operators and alternating sentences in arithmetic

1980 ◽  
Vol 45 (1) ◽  
pp. 144-154 ◽  
Author(s):  
Larry Manevitz ◽  
Jonathan Stavi
Keyword(s):  
Standard Model ◽  
Natural Number ◽  
Combinatorial Problem ◽  
The Other ◽  
Predicate Calculus ◽  
Completeness Proof ◽  
The Standard Model ◽  
Truth Value ◽  
The One ◽  
Definition Of

Determining the truth value of self-referential sentences is an interesting and often tricky problem. The Gödel sentence, asserting its own unprovability in P (Peano arithmetic), is clearly true in N(the standard model of P), and Löb showed that a sentence asserting its own provability in P is also true in N (see Smorynski [Sm, 4.1.1]). The problem is more difficult, and still unsolved, for sentences of the kind constructed by Kreisel [K1], which assert their own falsity in some model N* of P whose complete diagram is arithmetically defined. Such a sentence χ has the property that N ⊨ iff N* ⊭ χ (note that ¬χ has the same property).We show in §1 that the truth value in N of such a sentence χ, after a certain normalization that breaks the symmetry between it and its negation, is determined by the parity of a natural number, called the rank of N, for the particular construction of N* used. The rank is the number of times the construction can be iterated starting from N and is finite for all the usual constructions. We also show that modifications of, e.g., Henkin's construction (in his completeness proof of predicate calculus) allow arbitrary finite values for the rank of N. Thus, on the one hand the truth value of χ in N, for a given “nice” construction of N*, is independent of the particular (normalized) choice of χ, and we shall see that χ is unique up to (provable) equivalence in P. On the other hand, the truth value in question is sensitive to minor changes in the definition of N* and its determination seems to be largely a combinatorial problem.

scholarly journals STUECKELBERG: A FORERUNNER OF MODERN PHYSICS II

2008 ◽  
Vol 23 (08) ◽  
pp. 1105-1112 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
ORCHIDEA MARIA LECIAN
Keyword(s):  
Vector Field ◽  
Scattering Amplitudes ◽  
Standard Model ◽  
The Other ◽  
Massive Vector ◽  
Other Hand ◽  
The Standard Model ◽  
Modern Physics ◽  
The One ◽  
Definition Of

We will investigate some aspects of Stueckelberg's work, which have contributed to the development of modern physics. On the one hand, the definition of diffuse boundaries in the calculation of scattering amplitudes will be reviewed, and compared with the other proposals by physicists of that time. On the other hand, the applications of Stueckelberg's description of a massive vector field in the Standard Model will be discussed.

scholarly journals Weak scale from Planck scale: Mass scale generation in a classically conformal two-scalar system

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Junichi Haruna ◽  
Hikaru Kawai
Keyword(s):  
Scalar Field ◽  
Standard Model ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
The Other ◽  
Expectation Value ◽  
Weak Scale ◽  
The Standard Model ◽  
The One

Abstract In the standard model, the weak scale is the only parameter with mass dimensions. This means that the standard model itself cannot explain the origin of the weak scale. On the other hand, from the results of recent accelerator experiments, except for some small corrections, the standard model has increased the possibility of being an effective theory up to the Planck scale. From these facts, it is naturally inferred that the weak scale is determined by some dynamics from the Planck scale. In order to answer this question, we rely on the multiple point criticality principle as a clue and consider the classically conformal $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant two-scalar model as a minimal model in which the weak scale is generated dynamically from the Planck scale. This model contains only two real scalar fields and does not contain any fermions or gauge fields. In this model, due to a Coleman–Weinberg-like mechanism, the one-scalar field spontaneously breaks the $ \mathbb{Z}_2$ symmetry with a vacuum expectation value connected with the cutoff momentum. We investigate this using the one-loop effective potential, renormalization group and large-$N$ limit. We also investigate whether it is possible to reproduce the mass term and vacuum expectation value of the Higgs field by coupling this model with the standard model in the Higgs portal framework. In this case, the one-scalar field that does not break $\mathbb{Z}_2$ can be a candidate for dark matter and have a mass of about several TeV in appropriate parameters. On the other hand, the other scalar field breaks $\mathbb{Z}_2$ and has a mass of several tens of GeV. These results will be verifiable in near-future experiments.

Back to the Ether?

2018 ◽  
pp. 178-178
Author(s):  
Alvaro De Rújula
Keyword(s):  
Standard Model ◽  
Higgs Field ◽  
The Other ◽  
The Standard Model ◽  
The One

The vacuum is permeated by a constant Higgs field, does this bring the old “ether” back? No, velocities relative to the ether were thought to be detectable. The vacuum of the Standard Model does not make that possible, given the spin-0 nature of the Higgs field. Yet the other substance permeating our Universe, the CBR, constitutes an absolute system: the one in which it is maximally isotropic.

Comments on the Market Crash: Six Months After

1988 ◽  
Vol 2 (3) ◽  
pp. 45-50 ◽  
Author(s):  
Hayne Leland ◽  
Mark Rubinstein
Keyword(s):  
Standard Model ◽  
Real Life ◽  
The Other ◽  
Financial Equilibrium ◽  
The Standard Model ◽  
Trading Mechanisms

Six months after the market crash of October 1987, we are still sifting through the debris searching for its cause. Two theories of the crash sound plausible -- one based on a market panic and the other based on large trader transactions -- though there is other evidence that is difficult to reconcile. If we are to believe the market panic theory or the Brady Commission's theory that the crash was primarily caused by a few large traders, we must strongly reject the standard model. We need to build models of financial equilibrium which are more sensitive to real life trading mechanisms, which account more realistically for the formation of expectations, and which recognize that, at any one time, there is a limited pool of investors available with the ability to evaluate stocks and take appropriate action in the market.

Ring-diagram summations in the finite-temperature effective potential

1993 ◽  
Vol 71 (5-6) ◽  
pp. 227-236 ◽  
Author(s):  
M. E. Carrington
Keyword(s):  
Phase Transition ◽  
Standard Model ◽  
Effective Potential ◽  
Finite Temperature ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Ring Diagram ◽  
First Order Phase Transition ◽  
The Standard Model ◽  
The One

There has been much recent interest in the finite-temperature effective potential of the standard model in the context of the electroweak phase transition. We review the calculation of the effective potential with particular emphasis on the validity of the expansions that are used. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electroweak phase transition. However, in the high-temperature regime, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram summation, and show that the standard model has a first-order phase transition in the weak coupling expansion.

scholarly journals Emotionally evaluative attitude of parents in the high conflict families to each other and the child

2016 ◽  
Vol 6 (4) ◽  
pp. 126-141
Author(s):  
S.S. Kulakov
Keyword(s):  
Negative Attitude ◽  
Semantic Differential ◽  
The Other ◽  
Dysfunctional Families ◽  
Psychiatric Examination ◽  
High Conflict ◽  
The One ◽  
Definition Of ◽  
The Relationship ◽  
Conflictual Relationship

The increasing number of dysfunctional families causes an increase in the number of civil litigation on the education of the child, where the relationship between the persons are highly conflictual. The actual task is study the one of components in the structure of the psychological relationship - emotional and semantic constructs underlying semantic perception of each other and the child's parents. Examination of 42 testees (parents) from harmonious families and 54 testees (parents) during the forensic psychological and psychiatric examination (regarding the definition of child`s residence or the order of meetings for the child and the parent who don`t live with it) by methods "Geometric test of relations" and "Semantic Differential" showed that in families where is highly conflictual relationship, there is positive assessments of herself and her child, while assessment of the spouse (wife) characterized inversion. This negative attitude toward the spouse (wife) is not the other parent's negative characteristics. It is the ignoring the other parent's positive characteristics. The positive acceptance of all family members was revealed in harmonious families.

scholarly journals Handling i narratologien, litteraturen og livet

2006 ◽  
Vol 34 (101) ◽  
pp. 122-139
Author(s):  
Thor Grünbaum
Keyword(s):  
The Other ◽  
Final Part ◽  
Communicative Function ◽  
Other Hand ◽  
The One ◽  
Definition Of

Action in Narratology, Literature, and LifeIn this article I argue that the representation of simple, bodily action has the function of endowing the narrative sequence with a visualizing power: It makes the narrated scenes or situations ready for visualization by the reader or listener. By virtue of this visualizing power or disposition, these narrated actions disrupt the theoretical divisions, on the one hand, between the narrated story and the narrating discourse, and on the other hand, between plot-narratology and discourse-narratology. As narrated actions they seem to belong to the domain of plot-narratology, but in so far as they serve an important visualizing function, these narrated actions have a communicative function and as such they can be said to belong to the domain of discourse-narratology. In a first part of the article, I argue that a certain type of plot-narratology, due to its retrospective epistemology and abstract definition of action, is unable to conceive of this visualizing function. In a second part, I argue that discourse-narratology fares no better since the visualizing function is independent of voice and focalization. In a final part, I sketch a possible account of the visualizing function of simple actions in narratives.

scholarly journals The one-loop tadpole in the geoSMEFT

2021 ◽  
Vol 11 (5) ◽  
Author(s):  
Tyler Corbett
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Power Counting ◽  
Leading Order ◽  
The Standard Model ◽  
The One ◽  
Near Future ◽  
Geometric Formulation

Making use of the geometric formulation of the Standard Model Effective Field Theory we calculate the one-loop tadpole diagrams to all orders in the Standard Model Effective Field Theory power counting. This work represents the first calculation of a one-loop amplitude beyond leading order in the Standard Model Effective Field Theory, and discusses the potential to extend this methodology to perform similar calculations of observables in the near future.

scholarly journals The Computational Strength of Extensions of Weak König’s Lemma

1998 ◽  
Vol 5 (41) ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Natural Number ◽  
Arbitrary Function ◽  
The Other ◽  
Binary Trees ◽  
Subsequent Paper ◽  
Bounded Functions ◽  
The One ◽  
Weak König’S Lemma ◽  
König’S Lemma

The weak König's lemma WKL is of crucial significance in the study of fragments of mathematics which on the one hand are mathematically strong but on the other hand have a low proof-theoretic and computational strength. In addition to the restriction to binary trees (or equivalently bounded trees), WKL<br />is also `weak' in that the tree predicate is quantifier-free. Whereas in general the computational and proof-theoretic strength increases when logically more complex trees are allowed, we show that this is not the case for trees which are<br />given by formulas in a class Phi where we allow an arbitrary function quantifier prefix over bounded functions in front of a Pi^0_1-formula. This results in a schema Phi-WKL.<br />Another way of looking at WKL is via its equivalence to the principle<br /> For all x there exists y<=1 for all z A0(x; y; z) -> there exists f <= lambda x.1 for all x, z A0(x, fx, z);<br />where A0 is a quantifier-free formula (x, y, z are natural number variables). <br /> We generalize this to Phi-formulas as well and allow function quantifiers `there exists g <= s'<br />instead of `there exists y <= 1', where g <= s is defined pointwise. The resulting schema is called Phi-b-AC^0,1.<br />In the absence of functional parameters (so in particular in a second order context), the corresponding versions of Phi-WKL and Phi-b-AC^0,1 turn out to<br />be equivalent to WKL. This changes completely in the presence of functional<br />variables of type 2 where we get proper hierarchies of principles Phi_n-WKL and<br />Phi_n-b-AC^0,1. Variables of type 2 however are necessary for a direct representation<br />of analytical objects and - sometimes - for a faithful representation of<br />such objects at all as we will show in a subsequent paper. By a reduction of<br />Phi-WKL and Phi-b-AC^0,1 to a non-standard axiom F (introduced in a previous paper) and a new elimination result for F relative to various fragment of arithmetic in all finite types, we prove that Phi-WKL and Phi-b-AC^0,1 do<br />neither contribute to the provably recursive functionals of these fragments nor to their proof-theoretic strength. In a subsequent paper we will illustrate the greater mathematical strength of these principles (compared to WKL).

scholarly journals REMARKS ON THE VALUE OF THE HIGGS MASS FROM THE PRESENT LEP DATA

1995 ◽  
Vol 10 (10) ◽  
pp. 845-852 ◽  
Author(s):  
M. CONSOLI ◽  
Z. HIOKI
Keyword(s):  
Standard Model ◽  
Higgs Mass ◽  
Detailed Comparison ◽  
The Other ◽  
Firm Conclusion ◽  
Other Hand ◽  
Model Predictions ◽  
The One

We perform a detailed comparison of the present LEP data with the one-loop standard model predictions. It is pointed out that for mt = 174 GeV the "bulk" of the data prefers a rather large value of the Higgs mass in the range of 500–1000 GeV, in agreement with the indications from the W mass. On the other hand, to accommodate a light Higgs it is crucial to include the more problematic data for the τ FB asymmetry. We discuss further improvements on the data which are required to obtain a firm conclusion.

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