental excitations of Type IIB superstring theory on AdS_3 x S^3 x T^4 with Ramond-Ramond flux. To this end, we study the off-shell symmetry algebra of the theory and its representations. We use these to determine the S matrix up to scalar factors and we derive the crossing equations that these scalar factors satisfy. Our treatment automatically includes fundamental massless excitations, removing a long-standing obstacle in using integrability to study the AdS_3/CFT_2 correspondence. The present paper contains a detailed derivation of results first announced in arXiv:1403.4543.
Axiomatic Quantification of Co-authors' Relative Contributions
Wang, Ge
2010-01-01
Over the past decades, the competition for academic resources has gradually intensified, and worsened with the current financial crisis. To optimize the resource allocation, individualized assessment of research results is being actively studied but the current indices, such as the number of papers, the number of citations, the h-factor and its variants have limitations, especially their inability of determining co-authors' credit shares fairly. Here we establish an axiomatic system and quantify co-authors' relative contributions. Our methodology avoids subjective assignment of co-authors' credits using the inflated, fractional or harmonic methods, and provides a quantitative tool for scientific management such as funding and tenure decisions.
Fuzzy Entropy： Axiomatic Definition and Neural Networks Model
Institute of Scientific and Technical Information of China (English)
QINGMing; CAOYue; HUANGTian-min
2004-01-01
The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.
Towards an axiomatic model of fundamental interactions at Planck scale
Kiselev, Arthemy V
2014-01-01
By exploring possible physical sense of notions, structures, and logic in a class of noncommutative geometries, we try to unify the four fundamental interactions within an axiomatic quantum picture. We identify the objects and algebraic operations which could properly encode the formation and structure of sub-atomic particles, antimatter, annihilation, CP-symmetry violation, mass endowment mechanism, three lepton-neutrino matchings, spin, helicity and chirality, electric charge and electromagnetism, as well as the weak and strong interaction between particles, admissible transition mechanisms (e.g., muon to muon neutrino, electron, and electron antineutrino), and decays (e.g., neutron to proton, electron, and electron antineutrino).
Stabilizing a missile radar antenna Using Axiomatic Design
Kjellberg, Malin
2007-01-01
This thesis work describes a brand new concept of how to, from a mechanical perspective, stabilize/mount a radar antenna. The antenna must be able to rotate ±60 degrees around pitch and yaw without disturbing the radar characteristics. At the same time the antenna diameter must be as large as possible to enhance radar quality. Axiomatic Design was applied as the work method which helped developing a brand new concept of how to mount the antenna. This concept study was made for Saab Bofors Dyn...
An SU(1|1)-Invariant S-Matrix with Dynamic Representations
Beisert, N
2006-01-01
The spin chains originating from large-N conformal gauge theories are of a special kind: The Hamiltonian is not invariant under the symmetry algebra, it is rather a part of it. This leads to interesting properties within the asymptotic Bethe ansatz. Here we study an S-matrix with u(1|1) symmetry which arises in a long-range spin chain with fundamental spins of su(2|1).
A Holographic Holographic Bound and the Black Hole S-Matrix
Gary, Michael
2012-01-01
Holographic bounds have been derived using explicitly gravitational arguments. Motivated by explicit constructions of bulk wavepackets from observables in the boundary CFT, we derive a holographic bound in the context of the gauge/gravity correspondence within the dual field theory. We verify the consistency of the bound with the program of determining the Black Hole S-Matrix from the AdS/CFT correspondence.
Dry Machining Process of Milling Machine using Axiomatic Green Methodology
Puspita Andriani, Gita; Akbar, Muhammad; Irianto, Dradjad
2016-02-01
Most of companies know that there are strategies to become green industry, and they realize that green efforts have impacts on product quality and cost. Axiomatic Green Methodology models the relationship between green, quality, and cost. This methodology starts with determining the green improvement objective and then continues with mapping the functional, economic, and green requirements. From the mapping, variables which affect the requirements are identified. Afterwards, the effect of each variable is determined by performing experiments and regression modelling. In this research, axiomatic green methodology was implemented to dry machining of milling machine in order to reduce the amount of coolant. Dry machining will be feasible if it is not worse than the minimum required quality. As a result, dry machining is feasible without producing any defect. The proposed machining parameter is to reduce the coolant flow rate from 6.882 ml/minute to 0 ml/minute, set the depth of cut at 1.2 mm, spindle rotation speed at 500 rpm, and feed rate at 128 mm/minute. This solution is also resulted in reduction of cost for 200.48 rupiahs for each process.
Twisted Bethe equations from a twisted S-matrix
Ahn, Changrim; Bombardelli, Diego; Nepomechie, Rafael I
2010-01-01
All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. Although the undeformed S-matrix factorizes into a product of two su(2|2) factors, the deformed S-matrix cannot be so factored. Diagonalization of the corresponding transfer matrix requires a generalization of the conventional algebraic Bethe ansatz approach, which we first illustrate for the simpler case of the twisted su(2) principal chiral model. We also demonstrate that the same twisted Bethe equations can alternatively be derived using instead untwisted S-matrices and boundary conditions with operatorial twists.
Coordinate Bethe ansatz for the string S-matrix
Energy Technology Data Exchange (ETDEWEB)
Leeuw, M de [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)
2007-11-30
We use the coordinate Bethe ansatz approach to derive the nested Bethe equations corresponding to the recently found S-matrix for strings in AdS{sub 5} x S{sup 5}, compatible with centrally extended su(2 vertical bar 2) symmetry.
An axiomatic approach to intrinsic dimension of a dataset
Pestov, Vladimir
2007-01-01
We perform a deeper analysis of an axiomatic approach to the concept of intrinsic dimension of a dataset proposed by us in the IJCNN'07 paper (arXiv:cs/0703125). The main features of our approach are that a high intrinsic dimension of a dataset reflects the presence of the curse of dimensionality (in a certain mathematically precise sense), and that dimension of a discrete i.i.d. sample of a low-dimensional manifold is, with high probability, close to that of the manifold. At the same time, the intrinsic dimension of a sample is easily corrupted by moderate high-dimensional noise (of the same amplitude as the size of the manifold) and suffers from prohibitevely high computational complexity (computing it is an $NP$-complete problem). We outline a possible way to overcome these difficulties.
Fuzzy Axiomatic Design approach based green supplier selection
DEFF Research Database (Denmark)
Kannan, Devika; Govindan, Kannan; Rajendran, Sivakumar
2015-01-01
proposes a multi-criteria decision-making (MCDM) approach called Fuzzy Axiomatic Design (FAD) to select the best green supplier for Singapore-based plastic manufacturing company. At first, the environmental criteria was developed along with the traditional criteria based on the literature review...... and company requirements. Next, the FAD methodology evaluates the requirements of both the manufacturer (design needs) and the supplier (functional needs), and because multiple criteria must be considered, a multi-objective optimization model of a fuzzy nature must be developed. The application...... responsible in addition to being efficiently managed. A significant way to implement responsible GSCM is to reconsider, in innovative ways, the purchase and supply cycle, and a preliminary step would be to ensure that the supplier of goods successfully incorporates green criteria. Therefore, this paper...
Applying axiomatic design to a medication distribution system
Raguini, Pepito B.
As the need to minimize medication errors drives many medical facilities to come up with robust solutions to the most common error that affects patient's safety, these hospitals would be wise to put a concerted effort into finding methodologies that can facilitate an optimized medical distribution system. If the hospitals' upper management is looking for an optimization method that is an ideal fit, it is just as important that the right tool be selected for the application at hand. In the present work, we propose the application of Axiomatic Design (AD), which is a process that focuses on the generation and selection of functional requirements to meet the customer needs for product and/or process design. The appeal of the axiomatic approach is to provide both a formal design process and a set of technical coefficients for meeting the customer's needs. Thus, AD offers a strategy for the effective integration of people, design methods, design tools and design data. Therefore, we propose the AD methodology to medical applications with the main objective of allowing nurses the opportunity to provide cost effective delivery of medications to inpatients, thereby improving quality patient care. The AD methodology will be implemented through the use of focused stores, where medications can be readily stored and can be conveniently located near patients, as well as a mobile apparatus that can also store medications and is commonly used by hospitals, the medication cart. Moreover, a robust methodology called the focused store methodology will be introduced and developed for both the uncapacitated and capacitated case studies, which will set up an appropriate AD framework and design problem for a medication distribution case study.
S -matrix algebra of the AdS2×S2 superstring
Hoare, Ben; Pittelli, Antonio; Torrielli, Alessandro
2016-03-01
In this paper, we find the Yangian algebra responsible for the integrability of the AdS2×S2×T6 superstring in the planar limit. We demonstrate the symmetry of the corresponding exact S matrix in the massive sector, including the presence of the secret symmetry. We give two alternative presentations of the Hopf algebra. The first takes the usual canonical form, which, as the relevant representations are long, leads to a Yangian representation that is not of evaluation type. After investigating the relationship between cocommutativity, evaluation representations and the shortening condition, we find an alternative realization of the Yangian whose representation is of the evaluation type. Finally, we explore two limits of the S matrix. The first is the classical r matrix, where we rediscover the need for a secret symmetry also in this context. The second is the simplifying zero-coupling limit. In this limit, taking the S matrix as a generating R matrix for the algebraic Bethe ansatz, we obtain an effective model of free fermions on a periodic spin-chain. This limit should provide hints to the one-loop anomalous dimension of the mysterious superconformal quantum mechanics dual to the superstring theory in this geometry.
S-matrix and quantum tunneling in gravitational collapse
Ciafaloni, M.; Colferai, D.
2008-11-01
Using the recently introduced ACV reduced-action approach to transplanckian scattering of light particles, we show that the S-matrix in the region of classical gravitational collapse is related to a tunneling amplitude in an effective field space. We understand in this way the role of both real and complex field solutions, the choice of the physical ones, the absorption of the elastic channel associated to inelastic multigraviton production and the occurrence of extra absorption below the critical impact parameter. We are also able to compute a class of quantum corrections to the original semiclassical S-matrix that we argue to be qualitatively sensible and which, generally speaking, tend to smooth out the semiclassical results.
S-matrix and Quantum Tunneling in Gravitational Collapse
Ciafaloni, M
2008-01-01
Using the recently introduced ACV reduced-action approach to transplanckian scattering of light particles, we show that the $S$-matrix in the region of classical gravitational collapse is related to a tunneling amplitude in an effective field space. We understand in this way the role of both real and complex field solutions, the choice of the physical ones, the absorption of the elastic channel associated to inelastic multigraviton production and the occurrence of extra absorption below the critical impact parameter. We are also able to compute a class of quantum corrections to the original semiclassical $S$-matrix that we argue to be qualitatively sensible and which, generally speaking, tend to smooth out the semiclassical results.
Chaos in the black hole S-matrix
Polchinski, Joseph
2015-01-01
Recent work by Shenker, Stanford, and Kitaev has related the black hole horizon geometry to chaotic behavior. We extend this from eternal black holes to black holes that form and then evaporate. This leads to an identity for the change in the black hole S-matrix (over times shorter than the scrambling time) due an addition infalling particle, elaborating an idea of 't Hooft.
q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
Hoare, Ben; Miramontes, J Luis
2011-01-01
A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function of two independent couplings g and q=exp(i\\pi/k). The main result is to find the scalar factor, or dressing phase, which ensures that the unitarity and crossing equations are satisfied. For generic (g,k), the S-matrices are branched functions on a product of rapidity tori. In the limit k->infinity, one of them is identified with the S-matrix describing the magnon excitations on the string world sheet in AdS5 x S5, while another is the mirror S-matrix that is needed for the TBA. In the g->infinity limit, the rapidity torus degenerates, the branch points disappear and the S-matrices become meromorphic functions, as required by relativistic S-matrix theory. However, it is only the mirror S-matrix which satisfies the correct relativistic crossing equation. The mirror S-matrix ...
The one-loop worldsheet S-matrix for the AdS n × S n × T 10-2 n superstring
Roiban, Radu; Sundin, Per; Tseytlin, Arkady; Wulff, Linus
2014-08-01
We compute the massive-sector worldsheet S-matrix for superstring theories in AdS n × S n × T 10-2 n (with n = 2 , 3 , 5) in the near BMN expansion up to one-loop order in inverse string tension. We show that, after taking into account the wave function renormalization, the one-loop S-matrix is UV finite. In an appropriate regularization scheme the S-matrix is consistent with the underlying symmetries of the superstring theory, i.e. for the n=3 ,5casesitcoincideswiththeoneimpliedbythelight-conegaugesymmetrieswiththe dressing phases determined from the crossing equations. For the n = 2 , 3 cases we observe that the massless modes decouple from the one-loop calculation of massive mode scattering, i.e. the 2 n-dimensional supercoset sigma model and the full 10-dimensional superstring happen to have the same massive one-loop S-matrix.
Energy Technology Data Exchange (ETDEWEB)
Requate, A.
2007-03-15
Theoretical analysis of the vibrational excitation of small molecules during multiphoton ionization in intense laser fields of optical and infrared frequencies. Analysis of the alignment dependence of the electron impact ionization of diatomic molecules in the presence of an intense laser field as the final step in the process of Nonsequential Double Ionization. Quantum mechanical description using S-matrix theory in Strong Field Approximation (SFA), i.e. beyond perturbation theory. (orig.)
Design evaluation of emergency core cooling systems using Axiomatic Design
International Nuclear Information System (INIS)
In designing nuclear power plants (NPPs), the evaluation of safety is one of the important issues. As a measure for evaluating safety, this paper proposes a methodology to examine the design process of emergency core cooling systems (ECCSs) in NPPs using Axiomatic Design (AD). This is particularly important for identifying vulnerabilities and creating solutions. Korean Advanced Power Reactor 1400 MWe (APR1400) adopted the ECCS, which was improved to meet the stronger safety regulations than that of the current Optimized Power Reactor 1000 MWe (OPR1000). To improve the performance and safety of the ECCS, the various design strategies such as independency or redundancy were implemented, and their effectiveness was confirmed by calculating core damage frequency. We suggest an alternative viewpoint of evaluating the deployment of design strategies in terms of AD methodology. AD suggests two design principles and the visualization tools for organizing design process. The important benefit of AD is that it is capable of providing suitable priorities for deploying design strategies. The reverse engineering driven by AD has been able to show that the design process of the ECCS of APR1400 was improved in comparison to that of OPR1000 from the viewpoint of the coordination of design strategies
[Psychosis and grammatical reality. Preliminary to an axiomatic system].
Schmidt, P
1981-05-01
This paper is elaborated in the same order of those who developpe the idea that, Psychosis is pleaded as an alibi of a totalitarian reality (Psychosis alibi). So it may allow to disengage the evolution of the Psychiatry outside of the anti-psychiatry ideologies. The main subject of this work, is to analyse the gap between the Reality which includes the psychosis as a part of herself (Psychosis as disease). On the second hand the Reality of the psychosis from the psycho-pathologic point of view (delirium, hallucinations, autism, etc...). Considering the importance of the formal grammatical functions in the linguistic matter to site the reference to the reality according to the rules of the communication and the oral expression; so we propose a grammatical analysis. Two parts are distinguishable in this work. The first part concerns a review of languages proposed in different psychiatric "theorization" established previously about mental disorder. So it could be considered that the psychosis is the one who "speaks" the psychiatry. The second part concerns an abstract of the "semiotiques" studies by which we can tackle the psychosis with a scientific language: The Psychiatric "speaking" the psychosis not the opposite. This way of analyse allows to realize the modifications in the part of both protagonists in the game. By the same way, it authorizes to introduce the psychiatry from the axiomatic point of view, allowing a self-contained definition as a branch of the medicine, and disengaging his subject: The psychosis; as a syntactic subject. PMID:7305183
The complete worldsheet S matrix of superstrings on AdS3×S3×T4 with mixed three-form flux
Directory of Open Access Journals (Sweden)
Thomas Lloyd
2015-02-01
Full Text Available We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on AdS3×S3×T4 with mixed R–R and NS–NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R–R theory.
The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
Lloyd, Thomas; Sfondrini, Alessandro; Stefanski, Bogdan
2014-01-01
We determine the off-shell symmetry algebra and representations of Type IIB superstring theory on $AdS_3\\times S^3 \\times T^4$ with mixed R-R and NS-NS three-form flux. We use these to derive the non-perturbative worldsheet S matrix of fundamental excitations of the superstring theory. Our analysis includes both massive and massless modes and shows how turning on mixed three-form flux results in an integrable deformation of the S matrix of the pure R-R theory.
S-matrix approach to the Z resonance
Riemann, T
2016-01-01
The proposed $e^+e^-$-collider FCC-ee aims at an unprecedented accuracy for $e^+e^-$ collisions into fermion pairs at the $Z$ peak, based on about $10^{13}$ events. The S-matrix approach to the $Z$ boson line shape allows the model-independent quantitative description of the reaction $e^+e^- \\to {\\bar f}f$ around the $Z$ peak in terms of few parameters, among them the mass $M_Z$ and width $\\Gamma_Z$ of the $Z$-boson. While weak and strong corrections remain "black", a careful theoretical description of the photonic interactions is mandatory. I introduce the method and describe applications and the analysis tool SMATASY/ZFITTER.
Longitudinal nonlocality in the string S-matrix
Dodelson, Matthew
2015-01-01
We analyze four and five-point tree-level open string S-matrix amplitudes in the Regge limit, exhibiting some basic features which indicate longitudinal nonlocality, as suggested by light cone gauge calculations of string spreading. Using wavepackets to localize the asymptotic states, we compute the peak trajectories followed by the incoming and outgoing strings, determined by the phases in the amplitudes. These trajectories trace back in all dimensions such that the incoming strings deflect directly into corresponding outgoing ones, as expected from a Reggeon analysis. Bremsstrahlung radiation at five points emerges from the deflection point, corroborating this picture. An explicit solution for the intermediate state produced at four points in the $s$-channel exists, with endpoints precisely following the corresponding geometry and a periodicity which matches the series of time delays predicted by the amplitude. We find a nonzero peak impact parameter for this process, and show that it admits an interpretati...
A philosophical assessment of decision theory
DEFF Research Database (Denmark)
Jensen, Karsten Klint
2012-01-01
The significance of decision theory consists of giving an account of rational decision making under circumstances of uncertainty. This question is important both from the point of view of what is in our personal interest and from the point of view of what is ethically right. But decision theory...... is often poorly understood and its significance only sparsely discussed in the literature. In a short history of decision theory, it is demonstrated how modern axiomatic decision theory works differently from classical decision theory, but also how it is confused with it. Further, it is explained how...... modern axiomatic decision theory is an instance of fundamental measurement theory. This is then followed by a thorough introduction to Savage’s version of modern axiomatic decision theory. Turning to the interpretation of the theory, the maxim “maximize expected utility,” which stems from classical...
Axiomatic Local Metric Derivatives for Low-Level Fractionality with Mittag-Leffler Eigenfunctions
Weberszpil, J
2016-01-01
In this contribution, we build up an axiomatic local metric derivative that exhibits the Mittag-Leffler as an eigenfunction and is valid for low-level fractionality, whenever the order parameter is close to $1$. This version of deformed or metric derivative may be a possible alternative to the versions by Jumarie and the inappropriately so-called local fractional derivative also based on the Jumarie's approach. With rules similar to the classical ones, but with a solid axiomatic basis in the limit pointed out here, we present our results and some comments on the limits of validity for the controversial formalism found in the literature of the area.
Decidability of formal theories and hyperincursivity theory
Grappone, Arturo G.
2000-05-01
This paper shows the limits of the Proof Standard Theory (briefly, PST) and gives some ideas of how to build a proof anticipatory theory (briefly, PAT) that has no such limits. Also, this paper considers that Gödel's proof of the undecidability of Principia Mathematica formal theory is not valid for axiomatic theories that use a PAT to build their proofs because the (hyper)incursive functions are self-representable.
S-matrix calculations of energy levels of alkalilike ions
Sapirstein, Jonathan; Cheng, K. T.
2013-05-01
A recent S-matrix based QED calculation of energy levels of the lithium isoelectronic sequence is extended to the general case of a valence electron outside an arbitrary filled core. Formulas are presented that allow calculation of the energy levels of valence ns , np1 / 2 , np3 / 2 , nd3 / 2 , and nd5 / 2 states. Emphasis is placed on modifications of the lithiumlike formulas required because more than one core state is present, and a discussion of an unusual feature of the two-photon exchange contribution involving autoiononizing states is given. The method is illustrated with a calculation of energy levels of the sodium isoelectronic sequence, with results for 3s1 / 2 , 3p1 / 2 , and 3p3 / 2 energies tabulated for the range Z = 20 - 100 . A detailed breakdown of the calculation is given for Z = 74 . Comparison with experiment and other calculations is given, and prospects for extension of the method to ions with more complex electronic structure discussed. The work of JS was supported in part by NSF Grant No. PHY-1068065. The work of KTC was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
The S-matrix of string bound states
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, Gleb [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: g.arutyunov@phys.uu.nl; Frolov, Sergey [School of Mathematics, Trinity College, Dublin 2 (Ireland)], E-mail: frolovs@maths.tcd.ie
2008-11-21
We find the S-matrix which describes the scattering of two-particle bound states of the light-cone string sigma model on AdS{sub 5}xS{sup 5}. We realize the M-particle bound state representation of the centrally extended su(2|2) algebra on the space of homogeneous (super)symmetric polynomials of degree M depending on two bosonic and two fermionic variables. The scattering matrix S{sup MN} of M- and N-particle bound states is a differential operator of degree M+N acting on the product of the corresponding polynomials. We require this operator to obey the invariance condition and the Yang-Baxter equation, and we determine it for the two cases M=1,N=2 and M=N=2. We show that the S-matrices found satisfy generalized physical unitarity, CPT invariance, parity transformation rule and crossing symmetry. Although the dressing factor as a function of four parameters x{sub 1}{sup +},x{sub 1}{sup -},x{sub 2}{sup +},x{sub 2}{sup -} is universal for scattering of any bound states, it obeys a crossing symmetry equation which depends on M and N.
The S-matrix of String Bound States
Arutyunov, Gleb
2008-01-01
We find the S-matrix which describes the scattering of two-particle bound states of the light-cone string sigma model on AdS5xS5. We realize the M-particle bound state representation of the centrally extended su(2|2) algebra on the space of homogeneous (super)symmetric polynomials of degree M depending on two bosonic and two fermionic variables. The scattering matrix S^{MN} of M- and N-particle bound states is a differential operator of degree M+N acting on the product of the corresponding polynomials. We require this operator to obey the invariance condition and the Yang-Baxter equation, and we determine it for the two cases M=1,N=2 and M=N=2. We show that the S-matrices found satisfy generalized physical unitarity, CPT invariance, parity transformation rule and crossing symmetry. Although the dressing factor as a function of four parameters x_1^+,x_1^-,x_2^+,x_2^- is universal for scattering of any bound states, it obeys a crossing symmetry equation which depends on M and N.
New symmetries for the Gravitational S-matrix
Campiglia, Miguel
2015-01-01
In [15] we proposed a generalization of the BMS group G which is a semidirect product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S^2) charges which we could not derive from first principles as G does not have a well defined action on the radiative phase space of gravity. Here we fill this gap and provide a first principles derivation of the Diff(S^2) charges. The result of this paper, in conjunction with the results of [4, 15] prove that the leading and subleading soft theorems are equivalent to the Ward identities associated to G.
The S-matrix Bootstrap I: QFT in AdS
Paulos, Miguel F; Toledo, Jonathan; van Rees, Balt C; Vieira, Pedro
2016-01-01
We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.
The bound state S-matrix for AdS{sub 5}xS{sup 5} superstring
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, G. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: g.e.arutyunov@uu.nl; Leeuw, M. de [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: m.deleeuw@uu.nl; Torrielli, A. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: a.torrielli@uu.nl
2009-10-01
We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in AdS{sub 5}xS{sup 5}. The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function {sub 4}F{sub 3}. We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Luescher approaches to the finite-size spectral problem. They also shed some light on the construction of the universal R-matrix for the centrally-extended psu(2|2) superalgebra.
Applying the V Model and Axiomatic Design in the Domain of IT Architecture Practice
Tarenskeen, Debbie; Bakker, René; Joosten, Stef
2015-01-01
This paper applies and discusses the principles of Axiomatic Design for changing IT architecture in health care. It presents three case studies positioned in the field of Enterprise architecture that explore how IT architects, as professionals, manage change and re-design the structure of the IT sys
Nickerson, Carol A.; McClelland, Gary H.
1988-01-01
A methodology is developed based on axiomatic conjoint measurement to accompany a fertility decision-making model. The usefulness of the model is then demonstrated via an application to a study of contraceptive choice (N=100 male and female family-planning clinic clients). Finally, the validity of the model is evaluated. (TJH)
International Nuclear Information System (INIS)
The relativistic second-order S-matrix elements for photon-atom scattering have been successfully calculated with numerical methods within the independent particle approximation (IPA). This permits an assessment of the validity of simpler approximate predictions which are commonly used and it offers the possibility of improved tabulations of theoretical predictions. A variety of unresolved issues remain, some associated with the relativistic theory, some with IPA. The systematic use of the second-order S-matrix in calculations of Rayleigh scattering from isolated atoms has led to significant progress in understanding this process and to a wide range of agreement with experiment. The energy and angular dependence of anomalous factors and the importance of relativistic, higher-multipole and bound-bound contributions in their calculation is better understood. However correlation effects must also be included to obtain predictions for the near-edge region, such extensions of the present S-matrix calculation have been discussed but few results are sofar available. Existing empirical approaches can be assessed in regard to their success in dealing with known IPA features. We have recently calculated the relativistic second-order S-matrix element for Compton scattering and have begun to try to understand this process in different regions. We can discuss when the more complete calculation confirms the standard Compton peak. In the softer part of the spectrum impulse approximation fails. There can be resonant Raman peaks, and in the soft-photon region the spectrum is infrared divergent, proportional to the photoeffect angular distribution. This means the traditional incoherent scattering factor is undefined in the absence of a low-energy detector efficiency cutoff
Logical frameworks for truth and abstraction an axiomatic study
Cantini, A
1996-01-01
This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential. These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these theories provide a new outlook on classical
Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
Hoare, Ben; Miramontes, J Luis
2012-01-01
The investigation of the q deformation of the S-matrix for excitations on the string world sheet in AdS5 x S5 is continued. We argue that due to the lack of Lorentz invariance the situation is more subtle than in a relativistic theory in that the nature of bound states depends on their momentum. At low enough momentum |p|1. This subtlety fixes a problem involving the consistency of crossing symmetry with the relativistic limit found in earlier work. With mirror kinematics, obtained after a double Wick rotation, the bound state structure is simpler and there are no marginally unstable bound states.
Tian, Jianhui; Porter, Adam; Zelkowitz, Marvin V.
1992-01-01
Identification of high cost modules has been viewed as one mechanism to improve overall system reliability, since such modules tend to produce more than their share of problems. A decision tree model was used to identify such modules. In this current paper, a previously developed axiomatic model of program complexity is merged with the previously developed decision tree process for an improvement in the ability to identify such modules. This improvement was tested using data from the NASA Software Engineering Laboratory.
Geometrical exposition of structural axiomatic economics (II): qualitative and temporal aggregation
Kakarot-Handtke, Egmont
2011-01-01
Behavioral assumptions are not solid enough to be eligible as first principles of theoretical economics. Hence all endeavors to lay the formal foundation on a new site and at a deeper level actually need no further vindication. Part (I) of the structural axiomatic analysis submits three nonbehavioral axioms as groundwork and applies them to the simplest possible case of the pure consumption economy. The geometrical analysis makes the interrelations between income, profit and...
An Incentive-Compatible Scheme for Electricity Cooperatives: An Axiomatic Approach
Ehsanfar, Abbas; Heydari, Babak
2016-01-01
This paper introduces a new scheme for autonomous electricity cooperatives, called predictive cooperative (PCP), which aggregates commercial and residential electricity consumers and participates in the electricity market on behalf of its members. An axiomatic approach is proposed to calculate the day-ahead bid and to disaggregate the collective cost among participating consumers. The resulting formulation is shown to keep the members incentivized to both participate in the cooperative and re...
A new axiomatic approach to the evaluation of population health
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Moreno-Ternero, Juan D.; Østerdal, Lars Peter Raahave
2013-01-01
represent social preferences, as a result of combinations of those axioms. Our results provide new rationale for popular theories in health economics, such as the unweighted aggregation of quality-adjusted life years (QALYs) or healthy years equivalents (HYEs) and generalizations of the two, aimed...... to capture concerns for distributive justice, without resorting to controversial assumptions on individual preferences....
A new axiomatic approach to the evaluation of population health
DEFF Research Database (Denmark)
Hougaard, Jens Leth; Moreno-Ternero, Juan D.; Østerdal, Lars Peter Raahave
functions, which represent social preferences, as a result of combinations of those axioms. Our results provide rationale for popular theories in health economics (such as the unweighted aggregation of QALYs or HYEs, and generalizations of the two, aimed to capture concerns for distributive justice) without...
Consistency and axiomatization of a natural extensional combinatory logic
Institute of Scientific and Technical Information of China (English)
蒋颖
1996-01-01
In the light of a question of J. L. Krivine about the consistency of an extensional λ-theory,an extensional combinatory logic ECL+U(G)+RU_∞+ is established, with its consistency model provedtheoretically and it is shown the it is not equivalent to any system of universal axioms. It is expressed bythe theory in first order logic that, for every given group G of order n, there simultaneously exist infinitelymany universal retractions and a surjective n-tuple notion, such that each element of G acts as a permutationof the components of the n-tuple, and as an Ap-automorphism of the model; further each of the universalretractions is invarian under the action of the Ap-automorphisms induced by G The difference between thetheory and that of Krivine is the G need not be a symmetric group.
The one-loop worldsheet S-matrix for the AdS(n) x S(n) x T(10-2n) superstring
Roiban, Radu; Tseytlin, Arkady; Wulff, Linus
2014-01-01
We compute the massive-sector worldsheet S-matrix for superstring theories in AdS(n) x S(n) x T(10-2n) (with n=2,3,5) in the near BMN expansion up to one-loop order in inverse string tension. We show that, after taking into account the wave function renormalization, the one-loop S-matrix is UV finite. In an appropriate regularization scheme the S-matrix is consistent with the underlying symmetries of the superstring theory, i.e. for the n=3,5 cases it coincides with the one implied by the light-cone gauge symmetries with the dressing phases determined from the crossing equations. For the n=2,3 cases we observe that the massless modes decouple from the one-loop calculation of massive mode scattering, i.e. the 2n-dimensional supercoset sigma model and the full 10-dimensional superstring happen to have the same massive one-loop S-matrix.
Borsato, Riccardo; Sfondrini, Alessandro; Stefański, Bogdan
2015-01-01
We investigate type IIB strings on $\\mathrm{AdS}_3\\times \\mathrm{S}^3\\times \\mathrm{S}^3\\times\\mathrm{S}^1$ with mixed Ramond-Ramond (R-R) and Neveu-Schwarz-Neveu-Schwarz (NS-NS) flux. By suitably gauge-fixing the closed string Green-Schwarz (GS) action of this theory, we derive the off-shell symmetry algebra and its representations. We use these to determine the non-perturbative worldsheet S-matrix of fundamental excitations in the theory. The analysis involves both massive and massless modes in complete generality. The S-matrix we find involves a number of phase factors, which in turn satisfy crossing equations that we also determine. We comment on the nature of the heaviest modes of the theory, but leave their identification either as composites or bound-states to a future investigation.
A Formal Axiomatization for Alphabet Reasoning with Parametrized Processes
Korver, H.
2008-01-01
In the process-algebraic verification of systems with three or more components put in parallel, alphabet axioms are considered to be very useful. These are rules that exploit the information about the alphabets of the processes involved. The alphabet of a process is the set of actions it can perform. In this paper, we extend μCRL (a formal proof system for ACP + data) with such axioms. The alphabet axioms that are added to the proof theory are completely formal and therefore highly suited for...
基于公理设计的集成模型及其应用%Axiomatic-design-based hybrid model for conceptual engineering design
Institute of Scientific and Technical Information of China (English)
刘刚; 卢耀祖; 田晋跃; 张氢
2007-01-01
提出了一种基于公理设计(axiomatic design,AD)理论与发明问题解决理论(theory of inventive problem solving,TRIZ)的集成模型.公理设计的优势在于流程分解,TRIZ的优势在于冲突解决.通过集成获得无耦合或解耦设计的创新方案,再比较方案的信息量,优选最佳方案.废旧沥青混合料加热装置设计的应用实例说明,所提出的方法能有效指导工程机械产品的方案设计.
Bates, David Robert
1962-01-01
Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postula
The Notion "Pathology" in Set Theory
DePauli-Schimanovich, Werner
2008-01-01
When we study the paradoxes of set theory we find out that there are mainly 2 types: the pathologies and the antinomies. These 2 notions are made precise and compared with the somehow inductively definable concept "abnormal". (See my paper "Naive Axiomatic Mengenlehre for Experiments" in arXiv.) In the following 5 Patho Theses are discussed in order to formalize this notion of pathology. This allows us to define formally the property "Hereditary-non-Pathological" for well-formed formulas. With this property the system NACT* of Naive Axiomatic Class Theory is constructed, which has a "unique maximal" universe (in a special sense).
Institute of Scientific and Technical Information of China (English)
樊兴菊; 李海涛; 陈通
2016-01-01
In order to identify and research the contradiction and conflicts existing in public cultural facili-ties management , TRIZ innovation tools and Axiomatic Design theory together are combined as a research method.Firstly, the contradiction between public demand and practical constraints are explored and ana -lyzed using Independent Axiom derived from Axiomatic Design theory .Secondly , the possible solution sets to previous contradiction are found through TRIZ method based on technical parameters of public cultural facilities management system , and then the optional schemes are evaluated and selected according to Infor-mation Axiom also from Axiomatic Design theory .Finally, the actual problems to Cultural Center of Tianjin City such as high vacancy rate of the gallery and low space utilization rate of the library are effectively re-solved .The combination of TRIZ and Axiomatic Design could effectively remedy the limitation of the TRIZ theory on finding the optimal solution , and provide a new thought on conflict management innovation of public cultural service facilities .%为了识别和研究公共文化设施管理中存在的矛盾冲突，把TRIZ创新工具和公理设计理论相结合，利用独立公理分解公众需求和现实约束之间的矛盾，再使用基于公共文化设施技术参数的TRIZ工具寻找解集，依据信息公理对可选方案进行评价筛选，有效解决了天津文化中心美术馆空置率高、图书馆空间利用率低等实际问题。该方法有效弥补了TRIZ理论在寻找最优解时低效的缺陷，为公共文化设施冲突管理提供了新的思路。
An Axiomatic Approach to Increase End-of-Life Recovery Profit
Directory of Open Access Journals (Sweden)
Guang Beng Lee
2015-10-01
Full Text Available This paper aims at examining the feasibility of using Axiomatic Design (AD for the purpose of increasing end-of-life (EOL recovery profit of a product. A case study that involves keypad assemblies of a mobile phone is presented to demonstrate the usage of AD in this area. Product recovery considerations are only involved in the second part of the case study. As a result, two different handset assemblies are produced. An evaluation of design was performed to determine the approximate EOL recovery profit by utilizing a methodology presented by Kwak et al. (2010. This is followed by a verification of evaluation results using multiple service action (MSA algorithm proposed by S.W. Lye et al. (2000. Both evaluation approaches yield identical and conclusive results: when recovery-related requirements are omitted, application of AD produces a keypad assembly that fulfills the functional requirements derived from customer needs but a more complicated product network is obtained. In contrast, when recovery-related requirements are included during problem definition using axiomatic approach, the disassemblability of the resulted keypad is improved and thus increasing recovery potential in the event of replacing defective keypad, while satisfying product-related requirements.
An MEG signature corresponding to an axiomatic model of reward prediction error.
Talmi, Deborah; Fuentemilla, Lluis; Litvak, Vladimir; Duzel, Emrah; Dolan, Raymond J
2012-01-01
Optimal decision-making is guided by evaluating the outcomes of previous decisions. Prediction errors are theoretical teaching signals which integrate two features of an outcome: its inherent value and prior expectation of its occurrence. To uncover the magnetic signature of prediction errors in the human brain we acquired magnetoencephalographic (MEG) data while participants performed a gambling task. Our primary objective was to use formal criteria, based upon an axiomatic model (Caplin and Dean, 2008a), to determine the presence and timing profile of MEG signals that express prediction errors. We report analyses at the sensor level, implemented in SPM8, time locked to outcome onset. We identified, for the first time, a MEG signature of prediction error, which emerged approximately 320 ms after an outcome and expressed as an interaction between outcome valence and probability. This signal followed earlier, separate signals for outcome valence and probability, which emerged approximately 200 ms after an outcome. Strikingly, the time course of the prediction error signal, as well as the early valence signal, resembled the Feedback-Related Negativity (FRN). In simultaneously acquired EEG data we obtained a robust FRN, but the win and loss signals that comprised this difference wave did not comply with the axiomatic model. Our findings motivate an explicit examination of the critical issue of timing embodied in computational models of prediction errors as seen in human electrophysiological data.
Dynamic Order Algebras as an Axiomatization of Modal and Tense Logics
Chajda, Ivan; Paseka, Jan
2015-12-01
The aim of the paper is to introduce and describe tense operators in every propositional logic which is axiomatized by means of an algebra whose underlying structure is a bounded poset or even a lattice. We introduce the operators G, H, P and F without regard what propositional connectives the logic includes. For this we use the axiomatization of universal quantifiers as a starting point and we modify these axioms for our reasons. At first, we show that the operators can be recognized as modal operators and we study the pairs ( P, G) as the so-called dynamic order pairs. Further, we get constructions of these operators in the corresponding algebra provided a time frame is given. Moreover, we solve the problem of finding a time frame in the case when the tense operators are given. In particular, any tense algebra is representable in its Dedekind-MacNeille completion. Our approach is fully general, we do not relay on the logic under consideration and hence it is applicable in all the up to now known cases.
Directory of Open Access Journals (Sweden)
Deljavan R
2012-07-01
Full Text Available Reza Deljavan,1 Homayoun Sadeghi-Bazarganim,2,3 Nasrin Fouladim,4 Shahnam Arshi,5 Reza Mohammadi61Injury Epidemiology and Prevention Research Center, 2Neuroscience Research Center, Department of Statistics and Epidemiology, Tabriz University of Medical Sciences, Tabriz, Iran; 3Public Health Department, Karolinska Institute, Stockholm, Sweden; 4Ardabil University of Medical Sciences, Ardabil, Iran; 5Shahid Beheshti University of Medical Sciences, Tehran, Iran; 6Public Health Department, Karolinska Institute, Stockholm, SwedenBackground: Little has been done to investigate the application of injury specific qualitative research methods in the field of burn injuries. The aim of this study was to use an analytical tool (Haddon’s matrix through qualitative research methods to better understand people’s perceptions about burn injuries.Methods: This study applied Haddon’s matrix as a framework and an analytical tool for a qualitative research methodology in burn research. Both child and adult burn injury victims were enrolled into a qualitative study conducted using focus group discussion. Haddon’s matrix was used to develop an interview guide and also through the analysis phase.Results: The main analysis clusters were pre-event level/human (including risky behaviors, belief and cultural factors, and knowledge and education, pre-event level/object, pre-event phase/environment and event and post-event phase (including fire control, emergency scald and burn wound management, traditional remedies, medical consultation, and severity indicators. This research gave rise to results that are possibly useful both for future injury research and for designing burn injury prevention plans.Conclusion: Haddon’s matrix is applicable in a qualitative research methodology both at data collection and data analysis phases. The study using Haddon’s matrix through a qualitative research methodology yielded substantially rich information regarding burn injuries
S-matrix theory for transmission through billiards in tight-binding approach
Sadreev, A F; Sadreev, Almas F.; Rotter, Ingrid
2003-01-01
In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittes we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the energy restriction of the conductance band. The complex eigenvalues of the effective Hamiltonian define the poles of the scattering matrix. For some simple cases, we present exact values for the poles. We derive also the condition for the appearance of double poles.
S-matrix theory for transmission through billiards in tight-binding approach
International Nuclear Information System (INIS)
In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittes we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the energy restriction of the conductance band. The complex eigenvalues of the effective Hamiltonian define the poles of the scattering matrix. For some simple cases, we present exact values for the poles. We derive also the condition for the appearance of double poles
Constructor Theory of Thermodynamics
Marletto, Chiara
2016-01-01
The laws of thermodynamics, powerful for countless purposes, are not exact: both their phenomenological and their statistical-mechanical versions are valid only at 'macroscopic scales', which are never defined. Here I propose a new, exact and scale-independent formulation of the first and second laws of thermodynamics, using the principles and tools of the recently proposed constructor theory. Specifically, I improve upon the axiomatic formulations of thermodynamics (Carath\\'eodory, 1909; Lieb and Yngvason, 1999) by proposing an exact and more general formulation of 'adiabatic accessibility'. This work provides an exact distinction between work and heat; it reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second); it resolves the clash between the irreversibility of the 'cycle'-based second law and time-reversal symmetric dynamical laws. It also achieves the long-sought unification of the axiomatic version of the second law with Kelvin's.
Naive Axiomatic Class Theory: A Solution for the Antinomies of Naive Mengenlehre
DePauli-Schimanovich, Werner
2008-01-01
Since the axioms in (Consi-CoS) are not recursively enumerable, NACT* is no axiom system in the classical sense . Therefore we construct a series of partial systems which form a recursive axiom system too. Starting with the "dichotomic" systems NACT# and its variant NACT#4, we are going on to the "disjunctive" systems NACT+ and NACT+4, and eventually to NACT+Strat. After that we discuss the medium classes of these systems. Finally we present the inconsistent NSA-systems based on Not-SelfAppli...
Liu, Baoding
2015-01-01
When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case. In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees. This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, c...
Hamiltonian Truncation Study of Supersymmetric Quantum Mechanics: S-Matrix and Metastable States
Balthazar, Bruno; Yin, Xi
2016-01-01
We implement the Rayleigh-Ritz method in supersymmetric quantum mechanics with flat directions, and extract the S-matrix and metastable resonances. The effectiveness of the method is demonstrated in two strongly coupled systems: an N=1 toy supermembrane model, and an N=4 model with a U(1) gauge multiplet and a charged chiral multiplet.
RNS derivation of N-point disk amplitudes from the revisited S-matrix approach
Directory of Open Access Journals (Sweden)
Luiz Antonio Barreiro
2014-09-01
Full Text Available Recently, in [7] we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL. This approach allows to compute the α′N terms of the OSLEEL using open superstring n-point amplitudes in which n is considerably lower than (N+2 (which is the order of the required amplitude to obtain those α′N terms by means of the conventional S-matrix approach. In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger [21], using the pure spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4,5,6 and 7. Also, following the spirit of the revisited S-matrix approach, we have found the α′ expansions for these amplitudes up to α′6 order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.
Bessel equation as an operator identity's matrix element in quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Fan Hongyi; Li Chao
2004-05-17
We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented.
RNS derivation of N-point disk amplitudes from the revisited S-matrix approach
Energy Technology Data Exchange (ETDEWEB)
Barreiro, Luiz Antonio, E-mail: luiz.a.barreiro@gmail.com [Departamento de Física, UNESP, Rio Claro, São Paulo (Brazil); Instituto de Matemática e Computação, Universidade Federal de Itajubá, Itajubá, Minas Gerais (Brazil); Medina, Ricardo, E-mail: rmedina50@gmail.com [Instituto de Matemática e Computação, Universidade Federal de Itajubá, Itajubá, Minas Gerais (Brazil)
2014-09-15
Recently, in [7] we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the α{sup ′N} terms of the OSLEEL using open superstring n-point amplitudes in which n is considerably lower than (N+2) (which is the order of the required amplitude to obtain those α{sup ′N} terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger [21], using the pure spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4,5,6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the α{sup ′} expansions for these amplitudes up to α{sup ′6} order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.
Woltzenlogel Paleo, Bruno
2010-01-01
Axiomatization of Physics (and Science in general) has many drawbacks that are correctly criticized by opposing philosophical views of Science. This paper shows that, by giving formal proofs a more promi- nent role in the formalization, many of the drawbacks can be solved and many of the opposing views are naturally conciliated. Moreover, this ap- proach allows, by means of Proof Theory, to open new conceptual bridges between the disciplines of Physics and Computer Science.
An Axiomatic Analysis Approach for Large-Scale Disaster-Tolerant Systems Modeling
Directory of Open Access Journals (Sweden)
Theodore W. Manikas
2011-02-01
Full Text Available Disaster tolerance in computing and communications systems refers to the ability to maintain a degree of functionality throughout the occurrence of a disaster. We accomplish the incorporation of disaster tolerance within a system by simulating various threats to the system operation and identifying areas for system redesign. Unfortunately, extremely large systems are not amenable to comprehensive simulation studies due to the large computational complexity requirements. To address this limitation, an axiomatic approach that decomposes a large-scale system into smaller subsystems is developed that allows the subsystems to be independently modeled. This approach is implemented using a data communications network system example. The results indicate that the decomposition approach produces simulation responses that are similar to the full system approach, but with greatly reduced simulation time.
Conditional Independence in Uncertainty Theories
Shenoy, Prakash P.
2013-01-01
This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and conditional independence in terms of factorization of the joint valuation. The definitions of independence and conditional independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but al...
On AdS{sub 5}xS{sup 5} string S-matrix
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, G. [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)]. E-mail: g.arutyunov@phys.uu.nl; Frolov, S. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany)]. E-mail: frolovs@aei.mpg.de
2006-08-10
Recently two interesting conjectures about the string S-matrix on AdS{sub 5}xS{sup 5} have been made. First, assuming the existence of a Hopf algebra symmetry Janik derived a functional equation for the dressing factor of the quantum string Bethe ansatz. Second, Hernandez and Lopez proposed an explicit form of 1/{lambda} correction to the dressing factor. In this Letter we show that in the strong coupling expansion Janik's equation is solved by the dressing factor up to the order of its validity. This observation provides a strong evidence in favor of a conjectured Hopf algebra symmetry for strings in AdS{sub 5}xS{sup 5} as well as the perturbative string S-matrix.
Influence of the absorptive part of the complex potential on the S-matrix poles
International Nuclear Information System (INIS)
A global method for all S-matrix poles analysis is used for non-relativistic scattering by a central rectangular potential V(r)=g V(r), with g of C . The pole function k=kl(g) is analysed by constructing the Riemann surface over the g-plane, on which k=kl(g) is a single valued and analytic function. A new class of poles is identified. The effect of the imaginary part of the potential on the S-matrix poles belonging to the old and new class of poles is clarified. Occurrence of the Σ-hypernuclear state poles as a function of the potential absorption is discussed. (authors)
S matrix approach to two pion production in e+ e- annihilation and tau decay
Bernicha, A.; Lopez Castro, G.; Pestieau, Jean
1995-01-01
Based on the S-matrix approach, we introduce a modified formula for the $\\pi^{\\pm}$ electromagnetic form factor which describes very well the experimental data in the energy region $2m_{\\pi} \\leq \\sqrt{s} \\leq 1.1$ GeV. Using the CVC hypothesis we predict $B(\\tpp) = (24.75 \\pm 0.38)\\% $, in excellent agreement with recent experiments. Comment: Latex, 10 pages, submitted to Phys. Rev. D
Gauge dependence of world lines and invariance of the S-matrix in relativistic classical mechanics
International Nuclear Information System (INIS)
The notion of world lines is studied in the constraint Hamiltonian formulation of relativistic point particle dynamics. The particle world lines are shown to depend in general (in the presence of interaction) on the choice of the equal-time hyperplane (the only exception being the elastic scattering of rigid balls). However, the relative motion of a two-particle system and the (classical) S-matrix are indepent of this choice. (author)
A Logical Framework for Set Theories
Directory of Open Access Journals (Sweden)
Arnon Avron
2012-03-01
Full Text Available Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for Mathematical Knowledge Management. However, in order to be used for this task it is necessary to overcome serious gaps that exist between the "official" formulations of set theory (as given e.g. by formal set theory ZF and actual mathematical practice. In this work we present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF. It allows the use of set terms, but provides a static check of their validity.
Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory
Andréka, H
2013-01-01
There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.
Willard, Dan E.
2006-01-01
Gödel’s Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show that axiomatizations for a computer’s floating point arithmetic can recognize their cut-free consistency in a stronger respect than is feasible under integer arithmetics. This paper will include both new generalizations of the Second Incompleteness Theorem and techniques for evading it.
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The basic ideas of game theory were originated from the problems of maximum and minimum given by J.Yon Neumann in 1928. Later, wars accelerated the study of game theory, there are many developments that contributed to the advancement of game theory, many problems of optimum appeared in economic development process. Scientists applied mathematic methods to studying game theory to make the theory more profound and perfect. The axiomatic structure of game theory was nearly complete in 1944. The path of the development of game theory started from finite to infinite, from two players to many players, from expressing gains with quantity to showing the ending of game theory with abstract result, and from certainty problems to random problems. Thus development of game theory is closely related to the economic development. In recent years, the research on the non-differentiability of Shapley value posed by Belgian Mertens is one of the advanced studies in game theory.
Self-organized evolution of mechanism kinetic scheme based on axiomatic design
Institute of Scientific and Technical Information of China (English)
Feng Yixiong; Tan Jianrong; Wei Zhe; Hao He
2007-01-01
The self-organized evolution technology of the mechanism kinetic scheme based on axiomatic design is presented.This technology tries to express the constraints between kinetic mechanisms briefly in a semantic form which is more familiar to the designers.Though the mapping process between the kinetic chain unit and the unit instance,the evolution from abstract unit to concrete engineering instance is achieved.The subdivision of unit coupling semantics is studied.and the evolution of semantics is finished.Also.the semantic constraints evolution of unit coupling semantics is described.The product structure models with function and assembly meanings are constructed based on the kinematic chain unit and unit coupling.It provides a basis to realize the inheritance and transfer of constraint information from conceptual design to design for assembly(DFA).As the engineering practice result shows,the method Can help the engineers express their design intension more clearly and naturally in a high semantic level.And the automation,recursion and visualization of the mechanism kinetic scheme design are realized.
Analytic structure of the S-matrix for singular quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, California 94117-1080 (United States); Epele, Luis N.; Fanchiotti, Huner; García Canal, Carlos A. [Laboratorio de Física Teórica, Departamento de Física, IFLP, CONICET, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67–1900 La Plata (Argentina)
2015-06-15
The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter (Ω) that determines the boundary conditions. Specifically, a characterization is given in terms of salient mathematical and physical properties governing its behavior. These properties involve unitarity and associated current-conserving Wronskian relations, time-reversal invariance, and Blaschke factorization. The approach leads to an interpretation of effective nonunitary solutions in singular quantum mechanics and their determination from the unitary family.
Irgaziev, B F
2014-01-01
We derive a useful relationship between the asymptotic normalization coefficient (ANC) of the Gamov radial wave function and the renormalized partial scattering amplitude. We use an analytical approximation in the form of a series for the non-resonant part of the phase shift which can be analytically continued to the point of an isolated resonance pole in the complex plane of the momentum. We find the corresponding fitting parameters for the $^5\\rm{He},\\,^5\\rm{Li}$ and $^{16}\\rm{O}$ concrete resonance states. Additionally, based on the theory of the effective range, we calculate the parameters of the $p_{3/2}$ and $p_{1/2}$ resonance states of the nuclei $^5\\rm{He}$ and $^5\\rm{Li}$ and compare them with the results obtained by the $S$-matrix pole method. ANC values are found which can be used to calculate the reaction rate through the $^{16}\\rm{O}$ resonances which lie slightly above the threshold for the $\\alpha^{12}\\rm{C}$ channel. Reactions of such type are interesting for nuclear astrophysics.
Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor
Energy Technology Data Exchange (ETDEWEB)
Saadi, Y., E-mail: S_yahiadz@yahoo.fr [Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 (Algeria); Maamache, M. [Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000 (Algeria)
2012-03-19
We present a complete derivation of the exact evolution of quantum mechanics for the case when the underlying spectrum is continuous. We base our discussion on the use of the Weyl eigendifferentials. We show that a quantum system being in an eigenstate of an invariant will remain in the subspace generated by the eigenstates of the invariant, thereby acquiring a generalized non-adiabatic or Aharonov–Anandan geometric phase linked to the diagonal element of the S matrix. The modified Pöschl–Teller potential and the time-dependent linear potential are worked out as illustrations. -- Highlights: ► In this Letter we study the exact quantum evolution for continuous spectra problems. ► We base our discussion on the use of the Weyl eigendifferentials. ► We give a generalized Lewis and Riesenfeld phase for continuous spectra. ► This generalized phase or Aharonov–Anandan geometric phase is linked to the S matrix. ► The modified Pöschl–Teller and the linear potential are worked out as illustrations.
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Toposes in General Theory of Relativity
Guts, Alexandr K.; Grinkevich, Egor B.
1996-01-01
We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein theory of space-time. This is a new theory of space-time, created in a purely logical manner. Four possibitities are investigated: axiomatic approach to causal theory of space-time, the smooth toposes as a models of Theory of Relativity, Synthetic Theory of ...
Pinter, Charles C
2014-01-01
Suitable for upper-level undergraduates, this accessible approach to set theory poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and
Subjective expected utility theory without states of the world
Karni, Edi
2005-01-01
This paper develops an axiomatic theory of decision making under uncertainty that dispenses with the state space. The results are subjective expected utility models with unique, action-dependent, subjective probabilities, and a utility function defined over wealth-effect pairs that is unique up to positive linear transformation.
The logical foundations of scientific theories languages, structures, and models
Krause, Decio
2016-01-01
This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicate...
Van Dalen, D; De Swart, H; Sneddon, I N
1978-01-01
Sets: Naïve, Axiomatic and Applied is a basic compendium on naïve, axiomatic, and applied set theory and covers topics ranging from Boolean operations to union, intersection, and relative complement as well as the reflection principle, measurable cardinals, and models of set theory. Applications of the axiom of choice are also discussed, along with infinite games and the axiom of determinateness.Comprised of three chapters, this volume begins with an overview of naïve set theory and some important sets and notations. The equality of sets, subsets, and ordered pairs are considered, together wit
Study on the New Axiomatic Method Giving the Solutions of Hilbert’s 2nd and 6th Problems
Ito, Yoshifumi
2010-01-01
In this paper, we propose the new axiomatic method completely different from old ones. Thereby we succeeded in giving the definition of the concept of natural number and solving the problem of its existence. This is the complete solution of Hilbert’s second problem. As for this, see Ito [4], [24]. Further we give the complete solution of Hilbert’s 6th problem concerning the natural statistical physics. As for this, see Ito [1]~[3], [5]~[23], [25], [26]. These solutions...
On the energy-momentum current of the electromagnetic field in a pre-metric axiomatic approach, 1
Hehl, F W; Hehl, Friedrich W.; Obukhov, Yuri N.
2001-01-01
We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Sigma of the electromagnetic field. We start from the Lorentz force density and motivate the form of Sigma. Then we postulate it (fourth axiom) and discuss its properties. In particular, it is found that Sigma is traceless and invariant under an electric-magnetic reciprocity transformation. By using the Maxwell-Lorentz spacetime relation (fifth axiom), Sigma is also shown to be symmetric, that is, it has 9 independent components
Manthe, Uwe; Ellerbrock, Roman
2016-05-28
A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail. PMID:27250291
Manthe, Uwe; Ellerbrock, Roman
2016-05-01
A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail.
The Notion "Pathology" in Set Theory
DePauli-Schimanovich, Werner
2008-01-01
When we study the paradoxes of set theory we find out that there are mainly 2 types: the pathologies and the antinomies. These 2 notions are made precise and compared with the somehow inductively definable concept "abnormal". (See my paper "Naive Axiomatic Mengenlehre for Experiments" in arXiv.) In the following 5 Patho Theses are discussed in order to formalize this notion of pathology. This allows us to define formally the property "Hereditary-non-Pathological" for well-formed formulas. Wit...
Nondemolition Principle of Quantum Measurement Theory
Belavkin, V.P.
2005-01-01
We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The "collapsed state-vector" after the "objectification" is simply treated as a random vector of the a posteriori state given by the quantum filtering, i.e., the conditioning of the a priori induced state on the corresponding reduced ...
S-matrix for strings on η-deformed AdS5×S5
International Nuclear Information System (INIS)
We determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS5×S5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...
Haag's theorem in renormalised quantum field theories
Klaczynski, Lutz
2016-01-01
We review a package of no-go results in axiomatic quantum field theory with Haag's theorem at its centre. Since the concept of operator-valued distributions in this framework comes very close to what we believe canonical quantum fields are about, these results are of consequence to quantum field theory: they suggest the seeming absurdity that this highly victorious theory is incapable of describing interactions. We single out unitarity of the interaction picture's intertwiner as the most salient provision of Haag's theorem and critique canonical perturbation theory to argue that renormalisation bypasses Haag's theorem by violating this very assumption.
Székely, Gergely
2012-01-01
Within an axiomatic framework of kinematics, we prove that the existence of faster than light particles is logically independent of Einstein's special theory of relativity. Consequently, it is consistent with the kinematics of special relativity that there might be faster than light particles.
Rough Set Theory over Fuzzy Lattices
Institute of Scientific and Technical Information of China (English)
Guilong Liu
2006-01-01
Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of roug h sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set, and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices, respectively, based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak's rough sets and fuzzy rough sets.
Problematic aspects of string theories and their possible resolution
Santilli, R M
1999-01-01
We identify new, rather serious, physical and axiomatic inconsistencies of the current formulation of string theories due to the lack of invariant units necessary for measurements, lack of preservation in time of Hermiticity-observability, and other shortcomings. We propose three novel reformulations of string theories for {\\it matter} of progressively increasing complexity via the novel iso-, geno- and hyper-mathematics of hadronic mechanics, which resolve the current inconsistencies, while offering new intriguing possibilities, such as: an axiomatically consistent and invariant formulation on curved manifolds, the reduction of macroscopic irreversibility to the most primitive level of vibrations of the universal substratum (ether), or the treatment of multi-valued biological structures. We then identify three corresponding {\\it classical} formulations of string theories for {\\it antimatter} via the novel anti-isomorphic isodual mathematics. We finally outline the intriguing features of the emerging new cosm...
Mizuta, Hiroshi
1998-01-01
This paper presents a numerical study of single-electron resonant tunnelling (RT) assisted by a few ionised donors in a laterally-confined resonant tunnelling diode (LCRTD). The 3D multi-mode S-matrix simulation is performed newly introducing the scattering potential of discrete impurities. With a few ionised donors being placed, the calculated energy-dependence of the total transmission rate shows new resonances which are donor-configuration dependent. Visualised electron probability density...
Hiroshi Mizuta
1998-01-01
This paper presents a numerical study of single-electron resonant tunnelling (RT) assisted by a few ionised donors in a laterally-confined resonant tunnelling diode (LCRTD). The 3D multi-mode S-matrix simulation is performed newly introducing the scattering potential of discrete impurities. With a few ionised donors being placed, the calculated energy-dependence of the total transmission rate shows new resonances which are donor-configuration dependent. Visualised electron prob...
S-matrix for strings on η-deformed AdS{sub 5}×S{sup 5}
Energy Technology Data Exchange (ETDEWEB)
Arutyunov, Gleb; Borsato, Riccardo [Institute for Theoretical Physics and Spinoza Institute, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Frolov, Sergey [Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin (Germany); Hamilton Mathematics Institute and School of Mathematics,Trinity College, Dublin 2 (Ireland)
2014-04-01
We determine the bosonic part of the superstring sigma model Lagrangian on η-deformed AdS{sub 5}×S{sup 5}, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement.
S-matrix approach to two-pion production in e+e- annihilation and tau decay
Bernicha, A; Pestieau, J; Castro, G Lopez
1996-01-01
Based on the S-matrix approach, we introduce a modified formula for the \\pi^{\\pm} electromagnetic form factor which describes very well the experimental data in the energy region 2m_{\\pi} \\leq \\sqrt{s} \\leq 1.1 GeV. Using the CVC hypothesis we predict B(\\tpp) = (24.75 \\pm 0.38)\\% , in excellent agreement with recent experiments.
Time Breath of Psychological Theories
DEFF Research Database (Denmark)
Tateo, Luca; Valsiner, Jaan
2015-01-01
Psychology as a self-aspiring, ambitious, developmental science faces the crucial limit of time—both theoretically and practically. The issue of time in constructing psychology’s theories is a major unresolved metatheoretical task. This raises several questions about generalization of knowledge......: which is the time length of breath of psychological theories? Which is the temporal dimension of psychological processes? In this article we discuss the role of different axiomatic assumptions about time in the construction of psychological theories. How could different theories include a concept...... of time—or fail to do that? How can they generalize with respect to time? The different conceptions of time often remain implicit, while shaping the concepts used in understanding psychological processes. Any preconception about time in human development will foster the generalizability of theory, as well...
Probing the Structure of Quantum Mechanics : Nonlinearity, Nonlocality, Computation and Axiomatics
Durt, Thomas; Czachor, Marek
2002-01-01
During the last decade, scientists working in quantum theory have been engaging in promising new fields such as quantum computation and quantum information processing, and have also been reflecting on the possibilities of nonlinear behavior on the quantum level. These are challenging undertakings because (1) they will result in new solutions to important technical and practical problems that were unsolvable by the classical approaches (for example, quantum computers can calculate problems that are intractable if one uses classical computers); and (2) they open up new 'hard' problems of a fundamental nature that touch the foundation of quantum theory itself (for example, the contradiction between locality and nonlinearity and the interpretation of quantum computing as a universal process). In this book, one can distinguish two main streams of research to approach the just-mentioned problem field: (1) a theoretical structural part, which concentrates on the elaboration of a nonlinear quantum mechanics and the ...
Quantum stereodynamics of the F + H2 → HF + H reaction by the stereodirected S-matrix approach
International Nuclear Information System (INIS)
Reaction stereodynamics can be studied in quantum mechanics using alternative representations of the S matrix. In this paper we employ the equations for the orthogonal transformations (expressed in terms of Wigner 3j symbols) that convert the S matrix from the body fixed (vertical bar jΩ>) representation into the stereodirected one (vertical bar νΩ>). This representation is characterized by the introduction of the steric quantum number ν, which in the vector model of quantum mechanics is put into correspondence with given precession cones of attack of the incoming atom on the diatomic molecule for the reactants' channels, and of cones of escape for the departing atom away from the diatomic molecule for the products' channels. The angles of aperture of such cones are determined from the uncertainty principle. As the ν quantum number increases (semiclassical limit), the grid of discrete values of the precession cones more finely scans the angle between the Jacobi vectors. Using a time-independent hyperspherical coordinate method we have generated the full S matrix including all open reactive and inelastic channels for two potential energy surfaces corresponding to the F + H2 → HF + H reaction and they have been used to calculate, via vertical bar jΩ>→ vertical bar νΩ> matrix transformations, the attack and exit cumulative reaction probabilities. During the calculations, we have distinguished between ortho-H2 and para-H2. Clear stereodynamical effects have being identified, in particular, regarding the reaction entrance channel, that F-atom attacks are preferred at the transition state (bent) geometry, while for the exit channel the H-atom departs in a collinear geometry by the H-end side of HF
All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
Borsato, Riccardo; Sfondrini, Alessandro; Stefanski, Bogdan
2014-01-01
We obtain the all-loop worldsheet S matrix for fundamental excitations on AdS_3 x S^3 x T^4 by studying the off-shell symmetry algebra of the superspace action in lightcone gauge. The massless modes, unaccounted for in earlier works, are automatically included in our treatment. Their exact dispersion relation is found to be non-relativistic, of giant-magnon form and their scattering is naturally well-defined. This opens the way to a complete investigation of AdS_3/CFT_2 integrability.
An introduction to symmetry and supersymmetry in quantum field theory
Lopuszánski, Jan T
1991-01-01
This is a set of lecture notes given by the author at the Universities of Göttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.
Perturbative Quantization of Gravity Theories
Bern, Z.
2001-01-01
We discuss string theory relations between gravity and gauge theory tree amplitudes. Together with $D$-dimensional unitarity, these relations can be used to perturbatively quantize gravity theories, i.e. they contain the necessary information for calculating complete gravity $S$-matrices to any loop orders. This leads to a practical method for computing non-trivial gravity $S$-matrix elements by relating them to much simpler gauge theory ones. We also describe arguments that N=8 D=4 supergrav...
Compton scattering S-matrix and cross section in strong magnetic field
Mushtukov, Alexander A; Poutanen, Juri
2015-01-01
Compton scattering of polarized radiation in a strong magnetic field is considered. The recipe for calculation of the scattering matrix elements, the differential and total cross sections based on quantum electrodynamic (QED) second order perturbation theory is presented for the case of arbitrary initial and final Landau level, electron momentum along the field and photon momentum. Photon polarization and electron spin state are taken into account. The correct dependence of natural Landau level width on the electron spin state is taken into account in general case of arbitrary initial photon momentum for the first time. A number of steps in calculations were simplified analytically making the presented recipe easy-to-use. The redistribution functions over the photon energy, momentum and polarization states are presented and discussed. The paper generalizes already known results and offers a basis for accurate calculation of radiation transfer in strong $B$-field, for example, in strongly magnetized neutron st...
Time Breath of Psychological Theories:A Meta-theoretical focus
Tateo, Luca; Valsiner, Jaan
2015-01-01
Psychology as a self-aspiring, ambitious, developmental science faces the crucial limit of time—both theoretically and practically. The issue of time in constructing psychology’s theories is a major unresolved metatheoretical task. This raises several questions about generalization of knowledge: which is the time length of breath of psychological theories? Which is the temporal dimension of psychological processes? In this article we discuss the role of different axiomatic assumptions about t...
John von Neumann's mathematical "Utopia" in quantum theory
Valente, Giovanni
This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present the reasons why his axiomatic program remained an "unsolved problem" in mathematical physics. A recent unpublished result by Huzimiro Araki, proving that no algebra with a tracial state defined on it, such as the type II1 factors, can support any (regular) representation of the canonical commutation relations, is also reviewed and its consequences for von Neumann's projects are discussed.
MacIntosh, R S
1997-01-01
The iterative-perturbative (IP) procedure for S-matrix to potential inversion is applied to spin-one projectiles for the restricted case of vector spin-orbit interaction only. In order to evaluate this extension of IP inversion we have inverted the multi-channel RGM $S_{lj}$ of Kanada et al for deuterons scattering from $^4$He with deuteron distortion and then compared the central components with those derived from RGM with spin set to zero. Attention is given to the question of how well the resulting potentials are established. Reliable spin-1 inversion is demonstrated. Results relating to inversion, to deuteron-nucleus interactions and to RGM are presented and suggest the range of nuclear interaction information which the procedure makes possible. Unusual non-locality and parity dependence effects are found; these are of possible relevance to generic properties of nuclear potentials.
Fuzzy Entropy:Axiomatic Definition and Neural Networks Model%模糊熵:公理化定义和神经网络模型
Institute of Scientific and Technical Information of China (English)
卿铭; 曹悦; 黄天民
2004-01-01
The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly,the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.
Game theory, social choice and ethics
1979-01-01
There are problems to whose solution I would attach an infinitely greater import ancf! than to those of mathematics, for example touching ethics, or our relation to God, or conceming our destiny and our future; but their solution lies wholly beyond us and completely outside the province 0 f science. J. F. C. Gauss For a1l his prescience in matters physical and mathematieal, the great Gauss apparently did not foresee one development peculiar to OUT own time. The development I have in mind is the use of mathematical reasoning - in partieu lar the axiomatic method - to explicate alternative concepts of rationality and morality. The present bipartite collection of essays (Vol. 11, Nos. 2 and 3 of this journal) is entitled 'Game Theory, Social Choiee, and Ethics'. The eight papers represent state-of-the-art research in formal moral theory. Their intended aim is to demonstrate how the methods of game theory, decision theory, and axiomatic social choice theory can help to illuminate ethical questions central not...
Division Algebras and Quantum Theory
Baez, John C
2011-01-01
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly "complex" representations), those that are self-dual thanks to a symmetric bilinear pairing (which are "real", in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are...
Nullification in scalar theories with derivative couplings
Argyres, E. N.; Papadopoulos, C. G.; Bruinsma, M.; Kleiss, R.
1996-01-01
We discuss the structure of scalar field theories having the property that all on-shell S-matrix elements vanish in tree approximation. It is shown that there exists a large class of such theories, with derivative couplings, which are all locally related to a free theory by a nonlinear transformation. It is also shown that a field-dependent wave-function renormalization provides all necessary counterterms so that all on-shell S-matrix elements vanish also at the one-loop level.
Reflexive structures an introduction to computability theory
Sanchis, Luis E
1988-01-01
Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics.
Lee, Taesik; Jeziorek, Peter
2004-01-01
Large complex projects cost large sums of money throughout their life cycle for a variety of reasons and causes. For such large programs, the credible estimation of the project cost, a quick assessment of the cost of making changes, and the management of the project budget with effective cost reduction determine the viability of the project. Cost engineering that deals with these issues requires a rigorous method and systematic processes. This paper introduces a logical framework to a&e effective cost engineering. The framework is built upon Axiomatic Design process. The structure in the Axiomatic Design process provides a good foundation to closely tie engineering design and cost information together. The cost framework presented in this paper is a systematic link between the functional domain (FRs), physical domain (DPs), cost domain (CUs), and a task/process-based model. The FR-DP map relates a system s functional requirements to design solutions across all levels and branches of the decomposition hierarchy. DPs are mapped into CUs, which provides a means to estimate the cost of design solutions - DPs - from the cost of the physical entities in the system - CUs. The task/process model describes the iterative process ot-developing each of the CUs, and is used to estimate the cost of CUs. By linking the four domains, this framework provides a superior traceability from requirements to cost information.
Mathematical aspects of quantum field theories
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...
Distributions of the S-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials
Salamon, P; Vertse, T
2015-01-01
The positions of the $l=0$ $S$-matrix poles are calculated in generalized Woods-Saxon (GWS) potential and in cut-off generalized Woods-Saxon (CGWS) potential. The solutions of the radial equations are calculated numerically for the CGWS potential and analytically for GWS using the formalism of Gy. Bencze \\cite{[Be66]}. We calculate CGWS and GWS cases at small non-zero values of the diffuseness in order to approach the square well potential and to be able to separate effects of the radius parameter and the cut-off radius parameter. In the case of the GWS potential the wave functions are reflected at the nuclear radius therefore the distances of the resonant poles depend on the radius parameter of the potential. In CGWS potential the wave function can be reflected at larger distance where the potential is cut to zero and the derivative of the potential does not exist. The positions of most of the resonant poles do depend strongly on the cut-off radius of the potential, which is an unphysical parameter. Only the...
Distributions of the S-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials
Salamon, P.; Baran, Á.; Vertse, T.
2016-08-01
The positions of the l = 0S-matrix poles are calculated in generalized Woods-Saxon (GWS) potential and in cut-off generalized Woods-Saxon (CGWS) potential. The solutions of the radial equations are calculated numerically for the CGWS potential and analytically for GWS using the formalism of Gy. Bencze [1]. We calculate CGWS and GWS cases at small non-zero values of the diffuseness in order to approach the square well potential and to be able to separate effects of the radius parameter and the cut-off radius parameter. In the case of the GWS potential the wave functions are reflected at the nuclear radius therefore the distances of the resonant poles depend on the radius parameter of the potential. In CGWS potential the wave function can be reflected at larger distance where the potential is cut to zero and the derivative of the potential does not exist. The positions of most of the resonant poles do depend strongly on the cut-off radius of the potential, which is an unphysical parameter. Only the positions of the few narrow resonances in potentials with barrier are not sensitive to the cut-off distance. For the broad resonances the effect of the cut-off cannot be corrected by using a suggested analytical form of the first order perturbation correction.
Shan, Xiao; Connor, J N L
2016-08-18
We report two new contributions for understanding the quantum dynamics of the benchmark state-to-state reaction, F + H2(vi, ji, mi) → FH(vf, jf, mf) + H, where (vi, ji, mi) and (vf, jf, mf) are the initial and final vibrational, rotational, and helicity quantum numbers, respectively. We analyze product differential cross sections (DCSs) for the transitions, 000 → 300, 000 → 310, and 000 → 320, at a translational energy of 0.04088 eV using the potential energy surface of Fu-Xu-Zhang. The two new contributions are as follows: (1) We exploit the recently introduced QP decomposition of J. N. L. Connor [ J. Chem. Phys . 2013 , 138 , 124310 ] to transform numerical partial-wave scattering (S) matrix elements for the three transitions into parametrized (analytic) formulas, in which all terms in the three parametrized S matrices have a direct physical interpretation. In particular, they contain the positions and residues of Regge poles in the first quadrant of the complex angular momentum (CAM) plane. We obtain very close agreement between the values of the parametrized and numerical S matrix elements. (2) We then apply a uniform asymptotic Watson/CAM theory, which allows a Regge pole to be close to a saddle point. It uses the parametrized S matrices and is applied to the partial wave series (PWS) representation for the scattering amplitude to understand structure in a DCS in terms of three contributing subamplitudes. We prove using this powerful CAM theory that resonance Regge poles contribute to the small-angle scattering in the DCSs for all three transitions, with the oscillations at larger angles arising from nearside-farside interference. We obtain very good agreement between the uniform asymptotic Watson/CAM DCSs and the corresponding PWS DCSs, except for angles close to the forward and backward directions, where (as expected) the Watson/CAM formulas become nonuniform. PMID:27434264
M-Theory in the Gaugeon Formalism
Institute of Scientific and Technical Information of China (English)
Mir Faizal
2012-01-01
In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena （ABJM） theory in N = 1 superspace formalism. We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism. We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.
Salasnich, L
1997-01-01
We review the paper 'Integrability of the S-Matrix vs Integrability of the Hamiltonian' by C. Jung and T.H. Seligman (Phys. Rep. 285, 77-141 (1997)). This paper deals with the connection between the integrability of the scattering matrix $S$ and the integrability of the Hamiltonian $H$ for classical and quantum Hamiltonian systems.
Extracting S-matrix poles for resonances from numerical scattering data: Type-II Padé reconstruction
Sokolovski, D.; Akhmatskaya, E.; Sen, S. K.
2011-02-01
We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Padé approximant from given physical values (Bessis et al. (1994) [42]; Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [45]) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H 2 → HF + H, F + HD → HF + D, Cl + HCl → ClH + Cl and H + D 2 → HD + D reactions. Some detailed examples are given in the text. Program summaryProgram title: PADE II Catalogue identifier: AEHO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 19 959 No. of bytes in distributed program, including test data, etc.: 158 380 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Any computer equipped with a FORTRAN 90 compiler Operating system: UNIX, LINUX RAM: 256 Mb Classification: 16.8 External routines: NAG Program Library ( http://www.nag.co.uk/numeric/fl/FLdescription.asp) Nature of problem: The package extracts the positions and
Classes and Theories of Trees Associated with a Class Of Linear Orders
DEFF Research Database (Denmark)
Goranko, Valentin; Kellerman, Ruaan
2011-01-01
these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general...... results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees....
Towards applied theories based on computability logic
Japaridze, Giorgi
2008-01-01
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and completeness with respect to the semantics of CL. Conservatively extending classical predicate calculus and offering considerable additional expressive and deductive power, CL12 presents a reasonable, computationally meaningful, constructive alternative to classical logic as a basis for applied theories. To obtain a model example of such theories, this paper rebuilds the traditional, classical-logic-based Peano arithmetic into a computability-logic-b...
Bianchi, Matteo
2012-01-01
In [Mon11] are studied, for the axiomatic extensions of the monoidal t-norm based logic ([EG01]), the properties of single chain completeness. On the other side, in [GJKO07, Chapter 5] are studied many logical and algebraic properties (like Halld\\'en completeness, variable separation properties, amalgamation property etc.), in the context of substructural logics. The aim of this paper is twofold: first of all we will specialize the properties studied in [GJKO07, Chapter 5] from the case of substructural logics to the one of extensions of MTL, by obtaining some general characterization. Moreover we will show that some of these properties are indeed strictly connected to the topics developed in [Mon11]. This will help to have a better intuition concerning some open problems of [Mon11].
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2008-05-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out
Does the Peres experiment using photons test for hyper-complex (quaternionic) quantum theories?
Adler, Stephen L.
2016-01-01
Assuming the standard axioms for quaternionic quantum theory and a spatially localized scattering interaction, the $S$-matrix in quaternionic quantum theory is complex valued, not quaternionic. Using the standard connections between the $S$-matrix, the forward scattering amplitude for electromagnetic wave scattering, and the index of refraction, we show that the index of refraction is necessarily complex, not quaternionic. This implies that the recent optical experiment of Procopio et al. bas...
The pomeron in closed bosonic string theory
Fazio, A R
2010-01-01
We review the features of the pomeron in the S-matrix theory and in quantum field theory. We extend those general properties to the pomeron of closed bosonic string theory in a Minkowskian background. We compute the couplings of the pomeron to the lowest mass levels of closed bosonic string states in flat space. We recognize the deviation from the linearity of the Regge trajectories in a five dimensional anti De Sitter background.
The Epstein-Glaser causal approach to the Light-Front QED$_{4}$. I: Free theory
Bufalo, R.; Pimentel, B. M.; Soto, D. E.
2014-01-01
In this work we present the study of light-front field theories in the realm of axiomatic theory. It is known that when one uses the light-cone gauge pathological poles $(k^{+}) ^{-n}$ arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use rigorous mathematical machine...
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Mean-deviation analysis in the theory of choice.
Grechuk, Bogdan; Molyboha, Anton; Zabarankin, Michael
2012-08-01
Mean-deviation analysis, along with the existing theories of coherent risk measures and dual utility, is examined in the context of the theory of choice under uncertainty, which studies rational preference relations for random outcomes based on different sets of axioms such as transitivity, monotonicity, continuity, etc. An axiomatic foundation of the theory of coherent risk measures is obtained as a relaxation of the axioms of the dual utility theory, and a further relaxation of the axioms are shown to lead to the mean-deviation analysis. Paradoxes arising from the sets of axioms corresponding to these theories and their possible resolutions are discussed, and application of the mean-deviation analysis to optimal risk sharing and portfolio selection in the context of rational choice is considered.
Renormalization programme for effective theories
Vereshagin, Vladimir; Semenov-Tyan-Shanskiy, Kirill; Vereshagin, Alexander
2004-01-01
We summarize our latest developments in perturbative treating the effective theories of strong interactions. We discuss the principles of constructing the mathematically correct expressions for the S-matrix elements at a given loop order and briefly review the renormalization procedure. This talk shall provide the philosophical basement as well as serve as an introduction for the material presented at this conference by A. Vereshagin and K. Semenov-Tian-Shansky.
公理化设计基本理论及其应用模型%Theory and Design Model of Axiomatic Design
Institute of Scientific and Technical Information of China (English)
郑称德
2003-01-01
公理化设计是当前质量工程领域出现的一种新产品设计方法,该方法为新产品创新和已有产品诊断改进给出了基本原则和概念性框架,已引起了质量界的高度重视.本文对其基本理论和设计模型进行初步探讨的同时,介绍了其研究重点和热点,并对其优点和存在的一些问题进行了讨论.
On a Formalization of Cantor Set Theory for Natural Models of the Physical Phenomena
Directory of Open Access Journals (Sweden)
Nudel'man A. S.
2010-01-01
Full Text Available This article presents a set theory which is an extension of $ZFC$. In contrast to $ZFC$, a new theory admits absolutely non-denumerable sets. It is feasible that a symbiosis of the proposed theory and Vdovin set theory will permit to formulate a (presumably non-contradictory axiomatic set theory which will represent the core of Cantor set theory in a maximally full manner as to the essence and the contents of the latter. This is possible due to the fact that the generalized principle of choice and the generalized continuum hypothesis are proved in Vdovin theory. The theory, being more complete than $ZF$ and more natural according to Cantor, will allow to construct and study (in its framework only natural models of the real physical phenomena.
Vagner, Isaac
2014-01-01
Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with respect to the L-subgroups are considered. The geometric and corresponding physical characteristics of these motions are discussed: relativistic velocity, mass, relativistic momentum and mass/velocity ratio. It is shown that only one world line of inertial motion corresponds to each point on the plane in a space-like area, and the mass growth, dependent on the velocity, takes place only in the particle system. The mathematical model describing the aforementioned physical characteristics is developed in a geometric context, based on group theory.
International Nuclear Information System (INIS)
Several two dimensional quantum field theory models have more than one vacuum state. An investigation of super selection sectors in two dimensions from an axiomatic point of view suggests that there should be also states, called soliton or kink states, which interpolate different vacua. Familiar quantum field theory models, for which the existence of kink states have been proven, are the Sine-Gordon and the φ42-model. In order to establish the existence of kink states for a larger class of models, we investigate the following question: Which are sufficient conditions a pair of vacuum states has to fulfill, such that an interpolating kink state can be constructed? We discuss the problem in the framework of algebraic quantum field theory which includes, for example, the P(φ)2-models. We identify a large class of vacuum states, including the vacua of the P(φ)2-models, the Yukawa2-like models and special types of Wess-Zumino models, for which there is a natural way to construct an interpolating kink state. In two space-time dimensions, massive particle states are kink states. We apply the Haag-Ruelle collision theory to kink sectors in order to analyze the asymptotic scattering states. We show that for special configurations of n kinks the scattering states describe n freely moving non interacting particles. (orig.)
邻域粗糙集的矩阵表示与公理化%Matrix representation and axiomatization of neighborhood-based rough sets
Institute of Scientific and Technical Information of China (English)
王石平; 朱清新; 祝峰; 闵帆
2012-01-01
Boolean matrices representing a covering are proposed, and a square matrix, namely the Boolean product of a matrix representing a covering and its transpose, is obtained Using the square matrix, covering-based lower and upper approximation operators in covering-based rough sets are concisely described. Through a square Boolean matrix obtained by the definition of a new operation between Boolean matrices, neighborhood-based lower and upper approximation operators are concisely represented. By the fact that binary relations and square Boolean matrices have a one-to-one correspondence, the two square matrices are directly expressed by covering blocks. Finally, neighborhood-based lower and upper approximation operators are axiomatized using matrices.%文章提出覆盖的表示矩阵,通过一个方布尔矩阵,即覆盖表示矩阵与其转置的布尔乘积,简洁地表示覆盖粗糙集中常用的覆盖近似算子；通过定义类似布尔乘积的布尔矩阵间的运算,获得一个布尔方矩阵,通过这个布尔方阵,简洁地表示邻域近似算子；因为布尔方阵和二元关系是一一对应的,因此2种布尔方阵都有唯一的二元关系与之对应,直接通过覆盖块,这2个二元关系被简洁表示；最后给出了邻域近似算子的矩阵公理化.
Energy Technology Data Exchange (ETDEWEB)
Mahoux, G. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1969-02-01
It is shown that any regularized helicity amplitude, which is known from axiomatic local field theory to satisfy dispersion relations for -t{sub M} < t {<=} 0, is in fact analytic in the quasi-topological product ( |t| < R) product (s in the cut plane). This is the extension to the scattering of spin particles, of a result obtained by Martin in the scalar case. As a first consequence, the Froissart limits are extended to all helicity amplitudes. Furthermore, it is shown that for -t{sub M} < t < 0 and s going to infinity, the regularized helicity amplitudes in the t channel, with initial (resp. final) helicities {lambda}1 and {lambda}2 (resp. {mu}1 and {mu}2), are bounded by: C s{sup 1-Max} (|{lambda}|,|{lambda}|) log{sup 2}s if {lambda} + {mu} is even C s{sup 1-Max} (|{lambda}|,|{mu}|) log{sup 3}s if {lambda} + {mu} is odd where {lambda} = {lambda}1 - {lambda}2 and {mu} = {mu}1 - {mu}2. This gives super-convergent amplitudes as soon as one of the spins is larger than 1. The case of spin 0 - spin 1 scattering is marginal, and in the absence of any detailed dynamical information, one cannot obtain a super-convergent amplitude in that case. (author) [French] II est demontre que toute amplitude cinematiquement reguliere, qui decrit la diffusion elastique de deux particules de masses non nulles, et de spins quelconques, dont on sait par la theorie axiomatique des champs locaux, qu'elle satisfait des relations de dispersion en s a transfert t fixe (-t{sub M} < t {<=} 0), est en fait analytique dans le produit quasitopologique ( |t| < R) produit (s dans un plan coupe), ou R est une constante. Ce resultat etend aux particules de spins non nuls, le theoreme de Martin relatif au cas scalaire. Une premiere consequence est l'extension des bornes de Froissart a toute amplitude d'helicite. Puis il est montre que, pour t fixe (-t{sub M} < t {<=} 0) et s tendant vers l'infini, les amplitudes d'helicite regularisees dans la voie t, avec les helicites
生成语言学的公理演绎思想%On the Axiomatic Deduction in Generative Linguistics
Institute of Scientific and Technical Information of China (English)
李可胜
2011-01-01
乔姆斯基的转换生成语法将演绎思想引入语言学研究，对其后的语言学研究产生了革命性的影响，这是生成语言学的伟大贡献之一。演绎思想使得语言研究从经验主义向理性主义转变，并促使语言学开始向一门真正的自然科学转型。但是演绎思想在转换生成语法的不同理论阶段中的地位和影响并不相同，因而也影响着生成语言学的自然科学属性。%Chomsky introduces the deductive reasoning into linguistic studies, which exerts a revolutionary impact upon the linguistic theories thereafter; it is one of the achievements made by TG （transformational generative Grammar） . The deductive reasoning cause
Stochastic Gravity: Theory and Applications
Directory of Open Access Journals (Sweden)
Hu Bei Lok
2004-01-01
Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction
Normalizability analysis of the generalized quantum electrodynamics from the causal point of view
Bufalo, R.; Pimentel, B. M.; Soto, D. E.
2015-01-01
The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyse the impli...
Preface to a GUT (Grand Unified Theory)
International Nuclear Information System (INIS)
A Grand Unified Theory (GUT) is proposed exhibiting relativistic invariance and based on a physical model for vacuum space consisting of the superposition of oppositely charged continuous fluids. Models for the photon, electron, neutrino, proton, etc., consist of separate unique variations in the relative densities of the fluids and their flow patterns. This GUT is also based on the use of transfinite axiomatic number forms and on a concept of metrical relativity which hopefully reconciles the many logical dichotomies in and between Special Relativity and Quantum Mechanics. These ideas result in a number of experimental proposals and predicted results which appear to be underivable from present paradigms, first among which is a physical model for the hidden variable of Quantum Mechanics. It is on these features that attention should rest. (Auth.)
Homotopy Classification of Bosonic String Field Theory
Muenster, Korbinian; Sachs, Ivo
2012-01-01
We prove the decomposition theorem for the loop homotopy algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the op...
Quantum Theory and Human Perception of the Macro-World
Aerts, Diederik
2014-01-01
We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e. as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new 'conceptual quantum interpretati...
Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic limit of the S-matrix of a field theory, and when there is a well-defined mapping between the Hilbert spaces and operators of the two theories. This correspondence provides an efficient method to compu...
Three lectures on string field theory
International Nuclear Information System (INIS)
Presently there are severla major theoretical developments whose goal is to achieve a fundamental understanding of the equations that govern the structure of strign theory. In general, this basic structure is encoded in the interrelationship that exists between 2d conformal invariance and the spacetime gauge symmetries of the string theory. In an effort to formulate these explicitly, one has the approaches based on β-functions in 2d Σ-models, S-matrix functionals, string field theory, integrable analytic geometry, loop space and others. The basic purpose of these lectures is to review some of these approaches and comment on the interrelationships that exist among them. First, we concentrate on first quantized, Polyakov string approach. The basic equations which follow from the requirement of conformal invariance are summarized. The connection with the field theoretic formulation is given vbvased on an S-matrix generating functional method. Both the S-matrix and the field theoretic formulation still leave major open questions. These issues concern the understanding of the theory fo r closed strings and the orgin of general relativity. 55 refs
Theory of non-local point transformations - Part 2: General form and Gedanken experiment
Tessarotto, Massimo
2016-01-01
The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when expressed in arbitrary coordinate systems. It is shown that the solution permits to achieve an ideal (Gedanken) experiment realizing a suitable kind of phase-space transformation on point-particle classical dynamical systems. Applications of the theory are discussed both for diagonal and non-diagonal metric tensors.
S matrix for absorptive Hamiltonians
International Nuclear Information System (INIS)
The existence of a matrix S such that SS = 1 in the presence of absorption is demonstrated. In the limit a of hermitian Hamiltonian the unitarity conditions SS = 1 is recovered. A dispersion relation for forward scattering is derived and the properties of the reactance matrices K and K are obtained. It is shown that K = K
Axiomatizations of symmetrically weighted solutions
Kleppe, John; Reijnierse, Hans; Sudhölter, P.
2013-01-01
If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a su
The Theory of Biomedical Knowledge Integration(Ⅳ)
Institute of Scientific and Technical Information of China (English)
BAO Han-fei
2005-01-01
This paper presented some philosophic viewpoints of the Theory of BMKI (The Theory of Biomedical Knowledge Integration), a new exploration in BioMedical Informatics. It discussed an evolutional relation from propositional calculus, predicate calculus, through framework, to neural network.. The differences in exclusivity and other natures were explored for physical systems (the real world), quasi-physical systems (the copies of the real world) and mental systems(the abstracts of the real world). Based on their behaviours in cognitive sciences and knowledge engineering, the new concepts quasi-infinity or -infinitesimal,potential knowledge,dynamic knowledge were introduced. This paper has also described so called "big-or" space which is the base of scientific understanding or association. Furthermore the paper put forward the viewpoint that "reasoning only can implement in an axiomatic space" and then outlined the building processes of such kind of space. At last so called "beacon-andcompass strategy" in BMKI was introduced.
Mixed motives and algebraic K-theory
Jannsen, Uwe
1990-01-01
The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varietie...
Does the Peres experiment using photons test for hyper-complex (quaternionic) quantum theories?
Adler, Stephen L
2016-01-01
Assuming the standard axioms for quaternionic quantum theory and a spatially localized scattering interaction, the $S$-matrix in quaternionic quantum theory is complex valued, not quaternionic. Using the standard connections between the $S$-matrix, the forward scattering amplitude for electromagnetic wave scattering, and the index of refraction, we show that the index of refraction is necessarily complex, not quaternionic. This implies that the recent optical experiment of Procopio et al. based on the Peres proposal does not test for hyper-complex or quaternionic quantum effects arising within the standard Hilbert space framework. Such a test requires looking at near zone fields, not radiation zone fields.
Theory of relativistic direct interaction
International Nuclear Information System (INIS)
Report discusses the structure, the generality and the physical meaning of the relativistic Hamiltonian theory (RHT) as a whole, starting from its most general quantum-field version and finishing with its classical counterpart. It is shown, in particular, that in the absence of bound states any relativistic invariant S-matrix can be obtained in the framework of the RHT. The properties of causality and locality of RHT are discussed, and two mechanisms of interaction transfer are considered. The space-time interaction of the motion of particles inside the direct interaction range is formulated and shown to be non-unique
Off-shell amplitudes in superstring theory
Energy Technology Data Exchange (ETDEWEB)
Sen, Ashoke [Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad, 211019 (India)
2015-04-01
Computing the renormalized masses and S-matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off-shell amplitude with certain factorization properties. While in the bosonic string theory one can in principle construct such an amplitude from string field theory, there is no fully consistent field theory for type II and heterotic string theory. In this paper we give a practical construction of off-shell amplitudes satisfying the desired factorization property using the formalism of picture changing operators. We describe a systematic procedure for dealing with the spurious singularities of the integration measure that we encounter in superstring perturbation theory. This procedure is also useful for computing on-shell amplitudes, as we demonstrate by computing the effect of Fayet-Iliopoulos D-terms in four dimensional heterotic string theory compactifications using this formalism. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Models in theory building: the case of early string theory
International Nuclear Information System (INIS)
The history of the origins and first steps of string theory, from Veneziano's formulation of his famous scattering amplitude in 1968 to the 'first string revolution' in 1984, provides rich material for discussing traditional issues in the philosophy of science. This paper focusses on the initial phase of this history, that is the making of early string theory out of the 'dual theory of strong interactions' motivated by the aim of finding a viable theory of hadrons in the framework of the so-called S-matrix theory of the Sixties: from the first two models proposed (the Dual Resonance Model and the Shapiro-Virasoro Model) to all the subsequent endeavours to extend and complete the theory, including its string interpretation. As is the aim of this paper to show, by representing an exemplary illustration of the building of a scientific theory out of tentative and partial models this is a particularly fruitful case study for the current philosophical discussion on how to characterize a scientific model, a scientific theory, and the relation between models and theories.
Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory
Directory of Open Access Journals (Sweden)
Yafei Song
2015-01-01
Full Text Available Intuitionistic fuzzy (IF evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.
Off-shell Amplitudes in Superstring Theory
Sen, Ashoke
2014-01-01
Computing the renormalized masses and S-matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off-shell amplitude with certain factorization properties. While in the bosonic string theory one can in principle construct such an amplitude from string field theory, there is no fully consistent field theory for superstring and heterotic string theory. In this paper we give a practical construction of off-shell amplitudes satisfying the desired factorization property using the formalism of picture changing operators. We describe a systematic procedure for dealing with the spurious singularities of the integration measure that we encounter when the supermoduli space is not holomorphically projected. This procedure is also useful for computing on-shell amplitudes, as we demonstrate by computing the effect of Fayet-Iliopoulos D-terms in four dimensional heterotic string theory compactifications using this formalism.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Relativistic quantum theories and neutrino oscillations
Energy Technology Data Exchange (ETDEWEB)
Keister, B D [Physics Division, 1015N, National Science Foundation, 4201 Wilson Blvd., Arlington, VA 22230 (United States); Polyzou, W N, E-mail: polyzou@uiowa.ed [Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242 (United States)
2010-05-01
Neutrino oscillations are examined under the broad requirements of Poincare-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The aim of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable and how many factors that are important in principle end up being negligible in practice.
Notes on the firewall paradox, complexity, and quantum theory
Schlesinger, Karl-Georg
2014-01-01
We investigate what it means to apply the solution, proposed to the firewall paradox by Harlow and Hayden, to the famous quantum paradoxes of Sch\\"odinger's Cat and Wigner's Friend if ones views these as posing a thermodynamic decoding problem (as does Hawking radiation in the firewall paradox). The implications might point to a relevance of the firewall paradox for the axiomatic and set theoretic foundations underlying mathematics. We reconsider in this context the results of Benioff on the foundational challenges posed by the randomness postulate of quantum theory. A central point in our discussion is that one can mathematically not naturally distinguish between computational complexity (as central to the approach of Harlow and Hayden and further developed by Susskind) and proof theoretic complexity (since they represent the same concept on a Turing machine), with the latter being related to a finite bound on Kolmogorov entropy (due to Chaitin incompleteness).
Acceleration of the Universe, String Theory and a Varying Speed of Light
Moffat, J. W.
2001-01-01
The existence of future horizons in spacetime geometries poses serious problems for string theory and quantum field theories. The observation that the expansion of the universe is accelerating has recently been shown to lead to a crisis for the mathematical formalism of string and M-theories, since the existence of a future horizon for an eternally accelerating universe does not allow the formulation of physical S-matrix observables. Postulating that the speed of light varies in an expanding ...
Gauge Invariant Operators and Closed String Scattering in Open String Field Theory
Alishahiha, Mohsen; Garousi, Mohammad R.
2002-01-01
Using the recent proposal for the observables in open string field theory, we explicitly compute the coupling of closed string tachyon and massless states with the open string states up to level two. Using these couplings, we then calculate the tree level S-matrix elements of two closed string tachyons or two massless states in the open string field theory. Up to some contact terms, the results reproduce exactly the corresponding amplitudes in the bosonic string theory.
Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
Chu, Chong-Sun; Lukierski, Jerzy; Zakrzewski, Wojtek J.
2002-01-01
The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. Th...
A new approach to quantum field theory and a spacetime quantization
International Nuclear Information System (INIS)
A quantum logical approach to achieve a sound kinematical picture for LQFT (local quantum field theory) is reviewed. Then a general language in the framework of axiomatic set theory is presented, in which the 'local' description of a LQFT can be formulated in almost the same form as quantum mechanics was formulated by von Neumann. The main physical implication of this approach is that, in this framework, the quantization of a CRLFT (classical relativistic local field theory) requires not only the quantization of physical fields over M4 but the quantization of spacetime M4 itself, too. The uncertainty priciple is compatible with the Heisenberg uncertainty principle, but it requires the generalization of Poincare symmetries to all unitary symmetries. Some indications show that his approach might be successful in describing low laying hadronic phenomena. (author)
Meaning of the BRS Lagrangian theory
International Nuclear Information System (INIS)
A simplified treatment of the Becchi-Rouet-Stora (BRS) Lagrangian theory is presented. With this treatment we show that the BRS Lagrangian theory in general, and the Feynman-gauge field theory in particular, are effective theories, not the physical theory, and the Feynman gauge is not, strictly speaking, a gauge. The relationship between the quantum states in the BRS Lagrangian theory and those in the physical theory is explicitly given. We also show that one may obtain matrix elements of gauge-invariant operators in the physical theory by calculating corresponding ones in the BRS Lagrangian theory. The formulas which equate such matrix elements are called correspondence formulas. The correspondence formula for the S matrix enables us to equate the scattering amplitudes in the physical theory with those in the BRS Lagrangian theory, thus a proof of the unitary of the Feynman-gauge (as well as other covariant gauges) Feynman rules is rendered unnecessary. This treatment can be applied to various gauge field theories and the examples of the pure Yang-Mills theory and a gauge field theory with a Higgs field is explicitly worked out
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
DEFF Research Database (Denmark)
Caron Huot, Simon; He, Song
2013-01-01
We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
M. Kormos; G. Mussardo; B. Pozsgay
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Cutkosky Rules for Superstring Field Theory
Pius, Roji
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 ru...
Scattering amplitudes in gauge theories
Henn, Johannes M
2014-01-01
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...
Inverse Scattering and Locality in Integrable Quantum Field Theories
Alazzawi, Sabina
2016-01-01
We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix $S$ is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on $S$ that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the $O(N)$-invariant nonlinear $\\sigma$-models.
Infrared-Finite Amplitudes for Massless Gauge Theories
Forde, D A
2003-01-01
We present a method to construct infrared-finite amplitudes for gauge theories with massless fermions. Rather than computing $S$-matrix elements between usual states of the Fock space we construct order-by-order in perturbation theory dressed states that incorporate all long-range interactions. The $S$-matrix elements between these states are shown to be free from soft and collinear singularities. As an explicit example we consider the process $e^+ e^-\\to 2$ jets at next-to-leading order in the strong coupling. We verify by explicit calculation that the amplitudes are infrared finite and recover the well-known result for the total cross section $e^+ e^-\\to$ hadrons.
Relativistic quantum mechanics and introduction to field theory
Energy Technology Data Exchange (ETDEWEB)
Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-12-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.
Maharana, Jnanadeva
2016-01-01
The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is adopted. The analyticity properties of the causal, the retarded and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in $s$ and $t$ variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domai...
ON THE AXIOMS OF REVEALED PREFERENCE IN FUZZY CONSUMER THEORY
Institute of Scientific and Technical Information of China (English)
Irina GEORGESCU
2004-01-01
The revealed preference is a central subject in classical consumer theory. Authors like Samuelson, Arrow, Richter, Sen, Uzawa and others have proposed an axiomatic setting of revealed preference theory. Consequently revealed preference axioms WARP and SARP and congruence axioms WCA and SCA have been considered. An important theorem of Sen establishes the equivalence between these axioms provided thefamily of budgets includes all non-empty finite sets of bundles. Fuzzy consumer theory (=fuzzy choice functions) is a topic that appears in a lot of papers.Particularly, Banerjee studies in fuzzy context axioms of revealed preference and congruence extending some results of Arrow and Sen. In this paper we modify the Banerjee definition of a fuzzy choice function (=fuzzy consumer)and we study some fuzzy versions of the axioms of revealed preference and congruence. Banerjee fuzzifies only the range of a consumer; we use a fuzzification of both the domain and the range of a consumer. The axioms WAFRP, SAFRP, WFCA, SFCA generalize to fuzzy consumer theory the well-known axioms WARP, SARP, WCA, SCA. Our main result establishes some connections between WAFRP, SAFRP, WFCA, SFCA extending a significant part of Sen theorem. Generally, we work in a fuzzy set theory based on a continuous t-norm, but some results are obtained for Godel t-norm and others are obtained for Lukasiewicz t-norm.
Free Quantum Field Theory from Quantum Cellular Automata
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Scattering amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2014-03-01
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Next-to-simplest quantum field theories
Lal, Shailesh; Raju, Suvrat
2010-05-01
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
Fujimori, Toshiaki; Izumi, Keisuke; Kitamura, Tomotaka
2016-01-01
We study tree-unitarity and renormalizability in Lifshitz-scaling theory, which is characterized by an anisotropic scaling between the spacial and time directions. Due to the lack of the Lorentz symmetry, the conditions for both unitarity and renormalizability are modified from those in relativistic theories. For renormalizability, the conventional discussion of the power counting conditions has to be extended. Because of the dependence of $S$-matrix elements on the reference frame, unitarity requires stronger conditions than those in relativistic cases. We show that the conditions for unitarity and renormalizabilty are identical as in relativistic theories. We discuss the importance of symmetries for a theory to be renormalizable.
On the microscopic foundation of scattering theory
International Nuclear Information System (INIS)
The aim of the thesis is to give a contribution to the microscopic foundation of scattering theory, i. e. to show, how the asymptotic formalism of scattering theory with objects like the S-matrix as well the initial and final asymptotics ψin and ψout can be derived from a microscopic description of the basic system. First the final statistics from a N-particle system through farly distant surfaces is derived. Thereafter we confine us to the 1-particle scattering and apply the final statistics in order to derive the scattering cross section from a microscopical description of the scattering situation. The basing dynamics are Bohm's mechanics, a theory on the motion of point particles, which reproduces all results of nonrelativistic quantum mechanics
DEFF Research Database (Denmark)
Wæver, Ole
2009-01-01
Kenneth N. Waltz's 1979 book, Theory of International Politics, is the most influential in the history of the discipline. It worked its effects to a large extent through raising the bar for what counted as theoretical work, in effect reshaping not only realism but rivals like liberalism...... and reflectivism. Yet, ironically, there has been little attention to Waltz's very explicit and original arguments about the nature of theory. This article explores and explicates Waltz's theory of theory. Central attention is paid to his definition of theory as ‘a picture, mentally formed' and to the radical anti......-empiricism and anti-positivism of his position. Followers and critics alike have treated Waltzian neorealism as if it was at bottom a formal proposition about cause-effect relations. The extreme case of Waltz being so victorious in the discipline, and yet being consistently mis-interpreted on the question of theory...
Cremaschini, Claudio; 10.1140/epjp/i2011-11063-3
2012-01-01
A notorious difficulty in the covariant dynamics of classical charged particles subject to non-local electromagnetic (EM) interactions arising in the EM radiation-reaction (RR) phenomena is due to the definition of the related non-local Lagrangian and Hamiltonian systems. The lack of a standard Lagrangian/Hamiltonian formulation in the customary asymptotic approximation for the RR equation may inhibit the construction of consistent kinetic and fluid theories. In this paper the issue is investigated in the framework of Special Relativity. It is shown that, for finite-size spherically-symmetric classical charged particles, non-perturbative Lagrangian and Hamiltonian formulations in standard form can be obtained, which describe particle dynamics in the presence of the exact EM RR self-force. As a remarkable consequence, based on axiomatic formulation of classical statistical mechanics, the covariant kinetic theory for systems of charged particles subject to the EM RR self-force is formulated in Hamiltonian form....
Universal Dynamics, a Unified Theory of Complex Systems. Emergence, Life and Death
Mack, G
2001-01-01
A universal framework is proposed, where all laws are regularities of relations between things or agents. Parts of the world at one or all times are modeled as networks called SYSTEMS with a minimum of axiomatic properties. A notion of locality is introduced by declaring some relations direct (or links). Dynamics is composed of "atomic" constituents called mechanisms. They are conditional actions of basic local structural transformations (``enzymes''): indirect relations become direct (friend of friend becomes friend), links are removed, objects copied. This defines a kind of universal chemistry. I show how to model basic life processes in a self contained fashion as a kind of enzymatic computation. The framework also accommodates the gauge theories of fundamental physics. Emergence creates new functionality by cooperation - nonlocal phenomena arise out of local interactions. I explain how this can be understood in a reductionist way by multiscale analysis (e.g. renormalization group).
The Systemic Theory of Living Systems and Relevance to CAM
Directory of Open Access Journals (Sweden)
José A. Olalde Rangel
2005-01-01
Full Text Available The Systemic Theory of Living Systems is being published in several parts in eCAM. The theory is axiomatic. It originates from the phenomenological idea that physiological health is based on three factors: integrity of its structure or organization, O, functional organic energy reserve, E, and level of active biological intelligence, I. From the theory is derived a treatment strategy called Systemic Medicine (SM. This is based on identifying and prescribing phytomedicines and/or other medications that strengthen each factor. Energy-stimulating phytomedicines increase available energy and decrease total entropy of an open biological system by providing negative entropy. The same occurs with phytomedicines that act as biological intelligence modulators. They should be used as the first line of treatment in all ailments, since all pathologies, by definition, imply a higher than normal organic entropy. SM postulates that the state of health, H, of an individual, is effectively equal to the product of the strength of each factor H = O × E × I. SM observes that when all three factors are brought back to ideal levels, patients' conditions begin the recovery to normal health.
Institute of Scientific and Technical Information of China (English)
宋芝业; 董杰
2011-01-01
Western learning's coming to the Eastern Asia is a big event in the history of exchanges between China and West,and the axiomatics is the core thinking method of Western learning. Scholars do not have uniform point of view yet about how Chinese mathematicians understood,accepted and researched the axiomatics in Late Ming and Early Qing Dynasties. Through careful analysis of the materials which have not been examined in existing studies,we can know,at the beginning of that Euclid's Elements was printed in China, it was difficult for Chinese mathematicians to understand axiomatic thought, but they respected the Elements very much. In the process of communication between Chinese and Western mathematics, they accepted definitions and axioms,or two basic elements of axiomatics. And then they changed the main line of their studies from explaining Chinese learning by western one to the reverse. In a word, Chinese mathematicians succeeded partially on their target.%西学东渐是中西交流史上的大事,而公理化是西学的核心思想方法.对于中算家如何理解、接受、研究公理化思想,已有研究成果的观点尚不一致.通过研究认为,《几何原本》刊印之初,中算家对公理化难以理解,但对《几何原本》十分尊重,在中西数学会通中,中算家基本接受了公理化中的定义和公理两个要素,并对繁难的推理进行了简化,会通主线由“以中通西”转化为“以西通中”.总体而言,中算家超胜目标获得部分成功.
Normalizability analysis of the generalized quantum electrodynamics from the causal point of view
Bufalo, R; Soto, D E
2015-01-01
The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyse the implication of the gauge invariance onto the model and obtain the respective Ward-Takahashi-Fradkin identities.
Analytic Multi-Regge Theory and the Pomeron in QCD
International Nuclear Information System (INIS)
The formalism of Analytic Multi-Regge Theory is developed as a basis for the study of abstract Critical and Super-Critical Pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the Pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of Field Theory and S-Matrix Theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexographs. Further consequences are distinct Sommerfeld-Watson representations for each hexograph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of ''Reggeon Unitarity'' the Critical Pomeron solution of the Reggeon Field Theory gives the only known ''non-trivial'' unitary high-energy S-Matrix. By exploiting the full structure of multi-Regge amplitudes as the Pomeron becomes Super-Critical, the simultaneous modification of hadrons and the Pomeron can be studies. The result is a completely consistent description of the Super-Critical Pomeron appearing in hadron scattering. Reggeon Unitarity is satisfied in the Super-Critical Phase by the appearance of a massive ''gluon'' (Reggeised vector particle) coupling pair-wise to the Pomeron
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
Quantum Theory and Human Perception of the Macro-World
Directory of Open Access Journals (Sweden)
Diederik eAerts
2014-06-01
Full Text Available We investigate the question of 'why customary macroscopic entities appear to us humans as they do, i.e. as bounded entities occupying space and persisting through time', starting from our knowledge of quantum theory, how it affects the behavior of such customary macroscopic entities, and how it influences our perception of them. For this purpose, we approach the question from three perspectives. Firstly, we look at the situation from the standard quantum angle, more specifically the de Broglie wavelength analysis of the behavior of macroscopic entities, indicate how a problem with spin and identity arises, and illustrate how both play a fundamental role in well-established experimental quantum-macroscopical phenomena, such as Bose-Einstein condensates. Secondly, we analyze how the question is influenced by our result in axiomatic quantum theory, which proves that standard quantum theory is structurally incapable of describing separated entities. Thirdly, we put forward our new `conceptual quantum interpretation', including a highly detailed reformulation of the question to confront the new insights and views that arise with the foregoing analysis. At the end of the final section, a nuanced answer is given that can be summarized as follows. The specific and very classical perception of human seeing -- light as a geometric theory -- and human touching -- only ruled by Pauli's exclusion principle -- plays a role in our perception of macroscopic entities as ontologically stable objects in space. To ascertain quantum behavior in such macroscopic entities, we will need measuring apparatuses capable of its detection. Future experimental research will have to show if sharp quantum effects -- as they occur in smaller entities -- appear to be ontological aspects of customary macroscopic entities. It remains a possibility that standard quantum theory is an incomplete theory, and hence incapable of coping with separated entities, meaning that a more general
Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
Carrasco, John Joseph M; Schlotterer, Oliver
2016-01-01
In this paper we derive the tree-level S-matrix of the effective theory of Goldstone bosons known as the non-linear sigma model (NLSM) from string theory. This novel connection relies on a recent realization of tree-level open-superstring S-matrix predictions as a double copy of super-Yang-Mills theory with Z-theory --- the collection of putative scalar effective field theories encoding all the alpha'-dependence of the open superstring. Here we identify the color-ordered amplitudes of the NLSM as the low-energy limit of abelian Z-theory. This realization also provides natural higher-derivative corrections to the NLSM amplitudes arising from higher powers of alpha' in the abelian Z-theory amplitudes, and through double copy also to Born-Infeld and Volkov-Akulov theories. The Kleiss-Kuijf and Bern-Carrasco-Johansson relations obeyed by Z-theory amplitudes thereby apply to all alpha'-corrections of the NLSM. As such we naturally obtain a cubic-graph parameterization for the abelian Z-theory predictions whose kin...
AdS Field Theory from Conformal Field Theory
Fitzpatrick, A Liam
2012-01-01
We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative `1/N' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well-approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin ...
Negative-frequency modes in quantum field theory
Dickinson, Robert; Millington, Peter
2015-01-01
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.
Matter-enhanced transition probabilities in quantum field theory
International Nuclear Information System (INIS)
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments
Vereshkov, Grigory
2011-01-01
The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically equivalent to the operator equations of quantum theory of gravity with canonical rules of quantization of the gravitational and ghost fields. In its operator formulation, the theory can be used to calculate the graviton S-matrix as well as to describe the quantum evolution of macroscopic system of gravitons in the non-stationary Universe or in the vicinity of relativistic objects. In the S-matrix case, the standard results are obtained. For problems of the second type, the original Heisenberg equations of quantum gravity are converted to a self-consistent system of equations for the metric of the macroscopic spacetime and Heisenberg operators of quantum fields. It is shown that conditions of the compatibility and internal consistency of this system of equations are perform...
Energy Technology Data Exchange (ETDEWEB)
Johnson, J. D. (Prostat, Mesa, AZ); Oberkampf, William Louis; Helton, Jon Craig (Arizona State University, Tempe, AZ); Storlie, Curtis B. (North Carolina State University, Raleigh, NC)
2006-10-01
Evidence theory provides an alternative to probability theory for the representation of epistemic uncertainty in model predictions that derives from epistemic uncertainty in model inputs, where the descriptor epistemic is used to indicate uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. The potential benefit, and hence appeal, of evidence theory is that it allows a less restrictive specification of uncertainty than is possible within the axiomatic structure on which probability theory is based. Unfortunately, the propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for uncertainty, with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of uncertainty in predictions obtained from computationally intensive models. This presentation describes and illustrates a sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Preliminary trials indicate that the presented strategy can be used to propagate uncertainty representations based on evidence theory in analysis situations where naive sampling-based (i.e., unsophisticated Monte Carlo) procedures are impracticable due to computational cost.
Gauge parameter dependence in gauge theories (revised: subsection 2.3)
Kraus, E; Sibold, K.
1994-01-01
Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge parameter dependence algebraically. As application we discuss the anomaly coefficient in the Slavnov-Taylor identity, $S$-matrix elements, the vector two-point-function and the coefficients of renormalization group and Callan-Symanzik equation.
A pedagogical introduction to the Slavnov formulation of quantum Yang-Mills theory
Ghorbani, Hossein
2010-01-01
Over the last few years, Slavnov has proposed a formulation of quantum Yang-Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.
Alebastrov, Y A
2016-01-01
Attention is drawn to the mathematical equality of rights of symmetrical constituents derived affinorr of a vector field in relation to its antisymmetric constituents. In this regard, raises the question not only of equitable accounting, but and mainly question of the real existence of fields, represented by these constituents. In particular, we conclude that the classical electromagnetic field at any point of space\\,-\\,time accompanied, in the General case, independent {\\em physical} field, defined symmetrical derived affinor of 4-potential of classical electrodynamics. Discussed, within the framework of the Bogolyubov and Shirkov axiomatic, a theory of real vector field, clearly and equitably taking into account the symmetric derived affinors this field and found a number of important distinguishing features this model. Despite accounting explicitly gauge-noninvariant constituents, the proposed theory has specialized gauge invariance, which provides, in particular, conservation of electric current. In this ...
Axiomatic Specification of Database Domain Statics
Wieringa, Roel
1987-01-01
In the past ten years, much work has been done to add more structure to database models 1 than what is represented by a mere collection of flat relations (Albano & Cardelli [1985], Albano et al. [1986], Borgida eta. [1984], Brodie [1984], Brodie & Ridjanovic [1984], Brodie & Silva (1982], Codd (1979
On Axiomatic Approaches to Intertwining Operator Algebras
Chen, Ling
2015-01-01
We study intertwining operator algebras introduced and constructed by Huang. In the case that the intertwining operator algebras involve intertwining operators among irreducible modules for their vertex operator subalgebras, a number of results on intertwining operator algebras were given in [H9] but some of the proofs were postponed to an unpublished monograph. In this paper, we give the proofs of these results in [H9] and we formulate and prove results for general intertwining operator algebras without assuming that the modules involved are irreducible. In particular, we construct fusing and braiding isomorphisms for general intertwining operator algebras and prove that they satisfy the genus-zero Moore-Seiberg equations. We show that the Jacobi identity for intertwining operator algebras is equivalent to generalized rationality, commutativity and associativity properties of intertwining operator algebras. We introduce the locality for intertwining operator algebras and show that the Jacobi identity is equi...
Labour motivation : an axiomatic vector model
Kotliarov, Ivan
2008-01-01
En el presente artículo se da una lista de axiomas necesarios para la construcción de una teoría matemática de la motivación humana. Se propone un modelo matemático de la motivación en el trabajo. La motivación se representa como un vector resultante de la motivación parcial generada por grupos específicos de necesidades. El modelo de Vroom se incluye en el modelo propuesto como ejemplo de motivación. Se establece una correlación entre los gastos de motivación, el nivel de motivación y el niv...
Axiomatic approaches to Stevens' magnitude scaling
DEFF Research Database (Denmark)
Zimmer, Karin; Ellermeier, Wolfgang
2006-01-01
) and multiplicativity (the outcome of a sequence of two assessments equals a single assessment if the number associated with the single assessment equals the product of the numbers associated with the sequenced assessments). In an initial test of these axioms in the loudness production of 1 kHz-tones (Ellermeier...
Axiomatic Approach to Solutions of Games
Babichenko, Yakov
2014-01-01
We consider solutions of normal form games that are invariant under strategic equivalence. We consider additional properties that can be expected (or be desired) from a solution of a game, and we observe the following: - Even the weakest notion of individual rationality restricts the set of solutions to be equilibria. This observation holds for all types of solutions: in pure-strategies, in mixed strategies, and in correlated strategies where the corresponding notions of equilibria are pure-N...
Inclusive Fitness Maximization:An Axiomatic Approach
Okasha, Samir; Weymark, John A.; BOSSERT, Walter
2014-01-01
Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of qu...
An axiomatization of the Euclidean compromise solution
Voorneveld, M.; Nouweland, A. van den
2001-01-01
The Euclidean compromise solution in multicriteria optimization is a solution concept that assigns to a feasible set the alternative with minimal Euclidean distance to the utopia point The purpose of this paper is to provide a characterization of the Euclidean compromise solution
Cutkosky rules for superstring field theory
Pius, Roji; Sen, Ashoke
2016-10-01
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.
Nekrasov, Nikita
2004-01-01
We present the evidence for the existence of the topological string analogue of M-theory, which we call Z-theory. The corners of Z-theory moduli space correspond to the Donaldson-Thomas theory, Kodaira-Spencer theory, Gromov-Witten theory, and Donaldson-Witten theory. We discuss the relations of Z-theory with Hitchin's gravities in six and seven dimensions, and make our own proposal, involving spinor generalization of Chern-Simons theory of three-forms. Based on the talk at Strings'04 in Paris.
Black Holes and Spacetime Physics in String/M Theory
Li, Miao
2000-01-01
In addition to briefly reviewing recent progress in studying black hole physics in string/M theory, we describe several robust features pertaining to spacetime physics that one can glean by studying quantum physics of black holes. In particular, we review 't Hooft's S-matrix ansatz which results in a noncommutative horizon. A recent construction of fuzzy AdS2 is emphasized, this is a nice toy model for fuzzy black hole horizon. We demonstrate that this model captures some nonperturbative feat...
Nonrelativistic factorizable scattering theory of multicomponent Calogero-Sutherland model
Ahn, C; Nam, S; Ahn, Changrim; Lee, Kong Ju Bock; Nam, Soonkeon
1995-01-01
We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable S-matrix theory with SU(N)-invariance. We find complete solutions of the Yang-Baxter equations without implementing the crossing symmetry, and one of them is identified with the scattering amplitudes derived from the Schr\\"{o}dinger equation of the Calogero-Sutherland model. This particular solution is of interest in that it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the SU(N)-invariant Yang-Baxter equations.
Resonant Continuum in the Relativistic Mean-Field Theory
Institute of Scientific and Technical Information of China (English)
CAO Li-Gang; MA Zhong-Yu
2002-01-01
Energies, widths and wave functions of the single-particle resonant continuum are determined by solvingscattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativisticmean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. Theresonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as 1 14Sn, 1 16Sn, 1 18Sn,and 120Sn are calculated. Results show that the S-matrix method is a reliable and straightforward way in determiningenergies and widths of resonant states.
Resonant Continuum in the Relativistic Mean－Field Theory
Institute of Scientific and Technical Information of China (English)
CAOLi－Gang; MAZhong－Yu
2002-01-01
Energies,widths and wave functions of the single-particle resonant continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativistic mean-field theory.The relativistic regular and irregular Coulomb wave functions are calculated numerically.The resonance states in the continum for some closed-or sub-closed-shell nucleus in Sn-isotopes,such as 114Sn,116Sn,118Sn,and 120Sn are calculated.Results show that the S-matrix method is a reliable and straightforward way in determining energies and widths of resonant states.
Past, Present, and Future Multi-Regge Theory
White, Alan R
2014-01-01
The connection of the unitary Critical Pomeron to QUD - a unique massless, infra-red fixed-point, left-handed SU(5) field theory that might provide an unconventional underlying unification for the Standard Model, is discussed in the context of developments in past, present, and future multi-regge theory. The QUD bound-state S-Matrix is accessible via elaborate (non-planar) multi-regge theory. Standard Model states and interactions are replicated via massless fermion anomaly dynamics in which configurations of infra-red divergent anomalous gauge boson reggeons play a wee parton vacuum-like role. All particles, including neutrinos, are bound-states with dynamical masses and there is no Higgs field. A color sextet quark sector, that could be discovered at the LHC, produces both Dark Matter and Electroweak Symmetry Breaking and the very small QUD coupling should be reflected in the smallness of neutrino masses. The origin of the Standard Model could be that it is reproducing the unique, unitary, S-Matrix.
Spectral theory of linear operators and spectral systems in Banach algebras
Müller, Vladimir
2003-01-01
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...
First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers
Székely, Gergely
2010-01-01
This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andr\\'eka, Madar\\'asz and N\\'emeti. These extensions include extension to accelerated observers, relativistic dynamics and general relativity; however, its main subject is the extension to accelerated observers (AccRel). One surprising result is that natural extension to accelerated observers is not enough if we want our theory to imply certain experimental facts, such as the twin paradox. Even if we add the whole first-order theory of real numbers to this natural extension, it is still not enough to imply the twin paradox. Nevertheless, that does not mean that this task cannot be carried out within first-order logic since by approximating a second-order logic axiom of real numbers, we introduce a first-order axiom schema that solves the problem. Our theory AccRel nicely fills the gap between special and general relativity theories, and only one natural generalization step is needed to achieve a ...
Marino Beiras, Marcos
2001-01-01
We give an overview of the relations between matrix models and string theory, focusing on topological string theory and the Dijkgraaf--Vafa correspondence. We discuss applications of this correspondence and its generalizations to supersymmetric gauge theory, enumerative geometry and mirror symmetry. We also present a brief overview of matrix quantum mechanical models in superstring theory.
Jara, Pascual; Torrecillas, Blas
1988-01-01
The papers in this proceedings volume are selected research papers in different areas of ring theory, including graded rings, differential operator rings, K-theory of noetherian rings, torsion theory, regular rings, cohomology of algebras, local cohomology of noncommutative rings. The book will be important for mathematicians active in research in ring theory.
Optical potentials in algebraic scattering theory
Energy Technology Data Exchange (ETDEWEB)
Levay, Peter [Institute of Theoretical Physics, Technical University of Budapest, Budapest (Hungary)
1999-02-12
Using the theory of induced representations new realizations for the Lie algebras of the groups SO(2, 1), SO(2, 2), SO(3, 2) are found. The eigenvalue problem of the Casimir operators yield Schroedinger equations with non-Hermitian interaction terms (i.e. optical potentials). For the group SO(2, 2) we have a two-parameter family of (matrix-valued) potentials containing terms of Poeschl-Teller and Gendenshtein type. We calculate the S-matrices for special values of this two-parameter family. In particular we also include a derivation of the S-matrix for the two-dimensional scattering problem on a complex Gendenshtein potential. The canonically transformed realization results in a non-local optical potential. (author)
New Perturbation Theory for Nonstationary Anharmonic Oscillator
Bogdanov, A V; Bogdanov, Alexander V.; Gevorkyan, Ashot S.
1997-01-01
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wave function the variational-iterational method is proposed, that make it possible to correct both the amplitude and the phase of wave function. As an application the first order correction are proposed both for wave function and S-matrix elements for asymmetric perturbation potential of type $V(x,\\tau)=\\alpha (\\tau)x^3+\\beta (\\tau)x^4.$ The transition amplitude ''ground state - ground state'' $W_{00}(\\lambda ;\\rho)$ is analyzed in detail depending on perturbation parameter $\\lambda $ (including strong coupling region $% \\lambda $ $\\sim 1$) and one-dimensional refraction coefficient $\\rho $.
Proof theory of epistemic logic of programs
Maffezioli, Paolo; Naibo, Alberto
2014-01-01
A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system
The resolution of field identification fixed points in diagonal coset theories
International Nuclear Information System (INIS)
The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use ''orbit Lie algebras'' and ''twining characters'', which were introduced in a previous paper. The characters of the primary fields are expressed in terms branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of ''generalized diagonal cosets''. (orig.)
Double Soft Theorems in Gauge and String Theories
Volovich, Anastasia; Zlotnikov, Michael
2015-01-01
We investigate the tree-level S-matrix in gauge theories and open superstring theory with several soft particles. We show that scattering amplitudes with two or three soft gluons of non-identical helicities behave universally in the limit, with multi-soft factors which are not the product of individual soft gluon factors. The results are obtained from the BCFW recursion relations in four dimensions, and further extended to arbitrary dimensions using the CHY formula. We also find new soft theorems for double soft limits of scalars and fermions in N=4 and pure N=2 SYM. Finally, we show that the double-soft-scalar theorems can be extended to open superstring theory without receiving any alpha' corrections.
String theory and the crisis in particle physics
Schrör, B
2006-01-01
In the first section the history of string theory starting from its S-matrix bootstrap predecessor up to Susskind's recent book is critically reviewed. The aim is to understand its amazing popularity which starkly constrasts its fleeting physical content. A partial answer can be obtained from the hegemonic ideological stance which some of its defenders use to present and defend it. The second section presents many arguments showing that the main tenet of string theory which culminated in the phrase that it represents ``the only game in town'' is untenable. It is based on a wrong view about QFT being a mature theory which (apart from some missing details) already reached its closure.
Equivalence of Two Contour Prescriptions in Superstring Perturbation Theory
Sen, Ashoke
2016-01-01
Conventional superstring perturbation theory based on the world-sheet approach gives divergent results for the S-matrix whenever the total center of mass energy of the incoming particles exceeds the threshold of production of any final state consistent with conservation laws. Two systematic approaches have been suggested for dealing with this difficulty. The first one involves deforming the integration cycles over the moduli space of punctured Riemann surfaces into complexified moduli space. The second one treats the amplitude as a sum of superstring field theory Feynman diagrams and deforms the integration contours over loop energies of the Feynman diagram into the complex plane. In this paper we establish the equivalence of the two prescriptions to all orders in perturbation theory. Since the second approach is known to lead to unitary amplitudes, this establishes the consistency of the first prescription with unitarity.
Kawano, T; Hilaire, S
2016-01-01
A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenm\\"{u}ller. The ensemble average of $S$-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [Phys.Rev.C {\\bf 12}, 744 (1975)] using newly parametrized channel degree-of-freedom $\
Nonlocal Regularization For Non-Abelian Gauge Theories For Arbitrary Gauge Parameter
Basu, Anirban; Joglekar, Satish D.
2000-01-01
We study the nonlocal regularization for the non-abelian gauge theories for an arbitrary value of the gauge parameter (\\xi). We show that the procedure for the nonlocalization of field theories established earlier by the original authors, when applied in that form to the Faddeev-Popov effective action in a linear gauge cannot lead to a (\\xi)-independent result for the observables. We then show that an alternate procedure which is simpler can be used and that it leads to the S-matrix elements ...
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
Lindgren, Ingvar
2005-01-01
The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and t...
On space of integrable quantum field theories
Smirnov, F A
2016-01-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields $X_s$, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars $X_s$ are built from the components of the associated conserved currents in a universal way. The first of these scalars, $X_1$, coincides with the composite field $(T{\\bar T})$ built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by $X_1$ are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations $X_s$ are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit...
Perturbative quantum gravity in double field theory
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Perturbative quantum gravity in double field theory
Boels, Rutger H
2015-01-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
The Epstein-Glaser causal approach to the Light-Front QED$_{4}$. I: Free theory
Bufalo, R; Soto, D E
2014-01-01
In this work we present the study of light-front field theories in the realm of axiomatic theory. It is known that when one uses the light-cone gauge pathological poles $\\left( k^{+}\\right) ^{-n}$ arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use rigorous mathematical machinery of distributions combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how analytic representation for propagators arises by requiring general physical properties in the framework of Wightman's formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar, fermionic fields and for t...
Ultraviolet finite quantum field theory on quantum spacetime
International Nuclear Information System (INIS)
We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates qj-qk are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of qj-qk by its expectation value in optimally localized states, while leaving the mean coordinates 1/n(q1 +..+ qn) invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide [9]. Employing an adiabatic switching, we show that the S-matrix is term by term finite. The matrix elements of the transfer matrix are determined, at each order in the perturbative expansion, by kernels with Gaussian decay in the Planck scale. The adiabatic limit and the large scale limit of this theory will be studied elsewhere. (orig.)
International Nuclear Information System (INIS)
Of all supergravity theories, the maximal, i.e., N = 8 in 4-dimension or N = 1 in 11-dimension, theory should perform the unification since it owns the highest degree of symmetry. As to the N = 1 in d = 11 theory, it has been investigated how to compactify to the d = 4 theories. From the phenomenological point of view, local SUSY GUTs, i.e., N = 1 SUSY GUTs with soft breaking terms, have been studied from various angles. The structures of extended supergravity theories are less understood than those of N = 1 supergravity theories, and matter couplings in N = 2 extended supergravity theories are under investigation. The harmonic superspace was recently proposed which may be useful to investigate the quantum effects of extended supersymmetry and supergravity theories. As to the so-called Kaluza-Klein supergravity, there is another possibility. (Mori, K.)
DEFF Research Database (Denmark)
Linder, Stefan; Foss, Nicolai Juul
2015-01-01
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting, and informational conditions, the theory addresses problems of ex...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism....
DEFF Research Database (Denmark)
Linder, Stefan; Foss, Nicolai Juul
Agency theory studies the problems and solutions linked to delegation of tasks from principals to agents in the context of conflicting interests between the parties. Beginning from clear assumptions about rationality, contracting and informational conditions, the theory addresses problems of ex...... agency theory to enjoy considerable scientific impact on social science; however, it has also attracted considerable criticism....
Williams, Jeffrey
1994-01-01
Considers the recent flood of anthologies of literary criticism and theory as exemplifications of the confluence of pedagogical concerns, economics of publishing, and other historical factors. Looks specifically at how these anthologies present theory. Cites problems with their formatting theory and proposes alternative ways of organizing theory…
A critical look at 50 years particle theory from the perspective of the crossing property
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Freie Universitaet, Berlin (Germany). Inst. fuer Theoretische Physik
2010-02-15
The crossing property, which originated more than 5 decades ago in the aftermath of dispersion relations, was the central new concept which opened an S-matrix based line of research in particle theory. Many constructive ideas in particle theory outside perturbative QFT, among them the S-matrix bootstrap program, the dual resonance model and the various stages of string theory have their historical roots in this property. The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrix elements of the S-matrix or form factors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from 'modular localization' including a mathematic appendix on this subject. The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of the true meaning of crossing. The correct interpretation of string theory is that of a dynamic infinite component wave function or pointlike field i.e. a theory which under irreducible Poincare decomposition into an infinite mass/spin tower but which also contains operators which do not commute with the generators of the Poincare group but rather intertwine between different mass/spin levels. (author)
A critical look at 50 years particle theory from the perspective of the crossing property
International Nuclear Information System (INIS)
The crossing property, which originated more than 5 decades ago in the aftermath of dispersion relations, was the central new concept which opened an S-matrix based line of research in particle theory. Many constructive ideas in particle theory outside perturbative QFT, among them the S-matrix bootstrap program, the dual resonance model and the various stages of string theory have their historical roots in this property. The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrix elements of the S-matrix or form factors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from 'modular localization' including a mathematic appendix on this subject. The main content is an in-depth criticism of the dual model and its string theoretic extension. The conceptual flaws of these models are closely related to misunderstandings of the true meaning of crossing. The correct interpretation of string theory is that of a dynamic infinite component wave function or pointlike field i.e. a theory which under irreducible Poincare decomposition into an infinite mass/spin tower but which also contains operators which do not commute with the generators of the Poincare group but rather intertwine between different mass/spin levels. (author)
Harris, Tina
2015-04-29
Grounded theory is a popular research approach in health care and the social sciences. This article provides a description of grounded theory methodology and its key components, using examples from published studies to demonstrate practical application. It aims to demystify grounded theory for novice nurse researchers, by explaining what it is, when to use it, why they would want to use it and how to use it. It should enable nurse researchers to decide if grounded theory is an appropriate approach for their research, and to determine the quality of any grounded theory research they read.
Rowen, Louis H
1991-01-01
This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**""As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of non
Loring, FH
2014-01-01
Summarising the most novel facts and theories which were coming into prominence at the time, particularly those which had not yet been incorporated into standard textbooks, this important work was first published in 1921. The subjects treated cover a wide range of research that was being conducted into the atom, and include Quantum Theory, the Bohr Theory, the Sommerfield extension of Bohr's work, the Octet Theory and Isotopes, as well as Ionisation Potentials and Solar Phenomena. Because much of the material of Atomic Theories lies on the boundary between experimentally verified fact and spec
Soft Theorems from Effective Field Theory
Larkoski, Andrew J; Stewart, Iain W
2014-01-01
The singular limits of massless gauge theory amplitudes are described by an effective theory, called soft-collinear effective theory (SCET), which has been applied most successfully to make all-orders predictions for observables in collider physics and weak decays. At tree-level, the emission of a soft gauge boson at subleading order in its energy is given by the Low-Burnett-Kroll theorem, with the angular momentum operator acting on a lower-point amplitude. For well separated particles at tree-level, we prove the Low-Burnett-Kroll theorem using matrix elements of subleading SCET Lagrangian and operator insertions which are individually gauge invariant. These contributions are uniquely determined by gauge invariance and the reparametrization invariance (RPI) symmetry of SCET. RPI in SCET is connected to the infinite-dimensional asymptotic symmetries of the S-matrix. The Low-Burnett-Kroll theorem is generically spoiled by on-shell corrections, including collinear loops and collinear emissions. We demonstrate t...
A Positive Energy Theorem for $P(X, \\phi)$ Theories
Elder, Benjamin; Khoury, Justin; Tolley, Andrew J
2014-01-01
We descibe a positive energy theorem for Einstein gravity coupled to scalar fields with first-derivative interactions, so-called $P(X, \\phi)$ theories. We offer two independent derivations of this result. The first method introduces an auxiliary field to map the theory to a lagrangian describing two canonical scalar fields, where one can apply a positive energy result of Boucher and Townsend. The second method works directly at the $P(X, \\phi)$ level and uses spinorial arguments introduced by Witten. The latter approach follows that of arXiv:1310.1663, but the end result is less restrictive. We point to the technical step where our derivation deviates from theirs. One of the more interesting implications of our analysis is to show it is possible to have positive energy in cases where dispersion relations following from locality and S-Matrix analyticity are violated.
Massive ghost theories with a line of defects
Mosconi, P
2003-01-01
We study free massive fermionic ghosts, in the presence of an extended line of impurities. The corresponding scattering theory can be formulated by adding to the bulk S-matrix the scattering amplitudes, describing the interactions among the bulk excitations and the defect line (transmission and reflection amplitudes). Explicit expressions for such matrices can be found by solving a bootstrap system of equations (unitarity, crossing and factorization) or, alternatively, relying on a Lagrangian description in terms of Symplectic fermions. In this framework, two distinct defect interactions are proposed (a relevant and a marginal ones), and exact expressions for the correlation functions of the most significant operators in the theory are derived, exploiting the bulk form factors and the matrix elements relative to the defect operator, encoding the entire information about the inhomogeneities.
On purely transmitting defects in affine Toda field theory
Corrigan, E
2007-01-01
Affine Toda field theories with a purely transmitting integrable defect are considered and the model based on a_2 is analysed in detail. After providing a complete characterization of the problem in a classical framework, a suitable quantum transmission matrix, able to describe the interaction between an integrable defect and solitons, is found. Two independent paths are taken to reach the result. One is an investigation of the triangle equations using the S-matrix for the imaginary coupling bulk affine Toda field theories proposed by Hollowood, and the other uses a functional integral approach together with a bootstrap procedure. Evidence to support the results is collected in various ways: for instance, through the calculation of the transmission factors for the lightest breathers. While previous discoveries within the sine-Gordon model motivated this study, there are several new phenomena displayed in the a_2 model including intriguing disparities between the classical and the quantum pictures. For example...
Scattering theory in quantum mechanics and asymptotic completeness
International Nuclear Information System (INIS)
A trial for describing the status of the scattering theory in quantum mechanics is given. The S matrix being defined, its unitarity is a consequence of the asymptotic completeness relation which is one of the mean problems discussed. It is shown that the multichannel scattering theory can be reformulated in the two Hilbert space formalism with a suitable choice of H0 and J (one-body problem and N-body systems). Time-dependent methods try to solve directly the existence problem for wave-operators without recourse to resolvent methods. Emphasis is put on the fact that the success of such a method can be traced to its semi-classical aspect in the sense that the stationary phase method is a special way to single-out from the quantum dynamics the contribution of classical orbits
Chang, CC
2012-01-01
Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods - including classification theory and nonstandard analysis - the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Sko
Jaques, Thomas
2010-01-01
Generative Linguistics can and should be engaged by those with an interest in Translation Studies while developing their own positions on literary theory in general, but translation theory in particular. Generative theory provides empirical evidence for a free, creative mind that can comprehend, read, speak and translate a language. What is being proposed here contrasts radically with the dominant position of this generation's Translation Studies specialists, who freely incorporate Post-struc...
Cox, David A
2012-01-01
Praise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!"—Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galo
Hashiguchi, Koichi
2009-01-01
This book details the mathematics and continuum mechanics necessary as a foundation of elastoplasticity theory. It explains physical backgrounds with illustrations and provides descriptions of detailed derivation processes..
DEFF Research Database (Denmark)
Stein, Irene F.; Stelter, Reinhard
2011-01-01
Communication theory covers a wide variety of theories related to the communication process (Littlejohn, 1999). Communication is not simply an exchange of information, in which we have a sender and a receiver. This very technical concept of communication is clearly outdated; a human being...
International Nuclear Information System (INIS)
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
Manning, Phillip
2011-01-01
The study of quantum theory allowed twentieth-century scientists to examine the world in a new way, one that was filled with uncertainties and probabilities. Further study also led to the development of lasers, the atomic bomb, and the computer. This exciting new book clearly explains quantum theory and its everyday uses in our world.
Lukeš, Jaroslav; Netuka, Ivan; Veselý, Jiří
1988-01-01
Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal...
Bohm, David
1951-01-01
This superb text by David Bohm, formerly Princeton University and Emeritus Professor of Theoretical Physics at Birkbeck College, University of London, provides a formulation of the quantum theory in terms of qualitative and imaginative concepts that have evolved outside and beyond classical theory. Although it presents the main ideas of quantum theory essentially in nonmathematical terms, it follows these with a broad range of specific applications that are worked out in considerable mathematical detail. Addressed primarily to advanced undergraduate students, the text begins with a study of t
Lubliner, Jacob
2008-01-01
The aim of Plasticity Theory is to provide a comprehensive introduction to the contemporary state of knowledge in basic plasticity theory and to its applications. It treats several areas not commonly found between the covers of a single book: the physics of plasticity, constitutive theory, dynamic plasticity, large-deformation plasticity, and numerical methods, in addition to a representative survey of problems treated by classical methods, such as elastic-plastic problems, plane plastic flow, and limit analysis; the problem discussed come from areas of interest to mechanical, structural, and
DEFF Research Database (Denmark)
Smith, Shelley
This paper came about within the context of a 13-month research project, Focus Area 1 - Method and Theory, at the Center for Public Space Research at the Royal Academy of the Arts School of Architecture in Copenhagen, Denmark. This project has been funded by RealDania. The goals of the research...... project, Focus Area 1 - Method and Theory, which forms the framework for this working paper, are: * To provide a basis from which to discuss the concept of public space in a contemporary architectural and urban context - specifically relating to theory and method * To broaden the discussion of the concept...
Andrews, George E
1994-01-01
Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl
Directory of Open Access Journals (Sweden)
Kathleen Holtz Deal
2007-05-01
Full Text Available Psychodynamic theory, a theory of personality originated by Sigmund Freud, has a long and complex history within social work and continues to be utilized by social workers. This article traces the theory’s development and explains key concepts with an emphasis on its current relational focus within object relations theory and self-psychology. Empirical support for theoretical concepts and the effectiveness of psychodynamic therapies is reviewed and critiqued. Future directions are discussed, including addressing cultural considerations, increasing research, and emphasizing a relational paradigm
Hočevar, Mitja
2015-01-01
This BCs thesis deals with topics from graph theory. Ramsey theory in its most basic form deals with the problem of determining the minimal positive integer, such that for any edge-coloring of the complete graph of this size with a prescribed number of colors one can find a subgraph of predefined size all of whose edges are of the same colour. These minimal sizes are called Ramsey numbers. In this BCs thesis we present basic notions of graph theory needed to understand the basic theorem of...
Victor, Oluwafemi Oludu
2015-01-01
From ages to ages there had been expectation of individuals on a specific predictions and future occurrences. So also in a game, different participant that involves in those specified game have their various expectations of the results or the output of the game they are involved in. That is why we need a mathematical theory that helps in prediction of the future expectations in our day to day activities. Therefore the Martingale Theory is a very good theory that explains and dissects the expe...
The Epstein–Glaser causal approach to the light-front QED4. I: Free theory
International Nuclear Information System (INIS)
In this work we present the study of light-front field theories in the realm of the axiomatic theory. It is known that when one uses the light-cone gauge pathological poles (k+)−n arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have the correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use of rigorous mathematical machinery of the distributional theory combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how the analytic representation for propagators arises by requiring general physical properties within the framework of Wightman’s formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar and fermionic fields, as well as for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein–Glaser causal method in order to have a mathematical rigorous description of the free propagators of the theory, allowing us to discuss a general treatment for propagators of the type (k+)−n. Afterwards, we show that at given conditions our results reproduce known prescriptions in the literature. - Highlights: • We develop the analytic representation for propagators in Wightman’s framework. • We make use of the analytic representation to obtain equal-time (anti)commutation relations in the light-front. • We derive the free Feynman propagators for the light-front quantum electrodynamics in the Epstein–Glaser approach. • We determine a general expression for the propagator associated to the light-cone poles (k+)−n in the causal approach
Hodges, Wilfrid
1993-01-01
An up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians.
International Nuclear Information System (INIS)
This report discusses concepts in nuclear theory such as: neutrino nucleosynthesis; double beta decay; neutrino oscillations; chiral symmetry breaking; T invariance; quark propagator; cold fusion; and other related topics
DEFF Research Database (Denmark)
Hjørland, Birger
2009-01-01
Concept theory is an extremely broad, interdisciplinary and complex field of research related to many deep fields with very long historical traditions without much consensus. However, information science and knowledge organization cannot avoid relating to theories of concepts. Knowledge...... organizing systems (e.g. classification systems, thesauri and ontologies) should be understood as systems basically organizing concepts and their semantic relations. The same is the case with information retrieval systems. Different theories of concepts have different implications for how to construe......). It is also argued that the historicist and pragmatist understandings of concepts are the most fruitful views and that this understanding may be part of a broader paradigm shift that is also beginning to take place in information science. The importance of historicist and pragmatic theories of concepts...
International Nuclear Information System (INIS)
A series of lectures on plasma theory with the main headings: introduction; charged particles moving in em fields; the liquid model; transport phenomena in the plasma; wave propagation in plasmas; plasma instabilities. 57 figs. (qui)
DEFF Research Database (Denmark)
Carroll, Joseph; Clasen, Mathias; Jonsson, Emelie;
2015-01-01
Biocultural theory is an integrative research program designed to investigate the causal interactions between biological adaptations and cultural constructions. From the biocultural perspective, cultural processes are rooted in the biological necessities of the human life cycle: specifically huma...
Nel, Louis
2016-01-01
This book presents a detailed, self-contained theory of continuous mappings. It is mainly addressed to students who have already studied these mappings in the setting of metric spaces, as well as multidimensional differential calculus. The needed background facts about sets, metric spaces and linear algebra are developed in detail, so as to provide a seamless transition between students' previous studies and new material. In view of its many novel features, this book will be of interest also to mature readers who have studied continuous mappings from the subject's classical texts and wish to become acquainted with a new approach. The theory of continuous mappings serves as infrastructure for more specialized mathematical theories like differential equations, integral equations, operator theory, dynamical systems, global analysis, topological groups, topological rings and many more. In light of the centrality of the topic, a book of this kind fits a variety of applications, especially those that contribute to ...
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
On the General Theory of Production Functions
Directory of Open Access Journals (Sweden)
Catalin Angelo Ioan
2012-10-01
Full Text Available In this paper we will study from an axiomatic point of view the production functions. Also we will define the main indicators of a production function, extending the classical definitions to n inputs and introducing other new. We will modify the notion of global average productivity and replace it with more realistic indicators. On the other hand, the notion of global rate of substitution will be introduced to the analysis of n goods.
Beyond gauge theory: positivity and causal localization in the presence of vector mesons
Schroer, Bert
2016-07-01
The Hilbert space formulation of interacting s=1 vector-potentials stands is an interesting contrast with the point-local Krein space setting of gauge theory. Already in the absence of interactions the Wilson loop in a Hilbert space setting has a topological property which is missing in the gauge-theoretic description (Haag duality, Aharonov-Bohm effect); the conceptual differences increase in the presence of interactions. The Hilbert space positivity weakens the causal localization properties of interacting fields, which results in the replacement of the gauge-variant point-local matter fields in Krein space by string-local physical fields in Hilbert space. The gauge invariance of the perturbative S-matrix corresponds to its independence of the space-like string direction of its interpolating fields. In contrast to gauge theory, whose direct physical range is limited to a gauge-invariant perturbative S-matrix and local observables, its Hilbert space string-local counterpart is a full-fledged quantum field theory (QFT). The new setting reveals that the Lie structure of self-coupled vector mesons results from perturbative implementation of the causal localization principles of QFT.
Effective theories of universal theories
Wells, James D.; Zhang, Zhengkang
2016-01-01
It is well-known but sometimes overlooked that constraints on the oblique parameters (most notably S and T parameters) are generally speaking only applicable to a special class of new physics scenarios known as universal theories. In the effective field theory (EFT) framework, the oblique parameters should not be associated with Wilson coefficients in a particular operator basis, unless restrictions have been imposed on the EFT so that it describes universal theories. We work out these restrictions, and present a detailed EFT analysis of universal theories. We find that at the dimension-6 level, universal theories are completely characterized by 16 parameters. They are conveniently chosen to be: 5 oblique parameters that agree with the commonly-adopted ones, 4 anomalous triple-gauge couplings, 3 rescaling factors for the h 3, hf f , hV V vertices, 3 parameters for hV V vertices absent in the Standard Model, and 1 four-fermion coupling of order y f 2 . All these parameters are defined in an unambiguous and basis-independent way, allowing for consistent constraints on the universal theories parameter space from precision electroweak and Higgs data.
Possibility Theory versus Probability Theory in Fuzzy Measure Theory
Directory of Open Access Journals (Sweden)
Parul Agarwal
2015-05-01
Full Text Available The purpose of this paper is to compare probability theory with possibility theory, and to use this comparison in comparing probability theory with fuzzy set theory. The best way of comparing probabilistic and possibilistic conceptualizations of uncertainty is to examine the two theories from a broader perspective. Such a perspective is offered by evidence theory, within which probability theory and possibility theory are recognized as special branches. While the various characteristic of possibility theory within the broader framework of evidence theory are expounded in this paper, we need to introduce their probabilistic counterparts to facilitate our discussion.
Stewart, Ian
2003-01-01
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches.To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the g
Effective theories of universal theories
Wells, James D
2015-01-01
It is well-known but sometimes overlooked that constraints on the oblique parameters (most notably $S$ and $T$ parameters) are only applicable to a special class of new physics scenarios known as universal theories. In the effective field theory (EFT) framework, the oblique parameters should not be associated with Wilson coefficients in a particular operator basis, unless restrictions have been imposed on the EFT so that it describes universal theories. We work out these restrictions, and present a detailed EFT analysis of universal theories. We find that at the dimension-6 level, universal theories are completely characterized by 16 parameters. They are conveniently chosen to be: 5 oblique parameters that agree with the commonly-adopted ones, 4 anomalous triple-gauge couplings, 3 rescaling factors for the $h^3$, $hff$, $hVV$ vertices, 3 parameters for $hVV$ vertices absent in the Standard Model, and 1 four-fermion coupling of order $y_f^2$. All these parameters are defined in an unambiguous and basis-indepen...
New perturbation theory for the nonstationary anharmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Bogdanov, Alexander V. [Instiutute for High-Performance Computing and Data Bases, St. Petersburg (Russian Federation); Gevorkyan, Ashot S. [Instiutute for High-Performance Computing and Data Bases, St. Petersburg (Russian Federation); Institute of Applied Problems of Physics NAS of Armenia, Yerevan (Armenia)
1997-11-07
The new perturbation theory for the problem of the nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zeroth-order approximation, the exact wavefunction of the harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wavefunctions, the variational-iterational method is proposed, which makes it possible to correct both the amplitude and phase of the wavefunction. As an application, the first-order corrections are proposed for both the wavefunction and S-matrix elements for asymmetric perturbation potential of the type V({chi}, {tau})={alpha}({tau}){chi}{sup 3}+{beta}({tau}){chi}{sup 4}. The transition amplitude 'ground state-ground state' W{sub 00}({lambda}:{rho}) is analysed in detail depending on the perturbation parameter {lambda} (including the strong coupling region {lambda}{approx}1) and the one-dimensional refraction coefficient {rho}. (author)
Lenz, Alexander
2016-01-01
We set the scene for theoretical issues in charm physics that were discussed at CHARM 2016 in Bologna. In particular we emphasize the importance of improving our understanding of standard model contributions to numerous charm observables and we discuss also possible tests of our theory tools, like the Heavy Quark Expansion via the lifetime ratios of $D$-mesons
DEFF Research Database (Denmark)
Monthoux, Pierre Guillet de; Statler, Matt
2014-01-01
The recent Carnegie report (Colby, et al., 2011) characterizes the goal of business education as the development of practical wisdom. In this chapter, the authors reframe Scharmer’s Theory U as an attempt to develop practical wisdom by applying certain European philosophical concepts. Specifically...
R. Veenhoven (Ruut)
2014-01-01
markdownabstract__Abstract__ Assumptions Livability theory involves the following six key assumptions: 1. Like all animals, humans have innate needs, such as for food, safety, and companionship. 2. Gratification of needs manifests in hedonic experience. 3. Hedonic experience determines how much we
Plummer, MD
1986-01-01
This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.
Logarithmic conformal field theory, log-modular tensor categories and modular forms
Creutzig, Thomas
2016-01-01
The two pillars of rational conformal field theory and rational vertex operator algebras are modularity of characters on the one hand and its interpretation of modules as objects in a modular tensor category on the other one. Overarching these pillars is the Verlinde formula. In this paper we consider the more general class of logarithmic conformal field theories and $C_2$-cofinite vertex operator algebras. We suggest that their modular pillar are trace functions with insertions corresponding to intertwiners of the projective cover of the vacuum, and that the categorical pillar are finite tensor categories $\\mathcal C$ which are ribbon and whose double is isomorphic to the Deligne product $\\mathcal C\\otimes \\mathcal C^{opp}$. Overarching these pillars is then a logarithmic variant of Verlinde's formula. Numerical data realizing this are the modular $S$-matrix and modified traces of open Hopf links. The representation categories of $C_2$-cofinite and logarithmic conformal field theories that are fairly well un...
Quantum scattering theory in light of an exactly solvable model with rearrangement collisions
International Nuclear Information System (INIS)
We present an exactly solvable quantum field theory which allows rearrangement collisions. We solve the model in the relevant sectors and demonstrate the orthonormality and completeness of the solutions, and construct the S-matrix. In light of the exact solutions constructed, we discuss various issues and assumptions in quantum scattering theory, including the isometry of the Moeller wave matrix, the normalization and completeness of asymptotic states, and the nonorthogonality of basis states. We show that these common assertions are not obtained in this model. We suggest a general formalism for scattering theory which overcomes these and other shortcomings and limitations of the existing formalisms in the literature. copyright 1996 American Institute of Physics
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Schlotterer, Oliver
2016-01-01
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension alpha' and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
On the microscopic foundation of scattering theory; Zur mikroskopischen Begruendung der Streutheorie
Energy Technology Data Exchange (ETDEWEB)
Moser, T.
2007-02-26
The aim of the thesis is to give a contribution to the microscopic foundation of scattering theory, i. e. to show, how the asymptotic formalism of scattering theory with objects like the S-matrix as well the initial and final asymptotics {psi}{sub in} and {psi}{sub out} can be derived from a microscopic description of the basic system. First the final statistics from a N-particle system through farly distant surfaces is derived. Thereafter we confine us to the 1-particle scattering and apply the final statistics in order to derive the scattering cross section from a microscopical description of the scattering situation. The basing dynamics are Bohm's mechanics, a theory on the motion of point particles, which reproduces all results of nonrelativistic quantum mechanics.
Hashiguchi, Koichi
2014-01-01
This book was written to serve as the standard textbook of elastoplasticity for students, engineers and researchers in the field of applied mechanics. The present second edition is improved thoroughly from the first edition by selecting the standard theories from various formulations and models, which are required to study the essentials of elastoplasticity steadily and effectively and will remain universally in the history of elastoplasticity. It opens with an explanation of vector-tensor analysis and continuum mechanics as a foundation to study elastoplasticity theory, extending over various strain and stress tensors and their rates. Subsequently, constitutive equations of elastoplastic and viscoplastic deformations for monotonic, cyclic and non-proportional loading behavior in a general rate and their applications to metals and soils are described in detail, and constitutive equations of friction behavior between solids and its application to the prediction of stick-slip phenomena are delineated. In additi...
2015-01-01
A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.
Helms, Lester L
2014-01-01
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In ...
Milgrom, Mordehai
2014-01-01
A general account of MOND theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration -- below an acceleration constant a0 -- where dynamics become scale invariant. I list some of the salient predictions of these tenets. The special role of a0 and its significance are then discussed. In particular, I stress its coincidence with cosmologically relevant accelerations. The deep-MOND limit and the consequences of its scale ...
Friedrich, Harald
2016-01-01
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is k...
Theory of the Trojan-Horse Method
Baur, G; Baur, Gerhard; Typel, Stefan
2004-01-01
The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two-body and three-body cross sections becomes very transparent. Applications of the Trojan Horse Method are discussed. It is of special interest that electron screening corrections are negligible due...
Theory of the Trojan-Horse Method
Typel, S
2003-01-01
The Trojan-Horse method is an indirect approach to determine the energy dependence of S-factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effective suppression of the Coulomb barrier at low energies for the astrophysical reaction leading to finite cross sections at the threshold of the two-body reaction. In a modified plane wave approximation the relation between the two-body and three-body cross sections becomes very transparent. The appearing Trojan-Horse integrals are studied in detail.
Nielsen, Holger B
2014-01-01
Bosonic string theory with the possibility for an arbitrary number of strings - i.e. a string ?eld theory - is formulated by a Hilbert space (a Fock space), which is just that for massless noninteracting scalars. We earlier presented this novel type of string ?eld theory, but now we show that it leads to scattering just given by the Veneziano model amplitude. Generalization to strings with fermion modes would presumably be rather easy. It is characteristic for our formulation /model that: 1) We have thrown away some null set of information compared to usual string ?eld theory, 2)Formulated in terms of our \\objects" (= the non-interacting scalars) there is no interaction and essentially no time development(Heisenberg picture), 3) so that the S-matrix is in our Hilbert space given as the unit matrix, S=1, and 4) the Veneziano scattering amplitude appear as the overlap between the initial and the ?nal state described in terms of the \\objects". 5) The integration in the Euler beta function making up the Veneziano...
Goldie, Charles M
1991-01-01
This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.
Merris, Russell
2001-01-01
A lively invitation to the flavor, elegance, and power of graph theoryThis mathematically rigorous introduction is tempered and enlivened by numerous illustrations, revealing examples, seductive applications, and historical references. An award-winning teacher, Russ Merris has crafted a book designed to attract and engage through its spirited exposition, a rich assortment of well-chosen exercises, and a selection of topics that emphasizes the kinds of things that can be manipulated, counted, and pictured. Intended neither to be a comprehensive overview nor an encyclopedic reference, th
Diestel, Reinhard
2012-01-01
HauptbeschreibungThis standard textbook of modern graph theory, now in its fourth edition, combinesthe authority of a classic with the engaging freshness of style that is the hallmarkof active mathematics. It covers the core material of the subject with concise yetreliably complete proofs, while offering glimpses of more advanced methodsin each field by one or two deeper results, again with proofs given in full detail.The book can be used as a reliable text for an introductory course, as a graduatetext, and for self-study. Rezension"Deep, clear, wonderful. This is a serious book about the
DEFF Research Database (Denmark)
Bertelsen, Olav Wedege; Bødker, Susanne
2003-01-01
The rise of personal computer challenged mainframes systems for automation of existing work routine. Furthermore it brought forth a need to focus on how to work on materials and objects through the computer. In search for theoretical and methodical perspectives it seemed promising to turn towards...... the young HCI research tradition. But HCI was already facing problems: lack of consideration for other aspects of human behavior, for interaction with other people, for culture. Cognitive science-based theories lacked means to address several issues that came out of the empirical projects....
Can we make the second incompleteness theorem coordinate free?
de Visser, A.
2008-01-01
Is it possible to give a coordinate free formulation of the Second Incompleteness Theorem? We pursue one possible approach to this question. We show that (i) cutfree consistency for finitely axiomatized theories can be uniquely characterized modulo EA-provable equivalence, (ii) consistency for finitely axiomatized sequential theories can be uniquely characterized modulo EA-provable equivalence. The case of infinitely axiomatized ce theories is more delicate. We carefully discuss this in the p...
International Nuclear Information System (INIS)
Techniques used in conventional project appraisal are mathematically very simple in comparison to those used in reservoir modelling, and in the geosciences. Clearly it would be possible to value assets in mathematically more sophisticated ways if it were meaningful and worthwhile so to do. The DCf approach in common use has recognized limitations; the inability to select a meaningful discount rate being particularly significant. Financial Theory has advanced enormously over the last few years, along with computational techniques, and methods are beginning to appear which may change the way we do project evaluations in practice. The starting point for all of this was a paper by Black and Scholes, which asserts that almost all corporate liabilities can be viewed as options of varying degrees of complexity. Although the financial presentation may be unfamiliar to engineers and geoscientists, some of the concepts used will not be. This paper outlines, in plain English, the basis of option pricing theory for assessing the market value of a project. it also attempts to assess the future role of this type of approach in practical Petroleum Exploration and Engineering economics. Reference is made to relevant published Natural Resource literature
International Nuclear Information System (INIS)
With reference to highly debated sustainable growth strategies to counter pressing interrelated global environmental and socio-economic problems, this paper reviews economic and resource development theories proposed by classical and neoclassical economists. The review evidences the growing debate among public administration decision makers regarding appropriate methods to assess the worth of natural resources and ecosystems. Proposed methods tend to be biased either towards environmental protection or economic development. Two major difficulties in the effective implementation of sustainable growth strategies are also evidenced - the management of such strategies would require appropriate revisions to national accounting systems, and the dynamic flow of energy and materials between an economic system and the environment would generate a sequence of unstable structures evolving in a chaotic and unpredictable way
St-Amant, Patrick
2010-01-01
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization of the fundamental theorem of arithmetic for hyperoperations. We also give a generalized definition of the prime numbers that are associated to an arbitrary n-ary operation and take a few steps toward the development of its modulo arithmetic by investigating a generalized form of Fermat's little theorem. Those constructions give an interesting way to interpret diophantine equations and we will see that the uniqueness of factorization under an arbitrary operation can be linked with the Riemann zeta function. This language of generalized primes and composites can be used to restate and extend certain problems such as the Goldbach conjecture.
Chong, Chi Tat; Friedman, Sy D.
1996-01-01
In this article, intended for the Handbook of Recursion Theory, we survey recursion theory on the ordinal numbers, with sections devoted to $\\alpha$-recursion theory, $\\beta$-recursion theory and the study of the admissibility spectrum.
a Classical Isodual Theory of Antimatter and its Prediction of Antigravity
Santilli, Ruggero Maria
An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatment of matter and antimatter in due time, and as the classical foundations of an axiomatically consistent inclusion of gravitation in unified gauge theories recently appeared elsewhere, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with corresponding formulations at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is antiautomorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also antiautomorphic (and more generally, antiisomorphic), yet it is applicable beginning at the classical level and then persists at the quantum level where it becomes equivalent to charge conjugation. We therefore present, apparently for the first time, the classical isodual theory of antimatter, we identify the physical foundations of the theory as being the novel isodual Galilean, special and general relativities, and we show the compatibility of the theory with all available classical experimental data on antimatter. We identify the classical foundations of the prediction of antigravity for antimatter in the field of matter (or vice-versa) without any claim on its validity, and defer its resolution to specifically identified experiments. We identify the novel, classical, isodual electromagnetic waves which are predicted to be emitted by antimatter, the so-called space-time machine based on a novel non-Newtonian geometric propulsion, and other implications of the theory. We also introduce, apparently for the first time, the isodual space and time inversions and show that they are nontrivially different than the conventional ones, thus
String-theoretic breakdown of effective field theory near black hole horizons
Dodelson, Matthew
2015-01-01
We investigate the validity of the equivalence principle near horizons in string theory, analyzing the breakdown of effective field theory caused by longitudinal string spreading effects. An experiment is set up where a detector is thrown into a black hole a long time after an early infalling string. Light cone gauge calculations, taken at face value, indicate a detectable level of root-mean-square longitudinal spreading of the initial string as measured by the late infaller. This results from the large relative boost between the string and detector in the near horizon region, which develops automatically despite their modest initial energies outside the black hole and the weak curvature in the geometry. We subject this scenario to basic consistency checks, using these to obtain a relatively conservative criterion for its detectability. In a companion paper, we exhibit longitudinal nonlocality in well-defined gauge-invariant S-matrix calculations, obtaining results consistent with the predicted spreading albe...
General Theories of Regulation
Hertog, J.A. den
1999-01-01
This chapter makes a distinction between three types of theories of regulation: public interest theories, the Chicago theory of regulation and the public choice theories. The Chicago theory is mainly directed at the explanation of economic regulation; public interest theories and public choice theor
Polchinski, Joseph
1994-01-01
The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: 1. Conformal Field Theory 2. String Theory 3. Vacua and Dualities 4. String Field Theory or Not String Field Theory 5. Matrix Models
Review of Hydroelasticity Theories
DEFF Research Database (Denmark)
Chen, Xu-jun; Wu, You-sheng; Cui, Wei-cheng;
2006-01-01
Existing hydroelastic theories are reviewed. The theories are classified into different types: two-dimensional linear theory, two-dimensional nonlinear theory, three-dimensional linear theory and three-dimensional nonlinear theory. Applications to analysis of very large floating structures (VLFS...
Modular localization and the holistic structure of causal quantum theory, a historical perspective
Schroer, Bert
2015-02-01
Recent insights into the conceptual structure of localization in QFT (modular localization) led to clarifications of old unsolved problems. The oldest one is the Einstein-Jordan conundrum which led Jordan in 1925 to the discovery of quantum field theory. This comparison of fluctuations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jordan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the localization region places localization in QFT into a sharp contrast with quantum mechanics and justifies the attribute "holstic". In fact it positions the E-J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from "modular localization" also leads to a revision of the conceptual origin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suffered from incorrect use in the S-matrix settings of the dual model and string theory. The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and localization and presenting alternative solutions based on the use of stringlocal fields in Hilbert space. Among other things this leads to a reformulation of the Englert-Higgs symmetry breaking mechanism.
Inbasekar, Karthik; Mazumdar, Subhajit; Minwalla, Shiraz; Umesh, V; Yokoyama, Shuichi
2015-01-01
We study the most general renormalizable ${\\cal N}=1$ $U(N)$ Chern-Simons gauge theory coupled to a single (generically massive) fundamental matter multiplet. At leading order in the 't Hooft large $N$ limit we present computations and conjectures for the $2 \\times 2$ $S$ matrix in these theories; our results apply at all orders in the 't Hooft coupling and the matter self interaction. Our $S$ matrices are in perfect agreement with the recently conjectured strong weak coupling self duality of this class of theories. The consistency of our results with unitarity requires a modification of the usual rules of crossing symmetry in precisely the manner anticipated in arXiv:1404.6373, lending substantial support to the conjectures of that paper. In a certain range of coupling constants our $S$ matrices have a pole whose mass vanishes on a self dual codimension one surface in the space of couplings.
Approaches to high energy physics
International Nuclear Information System (INIS)
An overview of the present state of the art in high energy physics is presented highlighting the developments in hadron physics, field theory and nuclear democracy. To begin with, description of 'hadrons' is given on the basis of quantum electrodynamics. The role of the quantum numbers assigned to quarks are explained. Lepton-hadron scattering and hadron-hadron scattering are discussed. The quark-parton model of the nucleon is explained. The recently discovered Psi resonances and the consequent introduction of new quantum number 'charm' are mentioned. Next, Yang-Mills Gauge theories, the unification of weak and electromagnetic interactions and the concept of weak neutral currents are discussed. Gauge theories of strong interactions, quantum chromodynamics and the concept of 'Bags' are explained. Magnetic monopoles (solitons) are described with basis on non-linear field theories. High energy bounds in the axiomatic field theory are formulated. The general properties of S-matrix elements obtained in a quantum local field theory are mentioned. Lastly, the shifting of the reliance on field concepts to other approaches, specially through S-matrix and the application of Regge poles and cuts is explained. The duality hypothesis is postulated to explain processes such as pp→pp with the 'pomeron exchange' concept. Dual models of strong interactions are discussed. Future trends are indicated. (A.K.)
THEORIES OF CORPORATE GOVERNANCE
Directory of Open Access Journals (Sweden)
Sorin Nicolae BORLEA
2013-03-01
Full Text Available This study attempts to provide a theoretical framework for the corporate governance debate. The review of various corporate governance theories enhances the major objective of corporate governance which is maximizing the value for shareholders by ensuring good social and environment performances. The theories of corporate governance are rooted in agency theory with the theory of moral hazard’s implications, further developing within stewardship theory and stakeholder theory and evolving at resource dependence theory, transaction cost theory and political theory. Later, to these theories was added ethics theory, information asymmetry theory or the theory of efficient markets. These theories are defined based on the causes and effects of variables such as: the configuration of the board of directors, audit committee, independence of managers, the role of top management and their social relations beyond the legal regulatory framework. Effective corporate governance requires applying a combination
Proceedings of the 14. Claude Itzykson Meeting-2009 recent advances in string theory
International Nuclear Information System (INIS)
This document is made up of the slides of the presentations. The titles of the 20 presentations are the following: 1) On d=3 Yang-Mills Chern-Simons theories with 'fractional branes' and their gravity duals; 2) Holography and the S-Matrix; 3) Torsional heterotic geometries; 4) Spin chains from the topological AdS5xS5 string; 5) Harmony of Scattering Amplitudes: from N=4 Super-Yang-Mills Theory to N=8 Supergravity; 6) Quantum aspects of black holes; 7) Black-folds; 8) Supersymmetric String and Field Theory Scattering Amplitudes; 9) Quantum bosons for holographic superconductors; 10) The Point of E8 in F-theory GUTs; 11) Gauge/gravity duality and particle physics; 12) Coupling M2-branes to Background Fields; 13) Compactifications and Generalized Geometries; 14) Nonperturbative aspects of the topological string; 15) Lessons from the information paradox: 16) Inflation in String Theory; 17) Holographic descriptions of quantum liquids; 18) Holography from CFT; 19) Black hole hair removal; and 20) Type IIB GUT vacua and their F-theory uplift
A quantization of twistor Yang-Mills theory through the background field method
Boels, R
2007-01-01
Four dimensional Yang-Mills theory formulated through an action on twistor space has a larger gauge symmetry than the usual formulation, which in previous work was shown to allow a simple gauge transformation between text-book perturbation theory and the Cachazo-Svrcek-Witten rules. In this paper we study non-supersymmetric twistor Yang-Mills theory at loop level using the background field method. For an appropriate partial quantum field gauge choice it is shown the calculation of the effective action is equivalent to (the twistor lift of) the calculation in ordinary Yang-Mills theory in the Chalmers and Siegel formulation to all orders in perturbation theory. A direct consequence is that the twistor version of Yang-Mills theory is just as renormalizable in this particular gauge. As applications an explicit calculation of the Yang-Mills beta function and some preliminary investigations into using the formalism to calculate S-matrix elements at loop level are presented. In principle the technique described in ...
Introducing Novel Graph Database Cloud Computing For Efficient Data Management
Dr.Arunkumar B R,; Komala R
2015-01-01
Graph theory stands as a natural mathematical model for cloud networks, axiomatic cloud theory further defines the cloud with formal mathematical model. keeping axiomatic theory as a basis, paper proposes bipartite cloud and proposes graph database model as a suitable database for data management .it is highlighted that perfect matching in bipartite cloud can enhance searching in bipartite cloud.
The Global Approach to Quantum Field Theory
International Nuclear Information System (INIS)
theory. This is the so-called global approach to quantum field theory where time does not play any particular role, and quantization is then naturally realized covariantly using tools such as the Peierls bracket (a covariant generalization of Poisson bracket), the Schwinger variational principle and Feynman sums over histories. However, it should be noted that the boycott of canonical methods by DeWitt is not total: when he judges they genuinely illuminate the physics of a problem, he does not hesitate to descend from the global point of view and to use them. In a few words, we have in fact described the research program initiated by DeWitt forty years ago, which has progressively evolved in order to take into account the latest development of gauge theories. While the Les Houches Lectures of 1963 were mainly concentrated on the formal structure and the quantization of Yang--Mills and gravitational fields, the present book also deals with more general gauge theories including those with open gauge algebras and structure functions, and therefore supergravity theories. More precisely, the book, more than a thousand pages in length, consists of eight parts and is completed by six appendices where certain technical aspects are singled out. An enormous variety of topics is covered, including the invariance transformations of the action functional, the Batalin-Vilkovisky formalism, Green's functions, the Peierls bracket, conservation laws, the theory of measurement, the Everett (or many worlds) interpretation of quantum mechanics, decoherence, the Schwinger variational principle and Feynm an functional integrals, the heat kernel, aspects of quantization for linear systems in stationary and non-stationary backgrounds, the S-matrix, the background field method, the effective action and the Vilkovisky-DeWitt formalism, the quantization of gauge theories without ghosts, anomalies, black holes and Hawking radiation, renormalization, and more. It should be noted that DeWitt's book
de Boer, Jan
2002-01-01
An overview of some of the developments in string theory over the past two years is given, focusing on four topics: realistic (standard model like) models from string theory, geometric engineering and theories with fluxes, the gauge theory-gravity correspondence, and time dependent backgrounds and string theory. Plenary talk at ICHEP'02, Amsterdam, July 24-31, 2002.
Müller, Gert; Sacks, Gerald
1990-01-01
These proceedings contain research and survey papers from many subfields of recursion theory, with emphasis on degree theory, in particular the development of frameworks for current techniques in this field. Other topics covered include computational complexity theory, generalized recursion theory, proof theoretic questions in recursion theory, and recursive mathematics.
Ranked additive utility representations of gambles : Old and new axiomatizations
Luce, RD; Marley, AAJ
2005-01-01
A number of classical as well as quite new utility representations for gains are explored with the aim of understanding the behavioral conditions that are necessary and sufficient for various subfamilies of successively stronger representations to hold. Among the utility representations are: ranked
A Sound and Complete Axiomatization of Majority-n Logic
Amarù, Luca; Gaillardon, Pierre-Emmanuel; Chattopadhyay, Anupam; De Micheli, Giovanni
2015-01-01
Manipulating logic functions via majority operators recently drew the attention of researchers in computer science. For example, circuit optimization based on majority operators enables superior results as compared to traditional logic systems. Also, the Boolean satisfiability problem finds new solving approaches when described in terms of majority decisions. To support computer logic applications based on majority a sound and complete set of axioms is required. Most of the recent advances in...
Pharmacovigilance Among Surgeons and in Surgical Wards: Overlooked or Axiomatic?
Rodrigues, Gabriel Sunil; Khan, Sohil Ahmed
2010-01-01
To review the status of pharmacovigilance system among surgeons and in surgical wards with recommendations. Literature search using MEDLINE, cross-reference of published data and review of World Health Organization—Pharmacovigilance transcripts. Pharmacovigilance system is still in its infancy among surgeons and in surgical wards. No major studies have been published addressing this issue, till date. Surgeons are professionals least likely to report adverse drug reactions. Moreover widespread...
Feasible elimination procedures in social choice : an axiomatic characterization
Peleg, B.; Peters, H.J.M.
2016-01-01
Feasible elimination procedures (Peleg, 1978) play a central role in constructing social choice functions which have the following property: in the associated game form, for any preference profile there exists a strong Nash equilibrium resulting in the sincere outcome. In this paper we provide an ax
Motion and Emotion: The Global Appeal of Axiomatic Metaphors
DEFF Research Database (Denmark)
Børch, Marianne
2013-01-01
The article argues for the existence of linguistic and generic resources that may be globally shared, irrespective of cultural differences. Three main points are forwarded. First, animistic metaphors and personifications evoke an archaic vision that survives in all languages and conceptual systems......, and which is particularly strong in English, a “lingua franca” within many professional disciplines as well as that of fan fiction. Second, the anthropology of the imagination developed by the French scholar Gilbert Durand suggests linguistic areas not covered by Structuralism’s functional definition...... of verbal meaning: Durand distinguishes between words and images, argues that certain images are pre-conceptual and pre-linguistic, and concludes that such signs have inherent, not merely differential, meaning. Finally, the genre of romance—in modern terms fantasy or magic realism—may convey globally shared...
A Formal Axiomatization for Alphabet Reasoning with Parametrized Processes
Korver, H.
2008-01-01
In the process-algebraic verification of systems with three or more components put in parallel, alphabet axioms are considered to be very useful. These are rules that exploit the information about the alphabets of the processes involved. The alphabet of a process is the set of actions it can perform
Axiomatics for the external numbers of nonstandard analysis
Dinis, Bruno; Berg, Imme van den
2016-01-01
Neutrices are additive subgroups of a nonstandard model for the real numbers. An external number is the algebraic sum of a (hyper)real number and a neutrix. Due to the stability by some shifts, external numbers may be seen as mathematical models for orders of magnitude. The algebraic properties of external numbers gave rise to so-called solids, which are extensions of ordered fields, having a restricted distributivity law. However, necessary and sufficient conditions can be given for distribu...
Theory of decisions by intra-dimensional comparisons
Tserenjigmid, Gerelt
2015-01-01
Making a choice between multidimensional alternatives is a difficult task. Therefore, a decision maker may adopt some procedure (heuristic) to simplify this task. We provide an axiomatic model of one such heuristic called the Intra-Dimensional Comparison (IDC) heuristic. The IDC heuristic is well-documented in the experimental literature on choice under risk. The IDC heuristic is a procedure in which a decision maker compares multidimensional alternatives dimension-by-dimension and makes a de...
Affective Decision Making: A Behavioral Theory of Choice
Anat Bracha; Brown, Donald J.
2007-01-01
Affective decision-making is a strategic model of choice under risk and uncertainty where we posit two cognitive processes — the "rational" and the "emotional" process. Observed choice is the result of equilibirum in this intrapersonal game. As an example, we present applications of affective decision-making in insurance markets, where the risk perceptions of consumers are endogenous. We then derive the axiomatic foundation of affective decision making, and show that, although beliefs are end...
Guerra, Francesco
2005-01-01
A coincise review about Euclidean (Quantum) Field Theory is presented. It deals with the general structural properties, the connections with Quantum Field Theory, the exploitation in Constructive Quantum Field Theory, and the physical interpretation.
Mangani, P
2011-01-01
This title includes: Lectures - G.E. Sacks - Model theory and applications, and H.J. Keisler - Constructions in model theory; and, Seminars - M. Servi - SH formulas and generalized exponential, and J.A. Makowski - Topological model theory.
Decoding the architectural theory
Institute of Scientific and Technical Information of China (English)
Gu Mengchao
2008-01-01
Starting from the illustration of the definition and concept of the architectural theory, the author established his unique understanding about the framework of the architectural theory and the innovation of the architectural theory underlined by Chinese characteristics.
Grounded theory, feminist theory, critical theory: toward theoretical triangulation.
Kushner, Kaysi Eastlick; Morrow, Raymond
2003-01-01
Nursing and social science scholars have examined the compatibility between feminist and grounded theory traditions in scientific knowledge generation, concluding that they are complementary, yet not without certain tensions. This line of inquiry is extended to propose a critical feminist grounded theory methodology. The construction of symbolic interactionist, feminist, and critical feminist variants of grounded theory methodology is examined in terms of the presuppositions of each tradition and their interplay as a process of theoretical triangulation.
THEORIES OF CORPORATE GOVERNANCE
Sorin Nicolae BORLEA; Monica-Violeta ACHIM
2013-01-01
This study attempts to provide a theoretical framework for the corporate governance debate. The review of various corporate governance theories enhances the major objective of corporate governance which is maximizing the value for shareholders by ensuring good social and environment performances. The theories of corporate governance are rooted in agency theory with the theory of moral hazard’s implications, further developing within stewardship theory and stakeholder theory and evolving at re...
Murray, Paul R.; Paul R., Murray
2001-01-01
This paper deals with two difficult questions: (1) What is literary theory? and (2) What does literary theory do? Literary theory is contrasted to literary criticism, and theory is found to be a more all-embracing, inclusive field than criticism, which is tied more closely to literature itself. Literary theory is shown to be a multitude of differing ways of looking at literature, with each theory yielding differing results.
Supersymmetric Gauge Theories from String Theory
Metzger, Steffen
2005-01-01
The subject of this thesis are various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain subcycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. In particular, the low energy effective superpotential...
Foundations for a theory of gravitation theories
Thorne, K. S.; Lee, D. L.; Lightman, A. P.
1972-01-01
A foundation is laid for future analyses of gravitation theories. This foundation is applicable to any theory formulated in terms of geometric objects defined on a 4-dimensional spacetime manifold. The foundation consists of (1) a glossary of fundamental concepts; (2) a theorem that delineates the overlap between Lagrangian-based theories and metric theories; (3) a conjecture (due to Schiff) that the Weak Equivalence Principle implies the Einstein Equivalence Principle; and (4) a plausibility argument supporting this conjecture for the special case of relativistic, Lagrangian-based theories.
Jardine, John F
2015-01-01
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, n...
Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
Chu, C S; Zakrzewski, W J; Chu, Chong-Sun; Lukierski, Jerzy; Zakrzewski, Wojtek J.
2002-01-01
The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states; and allow us to see how the IR/UV mixing may lead to a breakdown of unitarity. Specifically, we show that the IR/UV singularity does not lead to the violation of unitarity in the space-space noncommutative case, but it does lead to its violation in a space-time noncommutative field theory. As a corollary, noncommutative field theory without IR/UV mixing will be unitary in both the space-space and space-time noncommutative...
Rationality, Theory Acceptance and Decision Theory
Directory of Open Access Journals (Sweden)
J. Nicolas Kaufmann
1998-06-01
Full Text Available Following Kuhn's main thesis according to which theory revision and acceptance is always paradigm relative, I propose to outline some possible consequences of such a view. First, asking the question in what sense Bayesian decision theory could serve as the appropriate (normative theory of rationality examined from the point of view of the epistemology of theory acceptance, I argue that Bayesianism leads to a narrow conception of theory acceptance. Second, regarding the different types of theory revision, i.e. expansion, contraction, replacement and residuals shifts, I extract from Kuhn's view a series of indications showing that theory replacement cannot be rationalized within the framework of Bayesian decision theory, not even within a more sophisticated version of that model. Third, and finally, I will point to the need for a more comprehensive model of rationality than the Bayesian expected utility maximization model, the need for a model which could better deal with the different aspects of theory replacement. I will show that Kuhn's distinction between normal and revolutionary science gives us several hints for a more adequate theory of rationality in science. I will also show that Kuhn is not in a position to fully articulate his main ideas and that he well be confronted with a serious problem concerning collective choice of a paradigm.
de Bruin, B.P.
2005-01-01
Game theory is the mathematical study of strategy and conflict. It has wide applications in economics, political science, sociology, and, to some extent, in philosophy. Where rational choice theory or decision theory is concerned with individual agents facing games against nature, game theory deals
Moschovakis, YN
1987-01-01
Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.
Contemporary theories of democracy
Directory of Open Access Journals (Sweden)
Mladenović Ivan
2008-01-01
Full Text Available The aim of this paper is two-fold: first, to analyze several contemporary theories of democracy, and secondly, to propose a theoretical framework for further investigations based on analyzed theories. The following four theories will be analyzed: pluralism, social choice theory, deliberative democracy and participatory democracy.
Bursa, Francis; Kroyter, Michael
2010-01-01
String field theory is a candidate for a full non-perturbative definition of string theory. We aim to define string field theory on a space-time lattice to investigate its behaviour at the quantum level. Specifically, we look at string field theory in a one dimensional linear dilaton background. We report the first results of our simulations.
DEFF Research Database (Denmark)
Hendricks, Vincent F.
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects....
Lassig, Michael
2011-01-01
A systematic theory is introduced that describes stochastic effects in game theory. In a biological context, such effects are relevant for the evolution of finite populations with frequency-dependent selection. They are characterized by quantum Nash equilibria, a generalization of the well-known Nash equilibrium points in classical game theory. The implications of this theory for biological systems are discussed in detail.
Zimmerman Jones, Andrew
2010-01-01
Making Everything Easier!. String Theory for Dummies. Learn:. The basic concepts of this controversial theory;. How string theory builds on physics concepts;. The different viewpoints in the field;. String theory's physical implications. Andrew Zimmerman Jones. Physics Guide, About.com. with Daniel Robbins, PhD in Physics. Your plain-English guide to this complex scientific theory. String theory is one of the most complicated sciences being explored today. Not to worry though! This informative guide clearly explains the basics of this hot topic, discusses the theory's hypotheses and prediction
Institute of Scientific and Technical Information of China (English)
梁景宏
2010-01-01
In this essay, I wish to invite young scholars to learn, use, and contribute to accounting theory. In this invitation, I argue theory has lineage, is important and can be fun. Its lineage comes from the post-WWII scientific revolution in management education and research. Theory is important because it is the successful interaction between theory and empirical work that ultimately advances an academic discipline. Theory can be fun because when done well, learning, using and contributing to theory can be an enjoyable activity for all scholars, either as consumers or as producers of theory.
String Theory, the Crisis in Particle Physics and the Ascent of Metaphoric Arguments
Schroer, Bert
This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of string theory within the broader context of six decades of failed attempts at an autonomous S matrix approach to particle theory. The central message, contained in Secs. 5 and 6, is that string theory is not what its name suggests, namely a theory of objects in space-time whose localization is string-instead of pointlike. Contrary to popular opinion, the oscillators corresponding to the Fourier models of a quantum-mechanical string do not become embedded in space-time and neither does the "range space" of a chiral conformal QFT acquire the interpretation of stringlike-localized quantum matter. Rather, string theory represents a solution to a problem which enjoyed some popularity in the 1960s: find a principle which, similar to the SO(4,2) group in the case of the hydrogen spectrum, determines an infinite component wave function with a (realistic) mass/spin spectrum. Instead of the group theory used in the old failed attempts, it creates this mass/spin spectrum by combining an internal oscillator quantum mechanics with a pointlike-localized quantum-field-theoretic object, i.e. the mass/spin tower "sits" over one point and does not arise from a wiggling string in space-time. The widespread acceptance of a theory whose interpretation has been based on metaphoric reasoning had a corroding influence on particle theory, a point which will be illustrated in the last section with some remarks of a more sociological nature. These remarks also lend additional support to observations on connections between the discourse in particle physics and the present Zeitgeist of the post-Cold War period that are made in the introduction.
Noncommutative Gauge Theories in Matrix Theory
Ho, P M; Ho, Pei-Ming; Wu, Yong-Shi
1998-01-01
We present a general framework for Matrix theory compactified on a quotient space of n dimensional Euclidean space over G, with G a discrete group of Euclidean motions. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We characterize the resulting noncommutative gauge theory in terms of the twisted group algebra of G associated with a projective regular representation.
The Global Approach to Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Folacci, Antoine; Jensen, Bruce [Faculte des Sciences, Universite de Corse (France); Department of Mathematics, University of Southampton (United Kingdom)
2003-12-12
formalism of quantum field theory. This is the so-called global approach to quantum field theory where time does not play any particular role, and quantization is then naturally realized covariantly using tools such as the Peierls bracket (a covariant generalization of Poisson bracket), the Schwinger variational principle and Feynman sums over histories. However, it should be noted that the boycott of canonical methods by DeWitt is not total: when he judges they genuinely illuminate the physics of a problem, he does not hesitate to descend from the global point of view and to use them. In a few words, we have in fact described the research program initiated by DeWitt forty years ago, which has progressively evolved in order to take into account the latest development of gauge theories. While the Les Houches Lectures of 1963 were mainly concentrated on the formal structure and the quantization of Yang--Mills and gravitational fields, the present book also deals with more general gauge theories including those with open gauge algebras and structure functions, and therefore supergravity theories. More precisely, the book, more than a thousand pages in length, consists of eight parts and is completed by six appendices where certain technical aspects are singled out. An enormous variety of topics is covered, including the invariance transformations of the action functional, the Batalin-Vilkovisky formalism, Green's functions, the Peierls bracket, conservation laws, the theory of measurement, the Everett (or many worlds) interpretation of quantum mechanics, decoherence, the Schwinger variational principle and Feynm an functional integrals, the heat kernel, aspects of quantization for linear systems in stationary and non-stationary backgrounds, the S-matrix, the background field method, the effective action and the Vilkovisky-DeWitt formalism, the quantization of gauge theories without ghosts, anomalies, black holes and Hawking radiation, renormalization, and more. It should
Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
Loran, Farhang
2015-01-01
Transfer matrix is an indispensable tool in the study of scattering phenomena in (effectively) one-dimensional systems. We introduce a genuine multidimensional notion of transfer matrix and use it to develop a powerful alternative to the standard S-matrix formulation of scattering theory. Because this transfer matrix shares the composition property of its one-dimensional analog, our formulation allows for the determination of the scattering properties of any scattering potential $v$ from that of any collection of its truncations $v_j$ along the scattering axis as long as $v=\\sum_jv_j$. This is the main advantage of our approach particularly with regard to the numerical solution of multidimensional scattering problems. We demonstrate its application in solving the scattering problem for delta-function potentials in two and three-dimensions and provide an analytic treatment of the scattering of electromagnetic waves from an infinite slab of optically active material with a surface line defect. In particular, we...
Gauge theory loop operators and Liouville theory
International Nuclear Information System (INIS)
We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S4 - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)
DEFF Research Database (Denmark)
Andersen, Jack
2015-01-01
Purpose To provide a small overview of genre theory and its associated concepts and to show how genre theory has had its antecedents in certain parts of the social sciences and not in the humanities. Findings The chapter argues that the explanatory force of genre theory may be explained with its...... emphasis on everyday genres, de facto genres. Originality/value By providing an overview of genre theory, the chapter demonstrates the wealth and richness of forms of explanations in genre theory....
Ali Rabbani Khorasghani; Mohammad Abbaszadeh
2010-01-01
AbstractAccording to social changes in global level, social scientist introduced new theories to explanation of socialphenomena. According to appearance new theories, research methods have changed. The Idea is that,Simultaneity with Appearance post positivist theories, research approaches such a grounded theory hasestablished. This method, acts in the base of qualitative methods and use systematic complex of multipleProcedures to gathering data for theory development upon induction. This meth...
Conlon, Joseph
2016-01-01
Is string theory a fraud or one of the great scientific advances? Why do so many physicists work on string theory if it cannot be tested? This book provides insight into why such a theory, with little direct experimental support, plays such a prominent role in theoretical physics. The book gives a modern and accurate account of string theory and science, explaining what string theory is, why it is regarded as so promising, and why it is hard to test.
Teaching Theory X and Theory Y in Organizational Communication
Noland, Carey
2014-01-01
The purpose of the activity described here is to integrate McGregor's Theory X and Theory Y into a group application: design a syllabus that embodies either Theory X or Theory Y tenets. Students should be able to differentiate between Theory X and Theory Y, create a syllabus based on Theory X or Theory Y tenets, evaluate the different syllabi…
Generalizability Theory and Classical Test Theory
Brennan, Robert L.
2011-01-01
Broadly conceived, reliability involves quantifying the consistencies and inconsistencies in observed scores. Generalizability theory, or G theory, is particularly well suited to addressing such matters in that it enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over…
[Topics in field theory and string theory
International Nuclear Information System (INIS)
In the past year, I have continued to investigate the relations between conformal field theories and lattice statistical mechanical models. I have also tried to extend some of these results to higher dimensions and to find applications in string theories and other contexts
Generalizability theory and item response theory
Glas, C.A.W.; Eggen, T.J.H.M.; Veldkamp, B.P.
2012-01-01
Item response theory is usually applied to items with a selected-response format, such as multiple choice items, whereas generalizability theory is usually applied to constructed-response tasks assessed by raters. However, in many situations, raters may use rating scales consisting of items with a s
Elements of a theory of algebraic theories
Hyland, Martin
2013-01-01
Kleisli bicategories are a natural environment in which the combinatorics involved in various notions of algebraic theory can be handled in a uniform way. The setting allows a clear account of comparisons between such notions. Algebraic theories, symmetric operads and nonsymmetric operads are treated as examples.
Fabris, J C
2015-01-01
General Relativity is the modern theory of gravitation. It has replaced the newtonian theory in the description of the gravitational phenomena. In spite of the remarkable success of the General Relativity Theory, the newtonian gravitational theory is still largely employed, since General Relativity, in most of the cases, just makes very small corrections to the newtonian predictions. Moreover, the newtonian theory is much simpler, technically and conceptually, when compared to the relativistic theory. In this text, we discuss the possibility of extending the traditional newtonian theory in order to incorporate typical relativistic effects, but keeping the simplicity of the newtonian framework. We denominate these extensions neo-newtonian theories. These theories are discussed mainly in the contexts of cosmology and compact astrophysical objects.
Directory of Open Access Journals (Sweden)
Ali Rabbani Khorasghani
2010-01-01
Full Text Available AbstractAccording to social changes in global level, social scientist introduced new theories to explanation of socialphenomena. According to appearance new theories, research methods have changed. The Idea is that,Simultaneity with Appearance post positivist theories, research approaches such a grounded theory hasestablished. This method, acts in the base of qualitative methods and use systematic complex of multipleProcedures to gathering data for theory development upon induction. This method with characteristics as ifflexibility, reflexivity, has caused many of researchers used it. In the present article, we paid to introductionof grounded theory and its critics.
Directory of Open Access Journals (Sweden)
Regina Szylit Bousso
2014-02-01
Full Text Available The theory framework of nursing science is built in a dynamic process that arises from practice and is reproduced through research, mainly by analysis and development of concepts and theories. This study presents a theory reflection on nursing knowledge construction and points out subsidies for future studies in the area. The interrelation among theory, research, and clinical practice is required for continuous development of nursing as a profession and science. Ideally, the practice must be based on theory that is validated by research. Therefore, theory, research, and practice affect each other reciprocally and continuously.
Hermitian analyticity, IR/UV mixing and unitarity of noncommutative field theories
Energy Technology Data Exchange (ETDEWEB)
Chu, C.-S. E-mail: chong-sun.chu@durham.ac.uk; Lukierski, Jerzy; Zakrzewski, Wojtek J
2002-06-17
The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established in an explicit form. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states and allow us to see how the IR/UV mixing may lead to a breakdown of unitarity. Specifically, we show that the IR/UV singularity does not lead to the violation of unitarity in the space-space noncommutative case, but it does lead to its violation in a space-time noncommutative field theory. As a corollary, noncommutative field theory without IR/UV mixing will be unitary in both the space-space and space-time noncommutative case. To illustrate this, we introduce and analyse the noncommutative Lee model--an exactly solvable quantum field theory. We show that the model is free from the IR/UV mixing in both the space-space and space-time noncommutative cases. Our analysis is exact. Due to absence of the IR/UV mixing one can expect that the theory is unitary. We present some checks supporting this claim. Our analysis provides a counter example to the generally held belief that field theories with space-time noncommutativity are nonunitary.
Hermitian analyticity, IR/UV mixing and unitarity of noncommutative field theories
International Nuclear Information System (INIS)
The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established in an explicit form. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states and allow us to see how the IR/UV mixing may lead to a breakdown of unitarity. Specifically, we show that the IR/UV singularity does not lead to the violation of unitarity in the space-space noncommutative case, but it does lead to its violation in a space-time noncommutative field theory. As a corollary, noncommutative field theory without IR/UV mixing will be unitary in both the space-space and space-time noncommutative case. To illustrate this, we introduce and analyse the noncommutative Lee model--an exactly solvable quantum field theory. We show that the model is free from the IR/UV mixing in both the space-space and space-time noncommutative cases. Our analysis is exact. Due to absence of the IR/UV mixing one can expect that the theory is unitary. We present some checks supporting this claim. Our analysis provides a counter example to the generally held belief that field theories with space-time noncommutativity are nonunitary
Low frequency sound scattering from spherical assemblages of bubbles using effective medium theory.
Hahn, Thomas R
2007-12-01
The determination of the acoustic field scattered by an underwater assembly of gas bubbles or similar resonant monopole scatterers is of considerable theoretical and practical interest. This problem is addressed from a theoretical point of view within the framework of the effective medium theory for the case of spherically shaped assemblages. Although being valid more generally, the effective medium theory is an ideal instrument to study multiple scattering effects such as low frequency collective resonances, acoustically coupled breathing modes of the entire assembly. Explicit expressions for the scattering amplitude and cross sections are derived, as well as closed form expressions for the resonance frequency and spectral shape of the fundamental collective mode utilizing analytical S-matrix methods. This approach allows, in principle, a simultaneous inversion for the assembly radius and void fraction directly from the scattering cross sections. To demonstrate the validity of the approach, the theory is applied to the example of idealized, spherically shaped schools of swim bladder bearing fish. The analytic results of the theory are compared to numerical first-principle benchmark computations and excellent agreement is found, even for densely packed schools and frequencies across the bladder resonance.
Supersymmetric gauge theories from string theory
International Nuclear Information System (INIS)
This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G2-manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G2-manifold is known. Here we construct families of metrics on compact weak G2-manifolds, which contain two conical singularities. Weak G2-manifolds have properties that are similar to the ones of proper G2-manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E8 x E8-heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the classical action. (author)
Covariant Noncommutative Field Theory
International Nuclear Information System (INIS)
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
Introduction to percolation theory
Stauffer, Dietrich
1991-01-01
Percolation theory deals with clustering, criticallity, diffusion, fractals, phase transitions and disordered systems. This book covers the basic theory for the graduate, and also professionals dealing with it for the first time
Combinatorics and field theory
Bender, Carl M.; Brody, Dorje C.; Meister, Bernhard K.
2006-01-01
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph theory.
DEFF Research Database (Denmark)
Clemmensen, Torkil; Kaptelinin, Victor; Nardi, Bonnie
2016-01-01
This paper reports a study of the use of activity theory in human–computer interaction (HCI) research. We analyse activity theory in HCI since its first appearance about 25 years ago. Through an analysis and meta-synthesis of 109 selected HCI activity theory papers, we created a taxonomy of 5...... different ways of using activity theory: (1) analysing unique features, principles, and problematic aspects of the theory; (2) identifying domain-specific requirements for new theoretical tools; (3) developing new conceptual accounts of issues in the field of HCI; (4) guiding and supporting empirical...... analyses of HCI phenomena; and (5) providing new design illustrations, claims, and guidelines. We conclude that HCI researchers are not only users of imported theory, but also theory-makers who adapt and develop theory for different purposes....
Zielenkiewicz, Wojciech
2004-01-01
The purpose of this book is to give a comprehensive description of the theoretical fundamentals of calorimetry. The considerations are based on the relations deduced from the laws and general equations of heat exchange theory and steering theory.
Theories of Career Development. A Comparison of the Theories.
Osipow, Samuel H.
These seven theories of career development are examined in previous chapters: (1) Roe's personality theory, (2) Holland's career typology theory, (3) the Ginzberg, Ginsburg, Axelrod, and Herma Theory, (4) psychoanalytic conceptions, (5) Super's developmental self-concept theory, (6) other personality theories, and (7) social systems theories.…