A wave equation for massive particles of arbitrary spin

1967 ◽  
Vol 297 (1450) ◽  
pp. 351-364 ◽  
Keyword(s):  
Wave Equation ◽  
Arbitrary Spin ◽  
Field Vector ◽  
Second Order ◽  
The Other ◽  
Particle Field ◽  
Gravitational Fields ◽  
Other Hand ◽  
Free Case ◽  
Unique Spin

A wave equation is given which, in the force-free case, describes a particle of unique spin and mass and which remains consistent when interactions are included. The equation is simple in the sense that it involves only matrices which satisfy the Pauli commutation rules. This simplicity is achieved at the expense of extending the particle field vector from one of 2j + 1 components to one of 4j. However, the extra 2j — 1 components are just what are needed to remove the inconsistency of the interacting system. In the force-free case these additional components vanish and the resulting equations are equivalent to the usual ones of Dirac, Fierz and Pauli. One the other hand, for the interacting system, the extra components do not vanish. The second order propagation equations are deduced in the case of external electromagnetic and gravitational fields.

scholarly journals Die konstruksie en evaluering van 'n werks tevredenheidvraelys vir predikante

1993 ◽  
Vol 19 (1) ◽  
Author(s):  
S. M. Van Vuuren ◽  
M. Schepers
Keyword(s):  
Job Satisfaction ◽  
Second Order ◽  
The Other ◽  
Self Concept ◽  
Factor Analyses ◽  
Multidimensional Construct ◽  
Other Hand ◽  
Order Factor ◽  
The One ◽  
Mate Waarin

The construction and evaluation of a job satisfaction inventory for ministers. Job satisfaction is a multidimensional construct indicating the degree of adjustment of a worker to his work. A questionnaire was constructed for measuring the various aspects of job satisfaction of ministers. It was administered to 307 ministers. First and second order factor analyses were performed on the items of the questionnaire. Three strong factors of the job satisfaction of ministers were identified, viz. satisfaction with the work as such, the minister's experience of the relationships between him and his wife on the one hand, and his church council and congregation on the other hand, and his vocational self concept. The implications of these findings are discussed. Opsomming Werkstevredenheid is 'n meerdimensionele konstruk wat 'n aanduiding gee van die mate waarin 'n werker in sy werk aanpas. 'n Vraelys om verskeie aspekte van die werkstevredenheid van predikante te meet, is gekonstrueer. Dit is op 'n steekproef van 307 predikante toegepas. Eerste- en tweedeorde-faktorontledings is op die items van die vraelys uitgevoer. Drie sterk faktore van die werkstevredenheid van predikante is geidentifiseer, te wete die belewing van sy werk as sodanig, die belewing van die verhouding tussen horn en sy vrou aan die een kant, en die kerkraad en gemeente aan die ander kant, en sy beroepselfkonsep. Die implikasies van die bevindinge word bespreek.

scholarly journals A Survey of Conceptualizations of Politeness

2015 ◽  
Vol 5 (6) ◽  
pp. 115
Author(s):  
Lei Qiu
Keyword(s):  
Second Order ◽  
The Other ◽  
Theoretical Construct ◽  
First Order ◽  
Relational Work ◽  
Other Hand ◽  
Uniform Definition

<p>Along with the general trends of research from traditional Gricean approach to postmodern approach, politeness has been conceptualized as facework, social indexing concept, relational work and interactional work. Based on examination of debates over East group-oriented and Western individual-oriented politeness, first-order and second-order politeness, as well as the universality and relativity of conceptualizations, this paper has roughly demonstrated that the tension between universality and relativity of politeness can help to explain the reason for lack of uniform definition and concept in this field. It is essential for researchers to seek a universal second-order culture-general theoretical construct on one hand, and to look at first-order culture-specific constructs on the other hand.</p>

PARADOXICAL KINEMATIC ACAUSALITY IN WEINBERG’S EQUATIONS FOR MASSLESS PARTICLES OF ARBITRARY SPIN

1992 ◽  
Vol 07 (22) ◽  
pp. 1967-1974 ◽  
Author(s):  
D.V. AHLUWALIA ◽  
D.J. ERNST
Keyword(s):  
Wave Equations ◽  
Classical Group ◽  
Arbitrary Spin ◽  
The Other ◽  
Finite Mass ◽  
Massless Particles ◽  
Paradoxical Situation ◽  
Other Hand ◽  
Free Particles

Weinberg’s equations for massless free particles of arbitrary spin are found to have acausal solutions. On the other hand, the m→0 limit of Joos-Weinberg’s finite-mass wave equations satisfied by (j, 0)⊕(0, j) j) covariant spinors are free from all kinematic acausality. This paradoxical situation is resolved and corrected by carefully studying the transition from the classical group theoretical arguments to quantum mechanically interpreted equations.

Etude des modes de ramification sympodiale chez Lycopersicum esculentum et L. pimpinellifolium

1974 ◽  
Vol 52 (10) ◽  
pp. 2207-2218 ◽  
Author(s):  
A. Silvy
Keyword(s):  
Seed Treatment ◽  
Second Order ◽  
The Other ◽  
Mature Plant ◽  
Leaf Number ◽  
Axillary Bud ◽  
Lycopersicum Esculentum ◽  
Other Hand ◽  
Macroscopic Observation

In Lycopersicum esculentum Mill, and L. pimpinellifolium Dun. ramification modes of plants with determinate and indeterminate habits are studied by macroscopic observation (apex evolution, phyllotaxis, and leaf number of the different branches of a mature plant) and also by analyzing mutated sectors after seed treatment. While the first inflorescence, a cyme, originates from the greater part of the prefloral apex, the top of which bears the first flower, second-order axes come up at the axils of the last two leaves. In all the varieties, the axillary bud of the second-last leaf produces a sympodial lateral ramification. On the other hand, that of the last leaf, which becomes visible on the side of the prefloral apex, as anticipated, immediately bears a second inflorescence in varieties with determinate habit, but makes up the second-order axis of the main sympodium in varieties with indeterminate habit. The characteristics of these two bud patterns are compared.

Reflections on the concept of symmetry

2005 ◽  
Vol 13 (S2) ◽  
pp. 3-11 ◽  
Author(s):  
KUNO LORENZ
Keyword(s):  
Binary Relation ◽  
Second Order ◽  
The Other ◽  
First Order ◽  
Broken Symmetries ◽  
Other Hand ◽  
Logical Notion ◽  
The One ◽  
Ancient Usage

The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, ‘being symmetric’ in general usage is synonymous with ‘being harmonious’, and in technical usage, as in Euclid's Elements, it is synonymous with ‘commensurable’. Due to the second meaning, which is close to the etymology of συ´μμετρoς, ‘with measure’ has likewise to be read as ‘being [in] rational [ratios]’ and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.

scholarly journals On the Domains of Bessel Operators

2021 ◽  
Author(s):  
Jan Dereziński ◽  
Vladimir Georgescu
Keyword(s):  
Sobolev Space ◽  
Schrödinger Operator ◽  
Second Order ◽  
The Other ◽  
Bessel Operator ◽  
Bilinear Forms ◽  
Minimal Realization ◽  
Schrodinger Operator ◽  
Bessel Operators ◽  
Other Hand

AbstractWe consider the Schrödinger operator on the halfline with the potential $$(m^2-\frac{1}{4})\frac{1}{x^2}$$ ( m 2 - 1 4 ) 1 x 2 , often called the Bessel operator. We assume that m is complex. We study the domains of various closed homogeneous realizations of the Bessel operator. In particular, we prove that the domain of its minimal realization for $$|\mathrm{Re}(m)|<1$$ | Re ( m ) | < 1 and of its unique closed realization for $$\mathrm{Re}(m)>1$$ Re ( m ) > 1 coincide with the minimal second-order Sobolev space. On the other hand, if $$\mathrm{Re}(m)=1$$ Re ( m ) = 1 the minimal second-order Sobolev space is a subspace of infinite codimension of the domain of the unique closed Bessel operator. The properties of Bessel operators are compared with the properties of the corresponding bilinear forms.

Boundary value problems with data on opposite characteristics for a second-order mixed-hyperbolic equation

2020 ◽  
Vol 20 (3) ◽  
pp. 6-13
Author(s):  
G.A. Balkizov ◽  
Keyword(s):  
Wave Equation ◽  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Wave Operator ◽  
Boundary Value ◽  
Second Order ◽  
The Other ◽  
The Given

Within the framework of this work, solutions of boundary value problems with data on “opposite” (“parallel”) characteristics are found for one mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic Gellerstedt operator in the other part. It is known that problems with data on opposite (parallel) characteristics for the wave equation in the characteristic quadrangle are posed incorrectly. However, as shown in this paper, the solution of similar problems for a mixed-hyperbolic equation consisting of a wave operator in one part of the domain and a degenerate hyperbolic Gellerstedt operator with an order of degeneracy in the other part of the domain, under certain conditions on the given functions, exists, is unique and is written explicitly.

Interactions of massless particles of arbitrary spin

1966 ◽  
Vol 294 (1437) ◽  
pp. 175-194 ◽  
Keyword(s):  
Massless Particle ◽  
Arbitrary Spin ◽  
Massless Particles ◽  
Reduced Representation ◽  
Gravitational Fields ◽  
Group Theoretic Method ◽  
Homogeneous Lorentz Group ◽  
Higher Spin ◽  
Free Case ◽  
Consistency Problem

The self-consistency problem s arising when massless particles of higher spin are coupled to the electromagnetic and gravitational fields are investigated using a group theoretic method as opposed to the Lagrangian approach employed by Fierz & Pauli (1939) in their discussion for massive particles. A massless particle of spin j is described by a 4j dimensional vector satisfying a generalization of Rumer’s equation (1930). 2j + 1 of these 4j components form the conventional quantity associated with a particle of spin j and the remaining 2j — 1 are supernumary quantities needed for the consistency of the in teracting system ; the whole object transforms according to the reduced representation (j, 0)⊕ (j — 1, 0) of the homogeneous Lorentz group. It is suggested that this formalismis a convenient way of writing higher-spin equations in particle-like form with attendant advantages (see, for example, Good 1959). In the force-free case the 2j — 1 auxiliary quantities can be set equal to zero but this is not possible in the interacting system with out inconsistency. One conclusion is that it is impossible for a (massless) particle of unique spin to be coupled minimally to gravitation unless either its spin is less than 1/2, space-time is conformally flat or its spin is two and it describes gravitation radiation itself.

On the consistency of an impredicative subsystem of Quine's NF

1982 ◽  
Vol 47 (1) ◽  
pp. 131-136 ◽  
Author(s):  
Marcel Crabbé
Keyword(s):  
Second Order ◽  
The Other ◽  
Third Order ◽  
Natural Manner ◽  
Second Order Arithmetic ◽  
Other Hand ◽  
Quick Proof ◽  
Order Arithmetic ◽  
The One

NFP is the predicative fragment of NF. In this system we do not allow a set to exist if it cannot be defined without using quantifiers ranging over its type or parameters of a higher type. NFI is a less restrictive fragment located between NFP and NF.We show that NFP is really weaker than NFI; similarly, NFI is weaker than NF. This result will be obtained in the following manner: on the one hand, we will show that NFP can be proved consistent in elementary arithmetic and that second order arithmetic is interpretable in NFI; on the other hand, we will prove the consistency of NFI in third order arithmetic, which is contained in NF.The paper is divided in four sections. In §1, we define the concepts needed and collect a few results together in such a way that they will be ready for later use. In §2, we will present a model-theoretic (quick) proof of the consistency of NFI (and thus of NFP). The proof will be chosen (it is not the quickest!) so as to motivate in a natural manner the details of the proof-theoretical version of it that will be presented in §3. §4 will be devoted to the axiom of infinity in NFP and NFI.

scholarly journals Impurity-induced and Second Order Raman Spectra of NaCl Crystals Doped with Different Ag+ Concentrations

1970 ◽  
Vol 25 (7) ◽  
pp. 1024-1029 ◽  
Author(s):  
W. Möller ◽  
R. Kaiser
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Second Order ◽  
The Other ◽  
Silver Concentration ◽  
Other Hand

Raman spectra of NaCl crystals doped with Ag+ ions up to 3.5 mol% have been measured in 4 scattering geometries. In the impurity induced part of the Eg- and F2g-spectra the strongest peaks are located at 85 and 171 cm-1. Their intensities increase proportional to the silver concentration. The second order Raman spectrum on the other hand appears to be independent of the Ag+ content. The spectra are fully explained by theory and by the assumption of Ag+ pairs

Sign in / Sign up

Export Citation Format

Share Document