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
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...... 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...
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
Plefka, J. C.; Serone, M.; Waldron, A.K.
1998-01-01
The technology required for eikonal scattering amplitude calculations in Matrix theory is developed. Using the entire supersymmetric completion of the v^4/r^7 Matrix theory potential we compute the graviton-graviton scattering amplitude and find agreement with eleven dimensional supergravity at tree level.
S-matrix theory for gravitational field
International Nuclear Information System (INIS)
Major results of the investigation conducted on the quantum theory of the gravitational field and reported to the conference are summarized. The S matrix has been constructed in the most general class of gauges including relativistic ones. The causes of the failure to apply the proper-time regularization technique to gravitational interaction are considered. The corrected and improved proper-time method makes it possible to obtain the universal expression for one-loop divergences in and arbitrary system of gravitational fields. Under the assumption of mass-shell renormalizability the quantum theory of the gravitational field is asymptotically free
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...... 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....
Premarital Sexual Intercourse: An Application of Axiomatic Theory Construction
Davidson, J. Kenneth, Sr.; Leslie, Gerald R.
1977-01-01
This study utilized an axiomatic approach to develop a middle-range theory of premarital sexual intercourse. Using an unanalyzed data base of 336 never-married coeds in a southern state college and in a southern medical complex, 15 propositions were either statistically significant or in the stated direction. (Author)
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...
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...
Alternative axiomatics and complexity of deliberative STIT theories
Balbiani, Philippe; Troquard, Nicolas
2007-01-01
We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of the Chellas STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and the Chellas' STIT.
Axiomatization of Mathematical and Physical Theories in t-norm logics
Czech Academy of Sciences Publication Activity Database
Běhounek, Libor
Brussel: CLEA, 2008. s. 21-22. [Trends in Logic /6./. 11.12.2008-12.12.2008, Brussels] Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy logic * axiomatic theory * real numbers Subject RIV: BA - General Mathematics
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...
The Gribov Legacy, Gauge Theories and the Physical S-Matrix
White, Alan R
2015-01-01
Reggeon unitarity and non-abelian gauge field copies are focussed on as two Gribov discoveries that, it is suggested, may ultimately be seen as the most significant and that could, in the far distant future, form the cornerstones of his legacy. The crucial role played by the Gribov ambiguity in the construction of gauge theory bound-state amplitudes via reggeon unitarity is described. It is suggested that the existence of a physical, unitary, S-Matrix in a gauge theory is a major requirement that could even determine the theory.
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.
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...
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
International Nuclear Information System (INIS)
In this paper we initiate the study of a non-potential scattering theory within the framework of Lie-admissible formulations. By working in a time-dependent approach, we assume as starting point the usual definition of S-matrix as the time development operator connecting states of our system (supposed interacting through nonpotential forces) in the infinite past to states in the infinite future. It is shown that the Lie-admissible generalization of quantum mechanics, needed to take into account nonconservative forces, leads to two different, non-unitary evolution operators in Schroedinger's representation, U/sub +/ and U/sub -/, describing, respectively, motion forward and backward in time. This implies the existence of two different S-matrices (and, therefore, of two different cross sections) for a given reaction and the inverse (time-reversed) one. Then, one expects a violation of time-reversal invariance whenever nonpotential forces are involved, predictably for strong (nuclear and hadronic) interactions, in agreement with some recent experimental results in nuclear physics. Lie-admissible generalizations of Schroedinger's equations, suggested by the equations of motion for U/sub +/ and U/sub -/, are proposed. Both U/sub +/ and U/sub -/ operators satisfy a Volterra-like integral equation, which can be expanded, under suitable assumptions, in a Neumann-Liouville series. By introducing the operators of chronological and antichronological ordering, one can express both the direct and inverse scattering matrix in the form of a perturbative expansion. The validity of the limiting procedure leading from the U-operators to the S-matrices is investigated by means of generalized Moller's operators
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. PMID:26801920
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 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
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 ...
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
On a third S-matrix in the theory of quantized fields on curved spacetimes
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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.)
On a third S-matrix in the theory of quantized fields on curved spacetimes
International Nuclear Information System (INIS)
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.)
Jain, Sachin; Minwalla, Shiraz; Takimi, Tomohisa; Wadia, Spenta R; Yokoyama, Shuichi
2014-01-01
We present explicit computations and conjectures for $2 \\to 2$ scattering matrices in large $N$ {\\it $U(N)$} Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.
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.
Implementation of Axiomatic Language
Wilson, Walter W.
2011-01-01
This report summarizes a PhD research effort to implement a type of logic programming language called "axiomatic language". Axiomatic language is intended as a specification language, so its implementation involves the transformation of specifications to efficient algorithms. The language is described and the implementation task is discussed.
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
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.)
Raju, Suvrat
2009-06-01
As a simple example of how recently developed on-shell techniques apply to nonlocal theories, we study the S-matrix of noncommutative gauge theories. In the complex plane, this S-matrix has essential singularities that signal the nonlocal behavior of the theory. In spite of this, we show that tree-level amplitudes may be obtained by BCFW type recursion relations. At one loop we find a complete basis of master integrals (this basis is larger than the corresponding basis in the ordinary theory). Any one-loop noncommutative amplitude may be written as a linear combination of these integrals with coefficients that we relate to products of tree amplitudes. We show that the noncommutative Script N = 4 SYM theory has a structurally simple S-matrix, just like the ordinary Script N = 4 SYM theory.
Directory of Open Access Journals (Sweden)
Stefan Hollands
2009-09-01
Full Text Available In this paper, we propose a new framework for quantum field theory in terms of consistency conditions. The consistency conditions that we consider are ''associativity'' or ''factorization'' conditions on the operator product expansion (OPE of the theory, and are proposed to be the defining property of any quantum field theory. Our framework is presented in the Euclidean setting, and is applicable in principle to any quantum field theory, including non-conformal ones. In our framework, we obtain a characterization of perturbations of a given quantum field theory in terms of a certain cohomology ring of Hochschild-type. We illustrate our framework by the free field, but our constructions are general and apply also to interacting quantum field theories. For such theories, we propose a new scheme to construct the OPE which is based on the use of non-linear quantized field equations.
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)
Phonology in Axiomatic Functionalism
Czech Academy of Sciences Publication Activity Database
Bičan, Aleš
2009-01-01
Roč. 57, 1-2 (2009), s. 19-33. ISSN 1803-7410 Institutional research plan: CEZ:AV0Z90610518 Keywords : phonology * Axiomatic Functionalism * Mulder * phonematics * phonotactics * prosody Subject RIV: AI - Linguistics
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
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.
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.
Bibliography of Axiomatic Functionalism
Czech Academy of Sciences Publication Activity Database
Bičan, Aleš
Bern : Peter Lang, 2011 - (Bičan, A.; Rastall, P.), s. 289-304 ISBN 978-3-0343-1033-8 R&D Projects: GA MŠk(CZ) LC546 Institutional research plan: CEZ:AV0Z90610518 Keywords : axiomatic * functionalism * bibliography Subject RIV: AI - Linguistics
Mathematical Fuzzy Logic and Axiomatic Arithmetic
Czech Academy of Sciences Publication Activity Database
Hájek, Petr
Linz : Johannes Kepler Universität, 2010 - (Cintula, P.; Klement, E.; Stout, L.). s. 63-63 [Linz Seminar on Fuzzy Set Theory /31./. 03.02.2010-07.02.2010, Linz] Institutional research plan: CEZ:AV0Z10300504 Keywords : mathematical fuzzy logic * axiomatic arithmetic Subject RIV: BA - General Mathematics
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 ...
The Quest for Equational Axiomatizations of Parallel Composition
DEFF Research Database (Denmark)
Aceto, Luca; Fokkink, Wan
2005-01-01
This essay recounts the story of the quest for equational axiomatizations of parallel composition operators in process description languages, and of similar results in the classic field of formal language theory. Some of the outstanding open problems are also mentioned......This essay recounts the story of the quest for equational axiomatizations of parallel composition operators in process description languages, and of similar results in the classic field of formal language theory. Some of the outstanding open problems are also mentioned...
International Nuclear Information System (INIS)
The covariant path integral quantization of the theory of the scalar and spinor fields interacting through the Abelian and non-Abelian Chern-Simons gauge fields in 2+1 dimensions is carried out using the De Witt-Fadeev-Popov method. The mathematical ill-definiteness of the path integral of theories with pure Chern-Simons' fields is remedied by the introduction of the Maxwell or Maxwell-type (in the non-Abelian case) terms, which make the resulting theories super-renormalizable and guarantees their gauge-invariant regularization and renormalization. The generating functionals are constructed and shown to be the same as those of quantum electrodynamics (quantum chromodynamics) in 2+1 dimensions with the substitution of the Chern-Simons propagator for the photon (gluon) propagator. By constructing the propagator in the general case, the existence of two limits; pure Chern-Simons and quantum electrodynamics (quantum chromodynamics) after renormalization is demonstrated. The Batalin-Fradkin-Vilkovisky method is invoked to quantize the theory of spinor non-Abelian fields interacting via the pure Chern-Simons gauge field and the equivalence of the resulting generating functional to the one given by the De Witt-Fadeev-Popov method is demonstrated. The S-matrix operator is constructed, and starting from this S-matrix operator novel topological unitarity identities are derived that demand the vanishing of the gauge-invariant sum of the imaginary parts of the Feynman diagrams with a given number of intermediate on-shell topological photon lines in each order of perturbation theory. These identities are illustrated by explicit examples. (author)
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...
Uncertainty and complementarity in axiomatic quantum mechanics
International Nuclear Information System (INIS)
An investigation of the uncertainty principle and the complementarity principle is carried through. The physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation of the theory. Two extra axioms are stated, reflecting the ideas of the uncertainty principle and the complementarity principle, respectively. The quantal features of these axioms are explicated. (author)
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)
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.
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.
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)
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
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...
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“.
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...
Empirical Aspects of Statistical MECHANICS' Axiomatics
Plastino, A.; Curado, E. M. F.
It is here shown how to use pieces of macroscopic thermodynamics to generate microscopic probability distributions for generalized ensembles, thereby directly connecting macro-state-axiomatics with microscopic results.
International Nuclear Information System (INIS)
We give a technical result necessary for a preceding paper on the logarithmic asymptotic behaviour (with respect to the external momenta, in the euclidean space) of the convolution product associated with a general graph, in quantum field theory
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.
Minimal theory of quantum electrodynamics
International Nuclear Information System (INIS)
Within the general framework of the Lehmann-Symanzik-Zimmermann axiomatic field theory, we obtain a simple and coherent formulation of quantum electrodynamics. The definitions of the current densities fulfill the one-particle stability condition, and the commutation relations for the interacting fields are obtained rather than being postulated a priori, thus avoiding the inconsistencies which appear in the canonical formalism. This is possible due to the fact that we use the integral form of the equations of motion in order to compute the propagators and the S matrix. The resulting spectral representations automatically fulfill the correct boundary conditions thus fixing the ubiquitous quasilocal operators in a unique fashion
Some problems with two axiomatizations of discussive logic
Alama, Jesse
2014-01-01
Problems in two axiomatizations of Ja\\'skowski's discussive (or discursive) logic D2 are considered. A recent axiomatization of D2 and completeness proof relative to D2's intended semantics seems to be mistaken because some formulas valid according to the intended semantics turn out to be unprovable. Although no new axiomatization is offered, nor a repaired completeness proof given, the shortcomings identified here may be a step toward an improved axiomatization.
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...
A SIMPLE AXIOMATIZATION OF THE EGALITARIAN SOLUTION
Saglam, Ismail
2014-01-01
In this paper, we present a simple axiomatization of the n-person egalitarian solution. The single condition sufficient for characterization is a new axiom, called symmetric decomposability that combines the axioms of step-by-step negotiations, symmetry, and weak Pareto optimality used in an early characterization by Kalai [(1977) Proportional solutions to bargaining situations: Interpersonal utility comparisons, Econometrica 45, 1623–1630].
Axiomatic Characterizations of IVF Rough Approximation Operators
Guangji Yu
2014-01-01
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.
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.
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.
Measuring financial inclusion: An Axiomatic approach
Satya R. Chakravarty; Rupayan Pal
2010-01-01
This paper clearly demonstrates that the axiomatic measurement approach developed in the human development literature can be usefully applied to the measurement of financial inclusion. A conceptual framework for aggregating data on financial services in different dimensions is developed. The suggested index of financial inclusion allows calculation of percentage contributions of different dimensions to the overall achievement. This in turn enables us to identify the dimensions of inclusion th...
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 boundary S-matrix and the AdS to CFT dictionary
Giddings, Steven B
1999-01-01
An S-matrix is defined for anti-de Sitter space by constructing ``in'' and ``out'' states that asymptote to the timelike boundary. An analog of the LSZ formula shows that this boundary S-matrix is given directly by correlation functions in the boundary conformal theory. This provides a key entry in the AdS to CFT dictionary.
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.
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.
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.
An axiomatic characterization of the strong constrained egalitarian solution
Llerena Garrés, Francesc; Vilella Bach, Misericòrdia
2012-01-01
In this paper we axiomatize the strong constrained egalitarian solution (Dutta and Ray, 1991) over the class of weak superadditive games using constrained egalitarianism, order-consistency, and converse order-consistency. JEL classification: C71, C78. Keywords: Cooperative TU-game, strong constrained egalitarian solution, axiomatization.
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.
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 ...
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.
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.
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.
Non-axiomatic logic a model of intelligent reasoning
Wang, Pei
2013-01-01
This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author's research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelligence, as well as an abstract description of the "laws of thought" followed by the human mind. Different from "mathematical" logic, where the focus is the regularity required when demonstrating mathematical conclusions, Non-Axiomatic Logic is an attempt to return to the original aim of logic, that is, to formulate the regularity in actual human thin
Design of Safety Injection Tanks Using Axiomatic Design and TRIZ
Energy Technology Data Exchange (ETDEWEB)
Heo, Gyunyoung [Kyung Hee University, 1 Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701 (Korea, Republic of); Jeong, Yong Hoon [Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701 (Korea, Republic of)
2008-07-01
Design can be categorized into two steps: 'synthesis' and 'analysis'. While synthesis is the process of decision-making on design parameters, analysis is the process of optimizing the parameters selected. It is known from experience that the mistakes made in the synthesis process are hardly corrected in the analysis process. 'Systematic synthesis' is, therefore, easy to overlook but an important topic. 'Systematic' is interpreted as 'minimizing' uncertainty and subjectivity. This paper will introduce the design product achieved by using Axiomatic Design (AD) and TRIZ (Theory of Inventive Problem Solving romanized acronym for Russian), which is a new design of Safety Injection Tank (SIT). In designing a large-capacity SIT which should play an important role in mitigating the large break loss of coolant accidents, there are three issues: 1) the excessively large plenum for pressurized nitrogen gas; 2) the difficulties maintaining the high initial injection flow rate; and 3) the non-condensable nitrogen gas in the coolant. This study proposes a conceptual idea for SITs that are pressurized by the chemical reaction of solid propellants. The AD theory and the principles of TRIZ enable new approach in problem-solving for those three issues in an innovative way. The paper made an effort to clarify the systematic synthesis process to reach the final design solution. (authors)
An axiomatic characterization of the strong constrained egalitarian solution
Llerena, Francesc; Vilella, Cori
2012-09-01
In this paper we axiomatize the strong constrained egalitarian solution (Dutta and Ray, 1991) over the class of weak superadditive games using constrained egalitarianism, order-consistency, and converse order-consistency.
Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system
International Nuclear Information System (INIS)
In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that 'axiomatics', following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?
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.
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.
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)
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
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.
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.
Resonance information from the analytically continued S-matrix
Energy Technology Data Exchange (ETDEWEB)
Yamani, H.A.; Abdelmonem, M.S. [Dept. of Phys., King Fahd Univ. of Pet. and Miner., Dhahran (Saudi Arabia)
1994-08-07
The J-matrix method of scattering is used to calculate the scattering S-matrix at the set of energy eigenvalues of the full Hamiltonian matrix constructed from a finite set of square-integrable basis functions. The S-matrix is then analytically continued in the complex energy plane via a point-wise rational fraction scheme of Schlessinger. Numerical search techniques are then used to locate the poles of the S-matrix, which are identified with the resonance energies. Partial widths are easily calculated from the residues of the S-matrix at the designated complex resonance energies. (author)
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.
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.
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)
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 ...
Characterization of resonances using an exact model S-matrix
Energy Technology Data Exchange (ETDEWEB)
Yamani, H.A.; Abdelmonem, M.S. [Dept. of Phys., King Fahd Univ. of Pet. and Miner., Dhahran (Saudi Arabia)
1995-05-07
The S-matrix, which is exact for a model potential that can be made to closely approximate a given physical potential, is found in closed form as a function of complex system energy. This allows a calculation of the density of resonance states for real scattering energies, from which real resonance position, total widths, and partial widths can easily be extracted. Alternatively, a direct search of the poles of the S-matrix in the complex energy plane locates the complex resonance energies while the residues of the S-matrix elements at each pole yield the resonance partial widths. (author)
On the axiomatization of some classes of discrete universal integrals
Czech Academy of Sciences Publication Activity Database
Klement, E.P.; Mesiar, Radko
2012-01-01
Roč. 28, č. 1 (2012), s. 13-18. ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional research plan: CEZ:AV0Z10750506 Keywords : Comonotone modularity * Copula * Universal integral Subject RIV: BA - General Mathematics Impact factor: 4.104, year: 2012 http://library.utia.cas.cz/separaty/2012/E/mesiar-on the axiomatization of some classes of discrete universal integrals.pdf
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.
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...
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
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)
Perturbative S-matrix for massive scalar fields in global de Sitter space
International Nuclear Information System (INIS)
We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the coupling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays. (paper)
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.
A philosophical assessment of decision theory
DEFF Research Database (Denmark)
Jensen, Karsten Klint
2012-01-01
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...... decision theory, is shown to misrepresent the structure of modern axiomatic decision theory. Whereas the classical theory assumes a value assignment to outcomes and derives preferences over uncertain acts, the modern axiomatic approach assumes preferences over uncertain acts and derives the utility...... assignments. In the modern approach, the action guidance is to conform to the axioms. Analyzing decision theory as a theory of good, the maxim “maximize expected goodness” repeats the misunderstanding. Moreover, it implies risk neutrality about good and a cardinal measure of good, and both are problematic...
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.
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.
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...
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.
Microlocal study of S-matrix singularity structure
International Nuclear Information System (INIS)
Support is adduced for two related conjectures of simplicity of the analytic structure of the S-matrix and related function; namely, Sato's conjecture that the S-matrix is a solution of a maximally over-determined system of pseudo-differential equations, and our conjecture that the singularity spectrum of any bubble diagram function has the conormal structure with respect to a canonical decomposition of the solutions of the relevant Landau equations. This latter conjecture eliminates the open sets of allowed singularities that existing procedures permit. (orig.)
Singularities of the magnon boundstate S-matrix
Dorey, Nick; Okamura, Keisuke
2008-03-01
We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar Script N = 4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.
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.
The S-matrix algebra of the AdS2 X S2 superstring
Hoare, Ben; Torrielli, Alessandro
2015-01-01
In this paper we find the Yangian algebra responsible for the integrability of the AdS2 X S2 X T^6 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, along with related discussions on the issue of evaluation representations. We study the classical r-matrix, and re-discover the need for a secret symmetry also in this context. Finally, taking the simplifying zero-coupling limit of 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.
The one-loop worldsheet S-matrix for the AdS n × S n × T 10−2 n superstring
Radu Roiban; Per Sundin(Universitá di Milano-Bicocca and INFN Sezione di Milano-Bicocca, Dipartimento de Fisica, Piazza della Scienza 3, I-20126 Milano, Italy); Arkady Tseytlin; Linus Wulff
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 lig...
Ride comfort evaluation and suspension design using axiomatic design
International Nuclear Information System (INIS)
This study presents a theoretical formulation based on the axiomatic design (AD) approach to suspension systems for improving both ride comfort and static design factors (SDFs) of passenger vehicles. This approach was adapted to the kinematic design of suspension systems to create a decoupled or less coupled relationship between the functional requirements (FRs) and design parameters (DPs). SDFs related to wheel alignment and ride comfort are selected for FRs and suspension hardpoint positions are chosen for common DPs. A flexible commercial vehicle body model is used to mathematically express SDFs by defining the performance index and analyzing the dynamic characteristics for ride comfort evaluation. The sensitivity matrices are defined between the FRs and DPs. The SDF design sequences are proposed by using these matrices with the vehicle model. This study improves both ride comfort and SDFs by properly designing the kinematic DPs
Bochicchio, Marco
2016-05-01
Employing a new class of string theories we construct a family of S -matrix amplitudes that factorize over linear Regge trajectories, and that are good candidates to be asymptotically free, i.e. to lead to asymptotically-free correlation functions working out the LS Z formulae the other way around. In particular, we propose a candidate for a string solution of QCD with NF massless quarks in the large-N 't Hooft limit, for the glueball and meson spectrum, and for certain S-matrix amplitudes in the collinear limit. The solution extends to massive quarks of equal mass.
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.
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.
Energy-Momentum Conservation and Holographic S-Matrix
Li, Miao
1999-01-01
We investigate the consequence of the energy-momentum conservation law for the holographic S-matrix from AdS/CFT correspondence. It is shown that the conservation law is not a natural consequence of conformal invariance in the large N limit. We predict a new singularity for the four point correlation function of a marginal operator. Only the two point scattering amplitude is explicitly calculated, and the result agrees with what is expected.
Gauge amplitude identities by on-shell recursion relation in S-matrix program
International Nuclear Information System (INIS)
Using only the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion relation we prove color-order reversed relation, U(1)-decoupling relation, Kleiss-Kuijf (KK) relation and Bern-Carrasco-Johansson (BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color-ordered basis from (n-2)! to (n-3)!. Our proof gives also its physical interpretation as the mysterious bonus relation with 1/(z2) behavior under suitable on-shell deformation for no adjacent pair.
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.)
International Nuclear Information System (INIS)
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
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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.
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...
S-matrix approach to the superstring low energy effective revisited
International Nuclear Information System (INIS)
Full text: Conventional wisdom about the S-matrix approach to the (tree level) open string low energy effective Lagrangian (OSLEEL) states that, in order to obtain all its α'n order terms, it is necessary to know the open string (tree level) (n + 2)-point amplitude of gauge bosons, at least expanded at that order Lagrangian α'. In this work we review our recent result which clarifies that this common wisdom is indeed valid for the bosonic string but that, in the case of the open superstring, the situation is much more better than that. Spacetime Supersymmetry imposes constraints on the bosonic terms of the OSLEEL in such a way that (presumably) only the 4-point amplitude is needed to compute the complete nonabelian OSLEEL. If this is true it also implies, via KLT relations, that the closed superstring 4-point amplitude and Supersymmetry are enough to obtain completely the NS-NS sector of the (tree level) low energy effective action of the type II string theories. We apply this 'revisited' S-matrix approach to find the bosonic terms of the OSLEEL up to α'4 order terms. Our result is in perfect agreement with the 4 and 5-point amplitudes at that α' order and it also reproduces correctly the abelian limit of the F6 terms. This seems to agree completely with the previously known result obtained by the method of BPS configurations. (author)
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.
Diversification Preferences in the Theory of Choice
De Giorgi, Enrico G.; Mahmoud, Ola
2015-01-01
Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper reviews axiomatizations of the concept of diversification and their relationship to the r...
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.
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.
Non-Chiral S-Matrix of N=4 Super Yang-Mills
Huang, Yu-tin
2011-01-01
We discuss the construction of non-chiral S-matrix of four-dimensional N=4 super Yang-Mills using a non-chiral superspace. This construction utilizes the non-chiral representation of dual superconformal symmetry, which is the natural representation from the point of view of the six-dimensional parent theory. The superspace in discussion is projective superspace constructed by Hatsuda and Siegel, and is based on a half coset U(2,2|4)/U(1,1|2)^2_+. We obtain the non-chiral representation of the five-point and general n-point MHV and anti-MHV amplitude. The non-chiral formulation can be straightforwardly lifted to six dimensions, which is equivalent to massive amplitudes in four dimensions.
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.
Polarization-free generators and the S-matrix
International Nuclear Information System (INIS)
Polarization-free generators, i.e. ''interacting'' Heisenberg operators which are localized in wedge-shaped regions of Minkowski space and generate single particle states from the vacuum, are a novel tool in the analysis and synthesis of two-dimensional integrable quantum field theories. In the present article, the status of these generators is analyzed in a general setting. It is shown that such operators exist in any theory and in any number of spacetime dimensions. But in more than two dimensions they have rather delicate domain properties in the presence of interaction. If, for example, they are defined and temperate on a translation-invariant, dense domain, then the underlying theory yields only trivial scattering. In two-dimensional theories, these domain properties are consistent with non-trivial interaction, but they exclude particle production. Thus the range of applications of polarization-free generators seems to be limited to the realm of two-dimensional theories. (orig.)
An axiomatic framework for classical particle mechanics without space-time
San Sant'Adonai, A
1999-01-01
We present an axiomatic framework for non-relativistic classical particle mechanics, inspired on Tati's ideas about a non-space-time description for physics. The main advantage of our picture is that it allows us to describe causality without any reference to elapsed time intervals.
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
Revisiting the S-matrix approach to the open superstring low energy effective lagrangian
Barreiro, Luiz Antonio; Medina, Ricardo
2012-10-01
The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic α ' N order terms, it is necessary to know the open string (tree level) ( N + 2)-point amplitude of massless bosons, at least expanded at that order in α '. In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring n-point amplitude is needed to find all the α ' N order terms. In this `revisited' S-matrix approach we have checked that, at least up to α '4 order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian. The sort of results that we obtain seem to agree completely with the ones achieved by the method of BPS configurations, proposed about ten years ago. By means of the KLT relations, our results can be mapped to the NS-NS sector of the low energy effective lagrangian of the type II string theories implying that there one can also find kinematical constraints in the N-point amplitudes and that important informations can be inferred, at least up to α '4 order, by only using the (tree level) 4-point amplitude.
S-matrix approach to the superstring low energy effective revisited
Energy Technology Data Exchange (ETDEWEB)
Medina, Ricardo [Universidade Federal de Itajuba (UNIFEI), MG (Brazil); Barreiro, Luiz Antonio [Universidade Estadual Paulista (UNESP), Rio Claro, SP (Brazil)
2012-07-01
Full text: Conventional wisdom about the S-matrix approach to the (tree level) open string low energy effective Lagrangian (OSLEEL) states that, in order to obtain all its {alpha}{sup 'n} order terms, it is necessary to know the open string (tree level) (n + 2)-point amplitude of gauge bosons, at least expanded at that order Lagrangian {alpha}{sup '}. In this work we review our recent result which clarifies that this common wisdom is indeed valid for the bosonic string but that, in the case of the open superstring, the situation is much more better than that. Spacetime Supersymmetry imposes constraints on the bosonic terms of the OSLEEL in such a way that (presumably) only the 4-point amplitude is needed to compute the complete nonabelian OSLEEL. If this is true it also implies, via KLT relations, that the closed superstring 4-point amplitude and Supersymmetry are enough to obtain completely the NS-NS sector of the (tree level) low energy effective action of the type II string theories. We apply this 'revisited' S-matrix approach to find the bosonic terms of the OSLEEL up to {alpha}{sup '4} order terms. Our result is in perfect agreement with the 4 and 5-point amplitudes at that {alpha}{sup '} order and it also reproduces correctly the abelian limit of the F{sup 6} terms. This seems to agree completely with the previously known result obtained by the method of BPS configurations. (author)
Hilbertian quantum theory as the theory of complementarity
International Nuclear Information System (INIS)
It is demonstrated that the notion of complementary physical quantities assumes the possibility of performing ideal first-kind measurements of such quantities. This then leads to an axiomatic reconstruction of the Hilbertian quantum theory based on the complementarity principle and on its connection with the measurement theoretical idealization known as the projection postulate. As the notion of complementary physical quantities does not presuppose the notion of probability, the given axiomatic reconstruction reveals complementarity as an essential reason for the irreducibly probabilistic nature of the quantum theory. (author)
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
One-loop renormalization and the S-matrix
Huang, Yu-tin; Peng, Cheng
2012-01-01
In four-dimensional theories with massless particles, the one-loop amplitudes can be expressed in terms of a basis of scalar integrals and rational terms. Since the scalar bubble integrals are the only UV divergent integrals, the sum of the bubble coefficients captures the 1-loop UV behavior. In particular, in a renormalizable theory the sum of the bubble coefficients equals the tree-level amplitude times a proportionality constant that is related to the one-loop beta function coefficient beta_0. In this paper, we study how this proportionality is achieved from the viewpoint of on-shell amplitudes. For n-point MHV amplitude in (super) Yang-Mills theory, we demonstrate the existence of a hidden structure in each individual bubble coefficient which directly leads to systematic cancellations within the sum of them. The origin of this structure can be attributed to the collinear poles within a two-particle cut. Due to the cancellation, the one-loop beta function coefficient can be identified as a sum over the res...
The Automatic Integration of Folksonomies with Taxonomies Using Non-axiomatic Logic
Geldart, Joe; Cummins, Stephen
Cooperative tagging systems such as folksonomies are powerful tools when used to annotate information resources. The inherent power of folksonomies is in their ability to allow casual users to easily contribute ad hoc, yet meaningful, resource metadata without any specialist training. Older folksonomies have begun to degrade due to the lack of internal structure and from the use of many low quality tags. This chapter describes a remedy for some of the problems associated with folksonomies. We introduce a method of automatic integration and inference of the relationships between tags and resources in a folksonomy using non-axiomatic logic. We test this method on the CiteULike corpus of tags by comparing precision and recall between it and standard keyword search. Our results show that non-axiomatic reasoning is a promising technique for integrating tagging systems with more structured knowledge representations.
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...
Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
Basso, Benjamin; Vieira, Pedro
2014-01-01
We analyze the pentagon transitions involving arbitrarily many flux-tube gluonic excitations and bound states thereof in planar N=4 Super-Yang-Mills theory. We derive all-loop expressions for all these transitions by factorization and fusion of the elementary transitions for the lightest gluonic excitations conjectured in a previous paper. We apply the proposals so obtained to the computation of MHV and NMHV scattering amplitudes at any loop order and find perfect agreement with available perturbative data up to four loops.
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...
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
We explore in this paper the implications of ethical and operational principles for the evaluation of population health. We formalize those principles as axioms for social preferences over distributions of health for a given population. We single out several focal population health evaluation...... 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...
Toward a Quantum Theory of Observation
Zeh, H. D.
2003-01-01
The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the introduction of axiomatic observables. The conventional (collapse) and the Everett interpretations of quantum theory may in principle lead to different dynamical consequences. Finally, a formal ensemble description not based on a concept of lacking information is discussed.
Algebraic conformal quantum field theory in perspective
Rehren, Karl-Henning
2015-01-01
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.
Commutative monads as a theory of distributions
DEFF Research Database (Denmark)
Kock, Anders
2012-01-01
It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered...... here are the notions of convolution, density, expectation, and conditional probability....
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).
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.
S-matrix theory of single-channel ballistic transport through coupled quantum dots
Rotter, I.; Sadreev, A. F.
2004-01-01
We consider single-channel transmission through a double quantum dot system that consists of two single dots coupled by a wire of finite length L. In order to explain the numerically obtained results for a realistic double dot system we explore a simple model. It consists, as the realistic system, of two dots connected by a wire of length L. However, each of the two single dots is characterized by a few energy levels only, and the wire is assumed to have only one level whose energy depends on...
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
Three-body forces for electrons by the S-matrix method
International Nuclear Information System (INIS)
A electromagnetic three-body potential between eletrons is derived by the S-matrix method. This potential can be compared up to a certain point with other electromagnetic potentials (obtained by other methods) encountered in the literature. However, since the potential derived here is far more complete than others, this turns direct comparison with the potentials found in the literature somewhat difficult. These calculations allow a better understanding of the S-matrix method as applied to problems which involve the calculations of three-body nuclear forces (these calculations are performed in order to understand the 3He form factor). Furthermore, these results enable us to decide between two discrepant works which derive the two-pion exchange three-body potential, both by the S-matrix method. (author)
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
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...
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.
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.
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.
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.
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.
S-matrix approach calculation of the polarization contribution to the nucleosynthesis cross-section
International Nuclear Information System (INIS)
In the framework of the S-matrix approach, the influence of the electric dipole polarizability of colliding particles upon the low-energy nucleosynthesis cross-section is estimated. It is shown that the relative contribution of the polarization effects to the reaction cross-section does not exceed the quantity of the order of 0.1%
The Bound State S-matrix of the Deformed Hubbard Chain
de Leeuw, Marius; Matsumoto, Takuya
2011-01-01
In this work we use the q-oscillator formalism to construct the atypical (short) supersymmetric representations of the centrally extended Uq (su(2|2)) algebra. We then determine the S-matrix describing the scattering of arbitrary bound states. The crucial ingredient in this derivation is the affine extension of the aforementioned algebra.
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...
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...
Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes
Rubin, Jacques L
2009-01-01
On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, precisely and physically identified from experimental examples, together give a physical justification for the `chronometric hypothesis' of general relativity. Indeed, we show that, with a lack of these latter two ingredients, no clock paradox solution exists in which the clock and message functions are solely at the origin of the asymmetry. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian sheaf structure. In addition, the proper time parameterizations, as two point functions, cannot be defined irrespective of the processes in the relative changes of physical characteristics. These processes are included via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and...
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.
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)
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.
A Logical Framework for Set Theories
Avron, Arnon
2012-01-01
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.
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)
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.
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.
Dempster-Shafer theory and connections to information theory
Peri, Joseph S. J.
2013-05-01
The Dempster-Shafer theory is founded on probability theory. The entire machinery of probability theory, and that of measure theory, is at one's disposal for the understanding and the extension of the Dempster-Shafer theory. It is well known that information theory is also founded on probability theory. Claude Shannon developed, in the 1940's, the basic concepts of the theory and demonstrated their utility in communications and coding. Shannonian information theory is not, however, the only type of information theory. In the 1960's and 1970's, further developments in this field were made by French and Italian mathematicians. They developed information theory axiomatically, and discovered not only the Wiener- Shannon composition law, but also the hyperbolic law and the Inf-law. The objective of this paper is to demonstrate the mathematical connections between the Dempster Shafer theory and the various types of information theory. A simple engineering example will be used to demonstrate the utility of the concepts.
The complete one-loop BMN S-matrix in AdS(3) x S(3) x T(4)
Sundin, Per
2016-01-01
We compute the full one-loop 2-particle S-matrix for excitations of the type IIB AdS(3) x S(3) x T(4) BMN string. The S-matrix is found to respect the expected symmetries and the phases are consistent with the crossing equations. By analyzing how the relevant integrals scale with the IR regulator we show that scattering of massless bosons is trivial at two loops. Based on our results we argue that the additional su(2) S-matrix appearing in the massless sector in the exact solution should trivialize.
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.
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 ...
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.
Revisiting the S-matrix approach to the open superstring low energy effective lagrangian
Barreiro, Luiz Antonio
2012-01-01
The conventional S-matrix approach to the (tree level) open string low energy effective lagrangian assumes that, in order to obtain all its bosonic ${\\alpha'}^N$ order terms, it is necessary to know the open string (tree level) $(N+2)$-point amplitude of massless bosons, at least expanded at that order in $\\alpha'$. In this work we clarify that the previous claim is indeed valid for the bosonic open string, but for the supersymmetric one the situation is much more better than that: there are constraints in the kinematical bosonic terms of the amplitude (probably due to Spacetime Supersymmetry) such that a much lower open superstring $n$-point amplitude is needed to find all the ${\\alpha'}^N$ order terms. In this `revisited' S-matrix approach we have checked that, at least up to ${\\alpha'}^4$ order, using these kinematical constraints and only the known open superstring 4-point amplitude, it is possible to determine all the bosonic terms of the low energy effective lagrangian. The sort of results that we obtai...
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
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...
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.
Hyper-extensions in metric fixed point theory
Wiśnicki, Andrzej
2014-01-01
We apply a modern axiomatic system of nonstandard analysis in metric fixed point theory. In particular, we formulate a nonstandard iteration scheme for nonexpansive mappings and present a nonstandard approach to fixed-point problems in direct sums of Banach spaces.
A critical analysis of the quantum theory of measurement
International Nuclear Information System (INIS)
Keeping strictly in the positivist and probabilistic, hence hilbertian frame of Quantum Mechanics, the author tries to ascertain whether or not Quantum Mechanics, starting from its axioms, reaches the aim of any physical theory, that is, comparison with experiment. The answer is: no, as long as it keeps close to the existing axiomatics, and also to accurate mathematics. (Auth.)
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
Dempster-Shafer theory and connections to Choquet's theory of capacities and information theory
Peri, Joseph S. J.
2014-06-01
The axiomatic development of information theory, during the 1960's, led to the discovery of various composition laws. The Wiener-Shannon law is well understood, but the Inf law holds particular interest because it creates a connection with the Dempster-Shafer theory. Proceeding along these lines, in a previous paper, I demonstrated the connection between the Dempster-Shafer theory and Information theory. In 1954, Gustave Choquet developed the theory of capacities in connection with potential theory. The basic concepts of capacity theory arise from electrostatics, but a capacity is a generalization of the concept of measure in Analysis. It is well known that Belief and Plausibility in the Dempster-Shafer theory are Choquet capacities. However, it is not well known that the inverse of an information measure is a Choquet capacity. The objective of this paper is to demonstrate the connections among the Dempster- Shafer theory, Information theory and Choquet's theory of capacities.
Link Algebra: A new aproach to graph theory
Bustamante, Alfonso
2011-01-01
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once introduced Link Algebra, we will show the aplication on graph theory, like defining Paths, cycles and stars. Finally, we will se an alternative axiomatizations with Multisets and ordered pairs to algebraicaly define mutli, pseudo and oriented graphs.
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
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...
van de Vel, MLJ
1993-01-01
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear si
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.
A Theory of Bayesian Decision Making
Karni, Edi
2009-01-01
This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes' rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decisio...
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 ...
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......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...
Parametrization of the coupled channels S matrix in the inelastic case: Relation to Arndt-Roper form
International Nuclear Information System (INIS)
A previously introduced parametrization of the S matrix for two coupled channels is extended to allow use of Blatt-Biedenharn type phase shifts. It is then shown how the K-matrix parametrization of Arndt and Roper is related to the other schemes
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
Probability and logical structure of statistical theories
International Nuclear Information System (INIS)
A characterization of statistical theories is given which incorporates both classical and quantum mechanics. It is shown that each statistical theory induces an associated logic and joint probability structure, and simple conditions are given for the structure to be of a classical or quantum type. This provides an alternative for the quantum logic approach to axiomatic quantum mechanics. The Bell inequalities may be derived for those statistical theories that have a classical structure and satisfy a locality condition weaker than factorizability. The relation of these inequalities to the issue of hidden variable theories for quantum mechanics is discussed and clarified
Unequal Exchange, Assets, and Power: Recent Developments in Exploitation Theory
Veneziani, Roberto; Yoshihara, Naoki
2013-01-01
This paper surveys and extends some recent contributions on the theory of exploitation as the unequal exchange of labour. A model of dynamic economies with heterogeneous optimising agents is presented which encompasses the models used in the literature as special cases. It is shown that the notion of exploitation is logically coherent and can be meaningfully analysed in such a general framework. It is then shown that the axiomatic approach of social choice theory can be adopted to explore the...
Toward a Characterization of Uncertainty Measure for the Dempster-Shafer Theory
Harmanec, David
2013-01-01
This is a working paper summarizing results of an ongoing research project whose aim is to uniquely characterize the uncertainty measure for the Dempster-Shafer Theory. A set of intuitive axiomatic requirements is presented, some of their implications are shown, and the proof is given of the minimality of recently proposed measure AU among all measures satisfying the proposed requirements.
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.
Exact quantum S-matrix in the Liouville field theory. Corrigendum. J. Phys. A: Math. Gen. 28 5375-84
International Nuclear Information System (INIS)
The formula on page 5382, eighth line from the bottom, was incorrectly printed in the original article. It should be: u(x)=exp(-(i)/2(h/2π)∫-∞+∞ (log(1+Hey))exp(2π(y-x)/vertical bar (h/2π) vertical bar)+1dy). (author)
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 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.
Sommers, H J; Titov, M L; Fyodorov, Yan V.
1999-01-01
We study complex eigenvalues of large $N\\times N$ symmetric random matrices of the form ${\\cal H}=\\hat{H}-i\\hat{\\Gamma}$, where both $\\hat{H}$ and to describe the universal statistics of S-matrix poles (resonances) in the complex energy plane. We derive the ensuing distribution of the resonance widths which generalizes the well-known $\\chi^2$ distribution to the case of overlapping resonances. We also consider a different class of "almost real" matrices when
Set theory an introduction to independence proofs
Kunen, K
1984-01-01
Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing.The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and
Factorized three-body S-matrix restrained by the Yang–Baxter equation and quantum entanglements
International Nuclear Information System (INIS)
This paper investigates the physical effects of the Yang–Baxter equation (YBE) to quantum entanglements through the 3-body S-matrix in entangling parameter space. The explicit form of 3-body S-matrix Ř123(θ,φ) based on the 2-body S-matrices is given due to the factorization condition of YBE. The corresponding chain Hamiltonian has been obtained and diagonalized, also the Berry phase for 3-body system is given. It turns out that by choosing different spectral parameters the Ř(θ,φ)-matrix gives GHZ and W states respectively. The extended 1-D Kitaev toy model has been derived. Examples of the role of the model in entanglement transfer are discussed. - Highlights: • We give the relation between 3-body S-matrix and 3-qubit entanglement. • The relation between 3-qubit and 2-qubit entanglements is investigated via YBE. • 1D Kitaev toy model is derived by the Type-II solution of YBE. • The condition of YBE kills the “Zero boundary mode” in our chain model
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...
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.
Decision making by hybrid probabilistic: Possibilistic utility theory
Pap Endre
2009-01-01
It is presented an approach to decision theory based upon nonprobabilistic uncertainty. There is an axiomatization of the hybrid probabilistic possibilistic mixtures based on a pair of triangular conorm and triangular norm satisfying restricted distributivity law, and the corresponding non-additive Smeasure. This is characterized by the families of operations involved in generalized mixtures, based upon a previous result on the characterization of the pair of continuous t-norm and t-conorm su...
Features of Mathematical Theories in contraction-Free Logics
Czech Academy of Sciences Publication Activity Database
Běhounek, Libor; Cintula, Petr
Lisbon: Instituto Superior Técnico - Departemanto de Matemática, 2010 - (Béziau, J.; Caleiro, C.; Costa-Leite, A.; Ramos, J.). s. 39-39 ISBN 978-972-99289-2-5. [UniLog 2010. World Congress and School on Universal Logic /3./. 18.04.2010-25.04.2010, Monte Estoril] Institutional research plan: CEZ:AV0Z10300504 Keywords : propositional logics * axiomatic theory Subject RIV: BA - General Mathematics
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...
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
The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics
de Freitas, Elizabeth
2013-01-01
Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue…
Compton scattering S matrix and cross section in strong magnetic field
Mushtukov, Alexander A.; Nagirner, Dmitrij I.; Poutanen, Juri
2016-05-01
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 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 a general case of arbitrary initial photon momentum for the first time. A number of steps in the 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 the accurate calculation of radiation transfer in a strong B field, for example, in strongly magnetized neutron stars.
Notes On The S-Matrix Of Bosonic And Topological Non-Critical Strings
Nakamura, S; Nakamura, Shin; Niarchos, Vasilis
2005-01-01
We show that the equivalence between the c=1 non-critical bosonic string and the N=2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts $H_3^+$ correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2)/U(1) coset at level n>1, which has been argued recently to be equivalent with a c<1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT.
Notes on the S-matrix of bosonic and topological non-critical strings
Energy Technology Data Exchange (ETDEWEB)
Nakamura, Shin [Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Oe (Denmark); Niarchos, Vasilis [Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Oe (Denmark)
2005-10-15
We show that the equivalence between the c = 1 non-critical bosonic string and the N = 2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts H{sub 3}{sup +} correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2){sub n}/U(1) coset with n > 1, which has been argued recently to be equivalent with a c < 1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT.
Notes on the S-matrix of bosonic and topological non-critical strings
Nakamura, Shin; Niarchos, Vasilis
2005-10-01
We show that the equivalence between the c = 1 non-critical bosonic string and the Script N = 2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts H3+ correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2)n/U(1) coset with n > 1, which has been argued recently to be equivalent with a c < 1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT.
Notes on the S-matrix of bosonic and topological non-critical strings
International Nuclear Information System (INIS)
We show that the equivalence between the c = 1 non-critical bosonic string and the N = 2 topologically twisted coset SL(2)/U(1) at level one can be checked very naturally on the level of tree-level scattering amplitudes with the use of the Stoyanovsky-Ribault-Teschner map, which recasts H3+ correlation functions in terms of Liouville field theory amplitudes. This observation can be applied equally well to the topologically twisted SL(2)n/U(1) coset with n > 1, which has been argued recently to be equivalent with a c < 1 non-critical bosonic string whose matter part is defined by a time-like linear dilaton CFT
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...
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 ...
Statistical interpretation of the p-ADIC quantum field theory
International Nuclear Information System (INIS)
A p-adic generalization of the frequency theory of probability is developed. Within the framework of this theory frequency meaning is imparted to probabilities belonging to the field of p-adic numbers. The Bargmann-Fock representation is constructed for the p-adic field theory. A frequency interpretation of quantum states in the Bargmann-Fock representation is proposed. The p-adic generalization is essentially an introduction of new quantum states which are meaningless from the point of view of the standard theory of probability based on Kolmogorov's axiomatics. 10 refs
Czech Academy of Sciences Publication Activity Database
Greco, S.; Mesiar, Radko; Rindone, F.
Vol. 34. Linz : Universitätsdirektion JKU Austria, 2013. s. 62-64. [Linz Seminar on Fuzzy Set Theory /34./. 26.02.2013-02.03.2013, Linz] R&D Projects: GA ČR GAP402/11/0378 Keywords : universal integral * aggregation function * preference relation Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2013/E/mesiar-0422902.pdf
An axiomatic characterization of a value for games in partition function form
Hu, Cheng-Cheng; Yang, Yi-You
2010-01-01
An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307317, 1953) to characterize our value. In addition, we discuss a relations...
Foundations of Newtonian Dynamics: An Axiomatic Approach for the Thinking Student
Papachristou, C. J.
2012-01-01
Despite its apparent simplicity, Newtonian Mechanics contains conceptual subtleties that may cause some confusion to the deep-thinking student. These subtleties concern fundamental issues such as, e.g., the number of independent laws needed to formulate the theory, or, the distinction between genuine physical laws and derivative theorems. This article attempts to clarify these issues for the benefit of the student by revisiting the foundations of Newtonian Dynamics and by proposing a rigorous...
CERN. Geneva; CERN. Geneva
2001-01-01
Starting from the notion of path integrals as developed by Feynman, we discuss field theory in zero spacetime dimensions. The concepts of perturbation expansions, connected amplitudes, Feynman diagrams, classical solutions, renormalization and the effective action are developed. The model is extended to four spacetime dimensions, and the full Feynman rules for relativisitc scalar theory derived. The S matrix and the concept of unitarity are discussed, leading to the amputation rules for S matrix elements from considerations of unitarity. The rules are extended to include particles with spin-1/2 and spin-1. The high-energy behaviour of the theory is discussed as a method to derive the gauge symmetry of the various models.
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.
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...
Energy Technology Data Exchange (ETDEWEB)
Nasser, I; Abdelmonem, M S; Bahlouli, H [Physics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261 (Saudi Arabia); Alhaidari, A D [Shura Council, Riyadh 11212 (Saudi Arabia)
2008-11-14
This is the second article in which we study the rotating Morse potential model for diatomic molecules using the tridiagonal J-matrix approach. Here, we further improve the accuracy of computing the bound states and resonance energies for this potential model from the poles of the S-matrix for arbitrary angular momentum. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian, which is included in the computations analytically without truncation. Our method has been applied to both the regular and inverted Morse potential with favourable results in comparison with available numerical data. We have also shown that the present method adds a few significant digits to the accuracy obtained from the finite dimensional approach (e.g. the complex rotation method). Moreover, it allows us to easily handle both analytic and non-analytic potentials as well as 1/r singular potentials.
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.
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.
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.
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...
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.
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.
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.
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
Theory of Brownian motion with the Alder-Wainwright effect
International Nuclear Information System (INIS)
The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, the authors obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. The authors interested in whether or not it can be measured experimentally
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...
Finite field theories in three dimensions with and without supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Barfoot, D.T.; Broadhurst, D.J.
1987-01-01
Necessary and sufficient conditions are derived for the finiteness of the S-matrix and vacuum stress of theories with Yukawa, phi/sup 3/, and phi/sup 4/ couplings in three spacetime dimensions, and general supersymmetric solutions to these conditions are given. The requirement of a finite S-matrix allows many non-supersymmetric solutions, but with two bosons and two fermions the additional constraint of a finite vacuum stress allows only one simple alternative to supersymmetry.
Classes and Theories of Trees Associated with a Class Of Linear Orders
DEFF Research Database (Denmark)
Goranko, Valentin; Kellerman, Ruaan
2011-01-01
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....
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
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...
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].
Quantum field theory with a momentum space of constant curvature (perturbation theory)
International Nuclear Information System (INIS)
In the framework of the field-theoretical approach in which the off-the-mass shell extension proceeds in the p-space of constant curvature, the perburbation theory is developed. The configurational representation of the de Sitter space is introduced with the help of the Fourier transformation of the group of motions. On the basis of a natural generalization of the Bogolyubov causality condition to the case of the new configurational representation a perturbation theory is constructed with the local in xi space Lagrangian density fucntion. The obtained S matrix obeys the reguirement of translation invariance. The S matrix elements are given by convergent expressions
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.
Weak Quantum Theory: Formal Framework and Selected Applications
International Nuclear Information System (INIS)
Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli
Locally covariant quantum field theory and the spin-statistics connection
Fewster, Christopher J
2016-01-01
The framework of locally covariant quantum field theory, an axiomatic approach to quantum field theory in curved spacetime, is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which allows for a more operational description of theories with spin and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. This part of the text is based on arXiv:1503.05797 and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation.
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.
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.
S-matrices for perturbations of certain conformal field theories
International Nuclear Information System (INIS)
We present a family of factorizable S-matrix theories in 1+1 dimensions with an arbitrary number N of particles of distinct masses, and find the conservation laws of these theories. An analysis of the conservation laws of the family of nonunitary CFTs with central charge c=c2,2N+3=-2N(6N+5)/(2N+3) perturbed by the φ(1,3) operator, leads us to conjecture the identification of these perturbed CFTs with the S-matrix theories we found. The case N=1 was treated by Cardy and Mussardo. We also present the S-matrix of an E7-related unitary model. (orig.)
Perturbation theory of the space-time noncommutative real scalar field theories
International Nuclear Information System (INIS)
The perturbative framework of the space-time noncommutative real scalar field theory is formulated, based on the unitary S matrix. Unitarity of the S matrix is explicitly checked order by order using the Heisenberg picture of Lagrangian formalism of the second quantized operators, with emphasis on the so-called minimal realization of the time-ordering step function and of the importance of the *-time ordering. The Feynman rule is established and is presented using φ4 scalar field theory. It is shown that the divergence structure of space-time noncommutative theory is the same as the one of space-space noncommutative theory, while there is no UV-IR mixing problem in this space-time noncommutative theory
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.
Locally covariant quantum field theory and the spin-statistics connection
Fewster, Christopher J.
2016-03-01
The framework of locally covariant quantum field theory (QFT), an axiomatic approach to QFT in curved spacetime (CST), is reviewed. As a specific focus, the connection between spin and statistics is examined in this context. A new approach is given, which allows for a more operational description of theories with spin and for the derivation of a more general version of the spin-statistics connection in CSTs than previously available. This part of the text is based on [C. J. Fewster, arXiv:1503.05797.] and a forthcoming publication; the emphasis here is on the fundamental ideas and motivation.
On the theory of Brownian motion with the Alder-Wainwright effect
Okabe, Yasunori
1986-12-01
The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, we obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. We are interested in whether or not it can be measured experimentally.
International Nuclear Information System (INIS)
This series of lectures on basic scattering theory were given as part of a course for postgraduate high energy physicists and were designed to acquaint the student with some of the basic language and formalism used for the phenomenological description of nuclear reactions and decay processes used for the study of elementary particle interactions. Well established and model independent aspects of scattering theory, which are the basis of S-matrix theory, are considered. The subject is considered under the following headings; the S-matrix, cross sections and decay rates, phase space, relativistic kinematics, the Mandelstam variables, the flux factor, two-body phase space, Dalitz plots, other kinematic plots, two-particle reactions, unitarity, the partial-wave expansion, resonances (single-channel case), multi-channel resonances, analyticity and crossing, dispersion relations, the one-particle exchange model, the density matrix, mathematical properties of the density matrix, the density matrix in scattering processes, the density matrix in decay processes, and the helicity formalism. Some exercises for the students are included. (U.K.)
The Planckian Conspiracy: String Theory and the Black Hole Information Paradox
Lowe, David A.
1995-01-01
It has been argued that the consistency of quantum theory with black hole physics requires nonlocality not present in ordinary effective field theory. We examine the extent to which such nonlocal effects show up in the perturbative S-matrix of string theory.
International Nuclear Information System (INIS)
Like the circle number Pi or Euler's constant e determine mathematics, fundamental natural constants mark out the scales of natural sciences. But contrarily to mathematics the origin of the fundamental natural constants is still discussed controversely. This book presents by means of few axioms a new way of view and marks out by comparison with experimental data the content of truth resulting from this. By the axiomatic approach among others Sommerfeld's mysterious fine-structure constant and Dirac's cosmic number are fixed as pure number constants. Owing to these number constants it is possible to calculate the value for the anomalous magnetic moment of the isolated electron in a simple way in comparison to QED calculations: The calculated value agrees up to the 13th decimal point with the famous precision experiment of the Dyck-Schwinberg-Dehmelt group. The present book consists of two parts. In the first part exclusively experimental data from the literature are applied to the testing of the postulates. In the second part the author explains electrical-transport measurements with emergent behaviour, which were performed in a professional environment. The phenomena find by the critical quantities worked out in the first part of the book a partial explanation. This book presumes universitary knowledge in natural-scientific fields, is worth reading both for theoretically and experimentally working scientists and invites to deepened discussions.
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.)
Badran, R. I.; Al-Lehyani, I. H.
2016-06-01
Analyses of the angular distributions in the elastic scattering processes of 9, 10, 11Be by the target nucleus 64Zn at the laboratory energies of 27.95 MeV, and 4, 6, 8He by the target nucleus 208Pb at the laboratory energy of 22 MeV are performed. These analyses rely on a numerical model based on a parameterised scattering matrix (S-matrix) derived from Frahn and Venter. They confirm the absence of the Coulomb rainbow peak in angular distributions of elastic scattering in collisions of halo nuclei at energies around the Coulomb barrier. The correlation between the total reaction cross section and the halo structure for each scattering that involves a halo nucleus is discussed, and values of the total reaction cross section are found comparable with those of others. The diffractive features of the systems 16, 18O + 19F at specific laboratory energies are examined, and the effect of exchanging the projectile and target nuclei at such energies on these features are inspected. The incorporation of the Regge pole factor into the parameterised S-matrix calculations, which is found important in some cases, is employed in order to account for the oscillatory structure (if available) at backward angles. The theoretical results are found reasonable, reproducing the general pattern of the data. The trend of the extracted parameters meets the requirements proposed by the adopted models.
On Einstein's views of the relativity and quantum theories and their future progress. I
International Nuclear Information System (INIS)
The flux of Einstein's ideas and dialogues about the bases of contemporary physics -the relativity and quantum theories- are discussed, with stress placed upon his change of interpretations, from his earlier operational/positivistic approach in special relativity theory to his later epistemological approach of 'abstract realism', when his investigations progressed to general relativity theory. The thesis it put forward that his unified field approach, which was the culminating part of his life-work, was logically necessitated by the axiomatic basis of the theory of relativity, which, in turn, rejected the axiomatic basis of the Copenhagen interpretation of quantum mechanics. The requirement of the unified field theory was then to fuse the inertial manifestations of matter with its force manifestations, such as gravitation and electromagnetism, into a single self-consistent, non-singular field theory. The correspondence principle is applied in requiring the non-relativistic limit of the part of this (non-linear) formalism that relates to inertia to correspond with the linear mathematical structure of quantum mechanics
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
The theory of cosmic aberration
International Nuclear Information System (INIS)
Part I of this paper criticises current theory, which fails to solve the puzzle of the quasars and drives us to double thinking about the simple notions of distance and space. What is more, this current interpretation clashes with the almost axiomatic rule that the speed of light is constant in space: and it also comes into direct conflict with Special Relativity's equation for the addition of two velocities, one of which is that of light. Part II offers an alternative theory for the origin of the apparently recessional speeds leading to red-shifts. It claims that this recession is due to geometric perspective, which makes extra-galactic bodies appear to be moving, like the Sun, across the sky relative to the observer. Part III is essentially a refutation of a criticism put forward by the Royal Astronomical Society. They felt that the theory of transverse recession, due to rotation, was unacceptable because it implied a lack of isotropy at high latitudes in the distribution of the red-shifts, which actual observations did not support. This paper maintains, however, that the alleged isotropy is not factual but is based on an a priori argument, an argument which claims that extra-galactic sources with the same red-shift lie at the same distance, whatever the direction in which they are seen. (author)
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.
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...
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.)
Quantum Theory as a Critical Regime of Language Dynamics
Grinbaum, Alexei
2015-10-01
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars and combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing `bipartite systems,' we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as an effective description of a fundamental discrete theory in the critical regime.
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...
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.
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
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...
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...
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
Scientific Theories, Models and the Semantic Approach
Directory of Open Access Journals (Sweden)
Décio Krause
2007-12-01
Full Text Available According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a parallel between van Fraassen’s modal interpretation of quantum mechanics and Skolem’s relativism regarding set-theoretic concepts, we introduce a distinction between relative and absolute concepts in the context of the models of a scientific theory. And we discuss the significance of that distinction. Finally, by focusing on contemporary particle physics, we raise the question: since there is no general accepted unification of the parts of the standard model (namely, QED and QCD, we have no theory, in the usual sense of the term. This poses a difficulty: if there is no theory, how can we speak of its models? What are the latter models of? We conclude by noting that it is unclear that the semantic view can be applied to contemporary physical theories.
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.
Algebraic and analyticity properties of the n-point function in quantum field theory
International Nuclear Information System (INIS)
The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author)
Extensions of Theories from Soft Limits
Cachazo, Freddy; Mizera, Sebastian
2016-01-01
We study a variety of field theories with vanishing single soft limits. In all cases, the structure of the soft limit is controlled by a larger theory, which provides an extension of the original one by adding more fields and interactions. Our main example is the $U(N)$ non-linear sigma model in its CHY representation. Its extension is a theory in which the NLSM Goldstone bosons interact with a cubic biadjoint scalar. Other theories we study and extend are the special Galileon and Born-Infeld theory, including its maximally supersymmetric version in four dimensions, the DBI-Volkov-Akulov theory. In all the cases, we propose the CHY representation of the complete tree-level S-matrix of the extended theories. In fact, CHY formulas are the key technique for studying the single soft limit behavior of the original theories. As a byproduct, we show that the tree-level S-matrix of the extended NLSM theory can be constructed using a very compact BCFW-like recursion relation, where physical poles are at most linear in...
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
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.
S-matrices for perturbed N=2 superconformal field theory from quantum groups
International Nuclear Information System (INIS)
S-matrices for integrable perturbations of N=2 superconformal field theories are studied. The models we consider correspond to perturbations of the coset theory GkxHg-h/Hk+g-h. The perturbed models are closely related to G-affine Toda theories with a background charge tuned to H. Using the quantum group restriction of the affine Toda theories we derive the S-matrix. (orig.)
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)
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.
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.
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
International Nuclear Information System (INIS)
An exact S-matrix is conjectured for the imaginary coupled d4(3) affine Toda field theory, using the Uq(g2(1)) symmetry. It is shown that this S-matrix is consistent with the results for the case of real coupling using the breather-particle correspondence. For q a root of unity it is argued that the theory can be restricted to yield Φ(11 vertical stroke 14) perturbations of WA2 minimal models and the restriction is performed for the (3,p') minimal models. (orig.)
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...
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
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...
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.
Bargaining Theory over Opportunity Assignments and the Egalitarian Solution
Xu, Yongsheng; Yoshihara, Naoki
2009-01-01
This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on resource allocations. A framework in such a context is developed and the egalitarian solution to standard bargaining problems is reformulated and axiomatically characterized.
Energy-momentum tensor in the quantum field theory
International Nuclear Information System (INIS)
An energy-momentum tensor in the scalar field theory is built. The tensor must satisfy the finiteness requirement of the Green function. The Green functions can always be made finite by renormalizations in the S-matrix by introducing counter terms into the Hamiltonian (or Lagrangian) of the interaction. Such a renormalization leads to divergencies in the Green functions. Elimination of these divergencies requires the introduction of new counter terms, which must be taken into account in the energy-momentum tensor
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.
Galois and simple current symmetries in conformal field theory
International Nuclear Information System (INIS)
In this thesis various aspects of rational field theories are studied. In part I explicit examples for N=2 superconformal field theories are constructed by means of the coset approach. By means of these models string vacua are constructed, and the massless spectra of the string compactifications based on these models are computed. The symmetry of the S matrix, which implements the modular transformation on the space of characters is the subject of Part II. The developed methods are applied to the fusion rings of WZW theories. (HSI)
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...
Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field
International Nuclear Information System (INIS)
The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)
Physics of crypto-Hermitian and/or cryptosupersymmetric field theories
Smilga, A V
2007-01-01
We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of the supersymmetries are manifest and the existence of another half can be deduced from the structure of the spectrum. (iii) Generically, the conventionally defined S--matrix is not unitary for such theories.
Physics of crypto-Hermitian and crypto-supersymmetric field theories
International Nuclear Information System (INIS)
We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of the supersymmetries are manifest and the existence of another half can be deduced from the structure of the spectrum. (iii) Generically, the conventionally defined S-matrix is not unitary for such theories.
Scattering amplitudes in gauge theories
International Nuclear Information System (INIS)
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.
Quantum field theorie in the de Sitter space
International Nuclear Information System (INIS)
Based on well-known concepts, groundwork is laid for a quantum field theory in the de Sitter space-time considered as an exact soluble model of a more general theory in curved space-time. With respect to the horospherical coordinate system, invariant field equations for arbitrary spin are derived by means of induced representations of the symmetry group SO0(1.4). The additional terms, induced into the first order systems of relativistic wave equations by the space-time curvature, are formally interpreted as external fields. Normalized c-number solutions of the spin-dependent Klein-Gordon equation and of the Dirac equation are calculated explicitly. The analysis of the singular functions of quantum field theory is based on generalized eigenfunction expansions and, in the case of the Feynman propagator of scalar fields, on the method of Schwinger and De Witt, as well. An axiomatic approach to the quantization of neutral scalar fields is presented. Except for massless fields, the resulting 'second quantization' is distinguished by a causal commutation function and a unique vacuum. Recent developments in the regularization problem of the stress-energy tensor are reviewed. With respect to the de Sitter space-time the conclusion has been drawn that the quantum theory of 'free' scalar fields is renormalizable on the one-loop level. (author)
Theory of Finite or Infinite Trees Revisited
Djelloul, Khalil; Fruehwirth, Thom
2007-01-01
We present in this paper a first-order axiomatization of an extended theory $T$ of finite or infinite trees, built on a signature containing an infinite set of function symbols and a relation $\\fini(t)$ which enables to distinguish between finite or infinite trees. We show that $T$ has at least one model and prove its completeness by giving not only a decision procedure, but a full first-order constraint solver which gives clear and explicit solutions for any first-order constraint satisfaction problem in $T$. The solver is given in the form of 16 rewriting rules which transform any first-order constraint $\\phi$ into an equivalent disjunction $\\phi$ of simple formulas such that $\\phi$ is either the formula $\\true$ or the formula $\\false$ or a formula having at least one free variable, being equivalent neither to $\\true$ nor to $\\false$ and where the solutions of the free variables are expressed in a clear and explicit way. The correctness of our rules implies the completeness of $T$. We also describe an imple...
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
Non-integrable quantum field theories as perturbations of certain integrable models
International Nuclear Information System (INIS)
We approach the study of non-integrable models of two-dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact S-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the S-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at T ∼ Tc and the scaling region around the minimal model M2,τ. For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian. (author). 41 refs, 9 figs, 1 tab
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).
Algebraic Quantum Theory on Manifolds A Haag-Kastler Setting for Quantum Geometry
Rainer, M
2000-01-01
Motivated by the invariance of current representations of quantum gravity under diffeomorphisms much more general than isometries, the Haag-Kastler setting is extended to manifolds without metric background structure. First, the causal structure on a differentiable manifold M of arbitrary dimension (d+1>2) can be defined in purely topological terms, via cones (C-causality). Then, the general structure of a net of C*-algebras on a manifold M and its causal properties required for an algebraic quantum field theory can be described as an extension of the Haag-Kastler axiomatic framework. An important application is given with quantum geometry on a spatial slice within the causally exterior region of a topological horizon H, resulting in a net of Weyl algebras for states with an infinite number of intersection points of edges and transversal (d-1)-faces within any neighbourhood of the spatial boundary S^2.
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 ...
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
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
Analytic Multi-Regge Theory and the Pomeron in QCD
Energy Technology Data Exchange (ETDEWEB)
White, A.R.
1990-05-10
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.
Negative-frequency modes in quantum field theory
Dickinson, Robert; Forshaw, Jeff; Millington, Peter
2015-07-01
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.
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.
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...
Crypto-Hermiticity of nonanticommutative theories
Smilga, A V
2008-01-01
We note that, though nonanticommutative deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of crypto-Hermitian (or quasi-Hermitian) Hamiltonians having attracted recently a considerable attention. They can be made manifestly Hermitian via the similarity transformation H -> e^R H e^{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one though it is difficult in some cases to write explicit expressions for a half of supercharges. The deformed SQM models make perfect sense. It is not clear whether it is also the case for NAC Minkowski field theories -- the conventionally defined S--matrix is not unitary there.
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.
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.
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.
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.
Gluons in the hadronic S matrix
International Nuclear Information System (INIS)
We derive a theoretical explanation of the similarities which have been experimentally observed between final state distributions in soft processes (K-p interactions and pp collisions at ISR) and hard processes (e+e- annihilations and deep inelastic scattering). The theoretical framework is the correspondence between QCD and dual topological unitarization (DTU), which expresses confinement as the equivalence of the hadron and parton bases to account for unitarity. Starting from the interpretation of the zero handle topology in DTU in terms of the naive quark parton model, we show how to characterize gluons in the hadron basis: primordial gluons are associated with the one handle topology, and the cascading of hard gluons is related to the sum of all higher topologies in DTU. We get this way a QCD interpretation of the reggeon calculus which is the theoretical framework of soft hadronic processes at asymptotic energies. (orig.)
Quantum Theory of Reactive Scattering in Phase Space
Goussev, Arseni; Waalkens, Holger; Wiggins, Stephen
2010-01-01
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these phase space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schr\\"odinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the qu...
The holomorphic geometry of closed bosonic string theory and Diff S1/S1
International Nuclear Information System (INIS)
We present a proposal for a classical non-perturbative bosonic closed string field theory based on Kaehler geometry. Motivated by the observation that the loop space of Minkowski space-time is a Kaehler manifold, we conjecture that infinite-dimensional complex (Kaehler) geometry is the right setting for closed string field theory and that the correct dynamical variable (closed string field) is the Kaehler potential. To incorporate reparametrization invariance, one must consider the space of complex structures Diff S1/S1. Geometrical considerations then lead us to a (non-linear) equation of motion for the Kaehler potential which is that the curvature of a certain vector bundle over Diff S1/S1 vanish. This is basically the requirement of conformal invariance. Loops on flat Minkowski space are shown to be a solution only if the space-time dimension is 26. We also discuss geometric quantization since our approach can be viewed as an application of geometric quantization to string theory. Previously announced mathematical results that Diff S1/S1 is a homogeneous Kaehler manifold are established in more detail and its curvature is computed explicitly. We also give an axiomatic formulation of the minimal geometric setting we require - this is an attempt to avoid basing the theory on loops of a given riemannian manifold. Einstein's field equations are derived in an adiabatic approximation. The relation of our work to some other approaches to string theory is briefly discussed. (orig.)
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 ...
Singularities in quantum field theory
International Nuclear Information System (INIS)
The short-range behaviour of certain Feynman integrals reveals mathematical properties which are not those of either functions or distributions - they contain terms which are more singular than distributions and possess inherent ambiguities. Two classes of singularities exist: To the first one belong all those singularities which have a physical meaning in the sense that in a convergent (regluarized) quantum field theory they contribute to observable quantities, frequently as renormalization constants. Most of the singularities of the second, the spurious type, violate the symmetries of the Lagrangian. It is demonstrated that they are associated with certain mathematical difficulties of unregularized theories. Much of the analysis deals with the isolation of singularities of this type and with the study of the properties of the singular products of distribution. It is argued that the four-dimensional integration leading to the S-matrix in the perturbation expansion must be carried out over an open domain which leaves out the contributions from singularities of the contact type, that is terms proportional to delta4(x-y). (author)
Non-unitarity in quantum affine Toda theory and perturbed conformal field theory
International Nuclear Information System (INIS)
There has been some debate about the validity of quantum affine Toda field theory at imaginary coupling, owing to the non-unitarity of the action, and consequently of its usefulness as a model of perturbed conformal field theory. Drawing on our recent work, we investigate the two simplest affine Toda theories for which this is an issue -a2(1) and a2(2). By investigating the S-matrices of these theories before RSOS restriction, we show that quantum Toda theory (with or without RSOS restriction) indeed has some fundamental problems, but that these problems are of two different sorts. For a2(1), the scattering of solitons and breathers is flawed in both classical and quantum theories, and RSOS restriction cannot solve this problem. For a2(2) however, while there are no problems with breather-soliton scattering there are instead difficulties with soliton-excited soliton scattering in the unrestricted theory. After RSOS restriction, the problems with kink-excited kink may be cured or may remain, depending in part on the choice of gradation, as we found earlier [Nucl. Phys. B 489 [FS] (1997) 557]. We comment on the importance of regradations, and also on the survival of R-matrix unitarity and the S-matrix bootstrap in these circumstances
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.
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......-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...
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.
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.
Golledge, Reginald G.
2001-01-01
The emergence of geographical theory was an inevitable product of the desire to systematize existing geographic knowledge and to use that systematized base to explore new areas of knowledge. Although the usefulness of theory and predictive models in geography is by now a matter of record, it was not always the case. The usefulness and need for theories was often disputed, despite the oft-repeated argument that theories of location explained the laws of spatial distributions, theories of inter...
International Nuclear Information System (INIS)
The paper traces the development of the String Theory, and was presented at Professor Sir Rudolf Peierls' 80sup(th) Birthday Symposium. The String theory is discussed with respect to the interaction of strings, the inclusion of both gauge theory and gravitation, inconsistencies in the theory, and the role of space-time. The physical principles underlying string theory are also outlined. (U.K.)
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
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...
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...
An axiomatization of the Sequential Raiffa solution
Trockel, Walter
2009-01-01
This paper provides four axioms that uniquely characterize the sequential Raiffa solution proposed by Raiffa (1951, 1953) for two-person bargaining games. Three of these axioms are standard and are shared by several popular bargaining solutions. They suffice to characterize these solutions on TU-bargaining games where they coincide. The fourth axiom is a weakening of Kalai's (1977) axiom of step-by-step negotiating and turns out to be sort of a dual condition to a weaker version of Nash's IIA...
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
Analysis of interacting quantum field theory in curved spacetime
International Nuclear Information System (INIS)
A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green's functions are derived, special attention being paid to the possibility that the ''in'' and ''out'' vacuum states may not be equivalent. Green's functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for lambdaphi3/sub() 4,6/ field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, phi3/sub(4) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes
Statistical theory of nuclear reactions and the Gaussian orthogonal ensemble
International Nuclear Information System (INIS)
Using methods developed in Field Theory and Statistical Mechanics, especially in the context of the Anderson model as generalised by Wegner, we develop a novel approach to the Statistical Theory of Nuclear Reactions. We consider a finite set of N bound states, coupled to each other an ensemble of Gaussian orthogonal matrices, and coupled to a set of channels via fixed coupling matrix elements. We evaluate the ensemble average and the variance of the elements of the nuclear scattering matrix, using the method of a generating function combined with the replica trick, followed by the Hubbard-Stratonovitch transformation and a modified loop expansion. In the limit N -> infinite, we show quite generally that, aside from a trivial dependence on average S-matrix elements, the variance depends only on the transmission coefficients, and that the correlation width of a pair of S-matrix elements is given by a universal function of the transmission coefficients. A modified loop expansion yields an asymptotic series valid for strong absorption. The terms in this series are partly novel, and partly coincide with results obtained earlier in the framework of a model which did not take account of the GOE eigenvalue fluctuations. This suggests that average cross sections are mainly sensitive to the stiffness of the GOE spectrum. Fluctuation properties are also derived, and the link to Ericson fluctuation theory is established. (orig.)
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 ...
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.
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.)
The Origin of Space-Time as $W$ Symmetry Breaking in String Theory
Ellis, Jonathan Richard; Nanopoulos, Dimitri V; Ellis, John
1992-01-01
Physics in the neighbourhood of a space-time metric singularity is described by a world-sheet topological gauge field theory which can be represented as a twisted $N=2$ superconformal Wess-Zumino model with a $W_{1+\\infty} \\otimes W_{1+\\infty} $ bosonic symmetry. The measurable $W$-hair associated with the singularity is associated with Wilson loop integrals around gauge defects. The breaking of $W_{1+\\infty}$ $\\otimes $ $W_{1+\\infty}$ $\\rightarrow $ $W_{1+\\infty}$ is associated with expectation values for open Wilson lines that make the metric non-singular away from the singularity. This symmetry breaking is accompanied by massless discrete `tachyon' states that appear as leg poles in $S$-matrix elements. The triviality of the $S$-matrix in the high-energy limit of the $c=1$ string model, after renormalisation by the leg pole factors, is due to the restoration of double $W$-symmetry at the singularity.
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.)
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....
International Nuclear Information System (INIS)
This article is devoted to a nontechnical review on the present status of string theory towards an ultimate unification of all fundamental interactions including gravity. In particular, we emphasize the importance of string theory as a new theoretical framework in which the long-standing conflict between quantum theory and general relativity is resolved. (author)
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…
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 $\
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.
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
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...
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.)
The inertial mass of a pion from a quaternion field theory of matter
International Nuclear Information System (INIS)
The quaternion field theory of matter in general relativity that was developed by this author was applied earlier to the calculation of the inertial masses of the electron and the muon, as a consequence of their (electromagnetic) coupling to their environment, in accordance with the Mach principle. As a consequence of the axiomatic structure, in this theory, the most primitive matter fields are represented by two-component spinor variables. All other ''particle'' fields must then be built up from these. Thus the high-energy data that are interpreted as referred to massive boson particles must be viewed here in terms of a composite of (electromagnetically) bound spinor particles. In this paper, the general field expression for the inertial mass of a boson is derived as a composite of elementary spinor fields. The neutral pion is a composite of proton and antiproton, the charged pion is a composite of a proton or antiproton with the spinor electromagnetic-field representation of a bound proton-antiproton pair. The theory is applied to a calculation of the mass ratio m(πsup(deg))/m(π+-)) and it is found to be within o.1% of the experimental ratio
The notion of process in nonstandard theory and in Whiteheadian metaphysics
Directory of Open Access Journals (Sweden)
Stathis Livadas
2013-06-01
Full Text Available In this article I intend to show that certain aspects of A.N. Whitehead's philosophy of organism and especially his epochal theory of time, as mainly exposed in his well-known work Process and Reality, can serve in clarify the underlying assumptions that shape nonstandard mathematical theories as such and also as metatheories of quantum mechanics. Concerning the latter issue, I point to an already significant research on nonstandard versions of quantum mechanics; two of these approaches are chosen to be critically presented in relation to the scope of this work. The main point of the paper is that, insofar as we can refer a nonstandard mathematical entity to a kind of axiomatical formalization essentially 'codifying' an underlying mental process indescribable as such by analytic means, we can possibly apply certain principles of Whitehead's metaphysical scheme focused on the key notion of process which is generally conceived as the becoming of actual entities. This is done in the sense of a unifying approach to provide an interpretation of nonstandard mathematical theories as such and also, in their metatheoretical status, as a formalization of the empirical-experimental context of quantum mechanics.
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...
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)
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)
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...
Aubin, Jean-Pierre; Saint-Pierre, Patrick
2011-01-01
Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explai
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Sanfilippo, Antonio P.
2005-12-27
Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for the representation of grammar formalisms.
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..
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
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...
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.
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Hjørland, Birger
2009-01-01
, evaluate and use such systems. Based on "a post-Kuhnian view" of paradigms this paper put forward arguments that the best understanding and classification of theories of concepts is to view and classify them in accordance with epistemological theories (empiricism, rationalism, historicism and pragmatism...
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
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...
Kleiss, Ronald H P
1999-01-01
In these lectures I will build up the concept of field theory using the language of Feynman diagrams. As a starting point, field theory in zero spacetime dimensions is used as a vehicle to develop all the necessary techniques: path integral, Feynman diagrams, Schwinger-Dyson equations, asymptotic series, effective action, renormalization etc. The theory is then extended to more dimensions, with emphasis on the combinatorial aspects of the diagrams rather than their particular mathematical structure. The concept of unitarity is used to, finally, arrive at the various Feynman rules in an actual, four-dimensional theory. The concept of gauge-invariance is developed, and the structure of a non-abelian gauge theory is discussed, again on the level of Feynman diagrams and Feynman rules.
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...
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.
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
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
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...
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
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...
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
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.
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 ...
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)
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
Murdin, P.
2000-11-01
A theory based on the premise that, on the microscopic scale, physical quantities have discrete, rather than a continuous range of, values. The theory was devised in the early part of the twentieth century to account for certain phenomena that could not be explained by classical physics. In 1900, the German physicist, Max Planck (1858-1947), was able precisely to describe the previously unexplaine...
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
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.
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 human...... ideological beliefs, and artistic practices such as music, dance, painting, and storytelling. Establishing biocultural theory as a program that self-consciously encompasses the different particular forms of human evolutionary research could help scholars and scientists envision their own specialized areas of...... research as contributions to a coherent, collective research program. This article argues that a mature biocultural paradigm needs to be informed by at least 7 major research clusters: (a) gene-culture coevolution; (b) human life history theory; (c) evolutionary social psychology; (d) anthropological...
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
International Nuclear Information System (INIS)
This textbook for students of physics is oriented in the selection of matter by the contents of a two-semester course about quantum theory. Thereby the foundations of quantum theory, among them the quantum-mechanical measurement process, the mathematical formalism, and Bell's inequalities, are extensively treated. Also modern concepts like feynman's path integral are regarded. This work is equally suited for a self-study, as course-accompanying lecture, and for preparations of examina. Application examples, supplementary explanations, and numerous illustration take car for a good understanding of the theoretical contents
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Novaes, Marcel [Instituto de Física, Universidade Federal de Uberlândia, Ave. João Naves de Ávila, 2121, Uberlândia, MG 38408-100 (Brazil)
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
International Nuclear Information System (INIS)
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS†dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches
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...
International Nuclear Information System (INIS)
This is a summary of the advances in magnetic fusion energy theory research presented at the 17th International Atomic Energy Agency Fusion Energy Conference from 19 24 October, 1998 in Yokohama, Japan. Theory and simulation results from this conference provided encouraging evidence of significant progress in understanding the physics of thermonuclear plasmas. Indeed, the grand challenge for this field is to acquire the basic understanding that can readily enable the innovations which would make fusion energy practical. In this sense, research in fusion energy is increasingly able to be categorized as fitting well the 'Pasteur's Quadrant' paradigm, where the research strongly couples basic science ('Bohr's Quadrant') to technological impact ('Edison's Quadrant'). As supported by some of the work presented at this conference, this trend will be further enhanced by advanced simulations. Eventually, realistic three-dimensional modeling capabilities, when properly combined with rapid and complete data interpretation of results from both experiments and simulations, can contribute to a greatly enhanced cycle of understanding and innovation. Plasma science theory and simulation have provided reliable foundations for this improved modeling capability, and the exciting advances in high-performance computational resources have further accelerated progress. There were 68 papers presented at this conference in the area of magnetic fusion energy theory
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...
International Nuclear Information System (INIS)
Written by the author of the widely acclaimed textbook. Theoretical Atomic Physics Includes sections on quantum reflection, tunable Feshbach resonances and Efimov states. Useful for advanced students and researchers. This book presents a concise and modern coverage of scattering theory. 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. 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. The level of abstraction is kept as low as at all possible, and deeper questions related to mathematical foundations of scattering theory are passed by. The book should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. It is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Hall, Marshall
2011-01-01
Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.
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 p...
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.
International Nuclear Information System (INIS)
The text book composed of five parts, which are summary of this book, arrangement of electricity theory including electricity nad magnetism, a direct current, and alternating current. It has two dictionary electricity terms for a synonym. The last is an appendix. It is for preparing for test of officer, electricity engineer and fire fighting engineer.
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.
International Nuclear Information System (INIS)
An introduction to the unified gauge theories of weak and electromagnetic interactions is given. The ingredients of gauge theories and symmetries and conservation laws lead to discussion of local gauge invariance and QED, followed by weak interactions and quantum flavor dynamics. The construction of the standard SU(2)xU(1) model precedes discussion of the unification of weak and electromagnetic interactions and weak neutral current couplings in this model. Presentation of spontaneous symmetry breaking and spontaneous breaking of a local symmetry leads to a spontaneous breaking scheme for the standard SU(2)xU(1) model. Consideration of quarks, leptons, masses and the Cabibbo angles, of the four quark and six quark models and CP violation lead finally to grand unification, followed by discussion of mixing angles in the Georgi-Glashow model, the Higgses of the SU(5) model and proton/ neutron decay in SU(5). (JIW)
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...
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 ...
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.
DEFF Research Database (Denmark)
Stein, Irene F.; Stelter, Reinhard
2011-01-01
ascribe specific meanings to their experiences, their actions in life or work, and their interactions. Meaning is reshaped, adapted, and transformed in every communication encounter. Furthermore, meaning is cocreated in dialogues or in communities of practice, such as in teams at a workplace or in school......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...... is not a data processing device. In this chapter, communication is understood as a process of shared meaning-making (Bruner, 1990). Human beings interpret their environment, other people, and themselves on the basis of their dynamic interaction with the surrounding world. Meaning is essential because people...
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 ...
Petrosjan, L A
1996-01-01
Game theory is a branch of modern applied mathematics that aims to analyze various problems of conflict between parties that have opposed, similar or simply different interests.Games are grouped into several classes according to some important features. In this volume zero-sum two-person games, strategic n-person games in normal form, cooperative games, games in extensive form with complete and incomplete information, differential pursuit games and differential cooperative n-person games are considered.
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...
The Five-Axiom Theory of Indexing and Information Supply.
Fugmann, Robert
1985-01-01
Reports on axiomatic approach to systems design that has emanated from documentation work in field of chemistry and closely related disciplines. It is based on five axioms: definability, order, sufficient degree of order, representational predictability, and representational fidelity. Mandatory indexing is discussed; a glossary is appended. (106…
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...
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.
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
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It is shown how the S-matrix version of the Kohn variational method for quantum scattering can be readily adapted to compute matrix elements involving the scattering wave function and also matrix elements of the scattering Green's function. The former of these quantities is what is involved in computing photodissociation cross sections, photodetachment intensities from a bound negative ion to a neutral scattering state, or the intensity of any Franck--Condon transition from a bound state to a scattering state. The latter quantity (i.e., a matrix element of the scattering Green's function between two bound states) gives the resonance Raman cross section for the case that the intermediate state in the Raman process is a scattering state. Once the basic S-matrix Kohn scattering calculation has been performed, it is shown that little additional effort is required to determine these quantities. Application of this methodology is made to determine the electron energy distribution for photodetachment of H2F- to F+H2, HF+H. Resonance structure in the J=0 reaction probabilities is seen to appear in the electron energy distribution
Blyth, T S; Sneddon, I N; Stark, M
1972-01-01
Residuation Theory aims to contribute to literature in the field of ordered algebraic structures, especially on the subject of residual mappings. The book is divided into three chapters. Chapter 1 focuses on ordered sets; directed sets; semilattices; lattices; and complete lattices. Chapter 2 tackles Baer rings; Baer semigroups; Foulis semigroups; residual mappings; the notion of involution; and Boolean algebras. Chapter 3 covers residuated groupoids and semigroups; group homomorphic and isotone homomorphic Boolean images of ordered semigroups; Dubreil-Jacotin and Brouwer semigroups; and loli
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
International Nuclear Information System (INIS)
This book is divided into fourteen chapters, which deals with circuit theory of basis, sinusoidal alternating current on cycle and frequency, basics current circuit about R.L, C circuit and resonant circuit, current power, general linear circuit, inductive coupling circuit and vector locus on an alternating current bridge and mutual inductance and coupling coefficient, multiphase alternating current and method of symmetrical coordinates, non-sinusoidal alternating current, two terminal network, four terminal network, transient of circuits, distributed line circuit constant, frequency characteristic and a filter and Laplace transformation.
Yang-Mills Theories as Deformations of Massive Integrable Models
Cubero, Axel Cortés
2014-01-01
Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has massive excitations. We calculate all the form factors and two-point correlation functions of the Noether current and energy-momentum tensor, in 't~Hooft's large-$N$ limit (some form factors can be found even at finite $N$). We use these new form factors to calculate physical quantities in (2+1)-dimensional Yang-Mills theory, generalizing previous $SU(2)$ results from Orland to $SU(N)$. The anisotropic gauge theory is related to standard isotropic one by a Wilsonian renormalization group with ellipsoidal cutoffs in momentum. We calculate quantum corrections to the effective action of QED and QCD, as the theory flows from isotropic to anisotropic. The exact principal chiral sigma model S-matrix is also used to examine the spectrum of (1+1)-dimensional massive Yang Mills theor...
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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
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...
Unstable states in quantum theory
Kuksa, V. I.
2014-05-01
Various approaches to the problem of describing unstable particles are reviewed. Fundamental problems that arise in quantum field description of these particles and the ways of their solution are considered. Among them, there is an approach related to the notion of the smeared (continuous) mass, which originates from the finite lifetime of unstable particles. The quantum field model of unstable particles with smeared mass, which is built upon two basic axiomatic elements, is considered in detail. The basic processes with unstable particles (decay and scattering) are considered within the framework of the model and the formalism for describing physical characteristics of those processes is developed. The model is successfully applied to describing the processes of pair and triple boson production at the linear collider, top quark pair production, and certain hadronic decays. Based on this model, the factorization method is developed, which allows a description of complicated and multistep scattering and decay processes with unstable particles to be considerably simplified.
Completeness in Hybrid Type Theory
DEFF Research Database (Denmark)
Areces, Carlos; Blackburn, Patrick Rowan; Huertas, Antonia;
2014-01-01
We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types...... the way we interpret @i in propositional and first-order hybrid logic. This means: interpret @iαa , where αa is an expression of any type a , as an expression of type a that rigidly returns the value that αa receives at the i-world. The axiomatization and completeness proofs are generalizations of those...... found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting...
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.
Diestel, Reinhard
2000-01-01
This book is a concise, yet carefully written, introduction to modern graph theory, covering all its major recent developments. It can be used both as a reliable textbook for an introductory course and as a graduate text: on each topic it covers all the basic material in full detail, and adds one or two deeper results (again with detailed proofs) to illustrate the more advanced methods of that field. This second edition extends the first in two ways. It offers a thoroughly revised and updated chapter on graph minors, which now includes full new proofs of two of the central Robertson-Seymour theorems (as well as a detailed sketch of the entire proof of their celebrated Graph Minor Theorem). Second, there is now a section of hints for all the exercises, to enhance their value for both individual study and classroom use.
International Nuclear Information System (INIS)
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 sub volume (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 'holistic'. In fact it positions the E-J Gedankenexperiment into the same conceptual class as the cosmological constant problem and the Unruh Gedankenexperiment and the problem of the cosmological constant. 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 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 pointlike localization for massless higher spin fields. It hopefully also will contribute to its solution. (author)
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.
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
International Nuclear Information System (INIS)
This chapter presents the basic principles of cluster dynamics as a particular case of mesoscopic rate theory models developed to investigate fuel behaviour under irradiation such as in UO2. It is shown that as this method simulates the evolution of the concentration of every type of point or aggregated defect in a grain of material. It produces rich information that sheds light on the mechanisms involved in microstructure evolution and gas behaviour that are not accessible through conventional models but yet can provide for improvements in those models. Cluster dynamics parameters are mainly the energetic values governing the basic evolution mechanisms of the material (diffusion, trapping and thermal resolution). In this sense, the model has a general applicability to very different operational situations (irradiation, ion-beam implantation, annealing) provided that they rely on the same basic mechanisms, without requiring additional data fitting, as is required for more empirical conventional models. This technique, when applied to krypton implanted and annealed samples, yields a precise interpretation of the release curves and helps assess migration mechanisms and the krypton diffusion coefficient, for which data is very difficult to obtain due to the low solubility of the gas. (authors)
Resonances, scattering theory and rigged Hilbert spaces
International Nuclear Information System (INIS)
The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free, in, and out eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian; the singularities of the out eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of complete sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the out eigenvectors. The free, in and out eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee-Friedrichs model. 48 references
Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
Spill, Fabian
In the following paper, which is based on the author's PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this work is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which constrain the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the S-matrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with 𝔰𝔲(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. We give a pedagogical introduction into the subject, presenting a unified perspective of Yangians and their applications in physics. This paper should hence be accessible to mathematicians who would like to explore the application of algebraic objects to physics as well as to physicists interested in a deeper understanding of the mathematical origin of physical quantities.
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...
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
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
Modular localization and the holistic structure of causal quantum theory, a historical perspective
International Nuclear Information System (INIS)
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 string local fields in Hilbert space. Among other things this leads to a radical reformulation of the Englert-Higgs symmetry breaking mechanism. (author)
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.
Theory and Vocational Education.
Swanson, Gordon I.
1988-01-01
The search for an explanation of day-to-day problems is the appropriate framework for describing theory. Theory and research have reciprocal relationships: Theory gives direction to research and research refines theory. Vocational education occurs in the context of many theoretical frames. Understanding this theory relatedness is important to…
Copter: Cosmological perturbation theory
Carlson, Jordan
2013-04-01
Copter is a software package for doing calculations in cosmological perturbation theory. Specifically, Copter includes code for computing statistical observables in the large-scale structure of matter using various forms of perturbation theory, including linear theory, standard perturbation theory, renormalized perturbation theory, and many others. Copter is written in C++ and makes use of the Boost C++ library headers.
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.