Conformally covariant field equations I. first-order equations with non-vanishing mass

1975 ◽  
Vol 25 (2) ◽  
pp. 123-149 ◽  
Author(s):  
R. Kotecký ◽  
J. Niederle
Keyword(s):  
Field Equations ◽  
First Order ◽  
Covariant Field

Conformally covariant field equations II. First-order massless equations

1977 ◽  
Vol 12 (2) ◽  
pp. 237-249 ◽  
Author(s):  
R. Kotecký ◽  
J. Niederle
Keyword(s):  
Field Equations ◽  
First Order ◽  
Covariant Field

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

Strength of the Poincaré gauge field equations in first order formalism

1989 ◽  
Vol 139 (1-2) ◽  
pp. 21-26 ◽  
Author(s):  
Michael Sué ◽  
Eckehard W. Mielke
Keyword(s):  
Gauge Field ◽  
Field Equations ◽  
First Order

WEAK SOLUTIONS FOR WEAK SINGULARITIES

2002 ◽  
Vol 17 (20) ◽  
pp. 2769-2769
Author(s):  
B. C. NOLAN
Keyword(s):  
Existence And Uniqueness ◽  
Finite Measure ◽  
Generalized Solutions ◽  
Functions Of Bounded Variation ◽  
Field Equations ◽  
Finite Radius ◽  
Locally Finite ◽  
Naked Singularities ◽  
First Order ◽  
Bounded Functions

We revisit the problem of the development of singularities in the gravitational collapse of an inhomogeneous dust sphere. As shown by Yodzis et al1, naked singularities may occur at finite radius where shells of dust cross one another. These singularities are gravitationally weak 2, and it has been claimed that at these singularities, the metric may be written in continuous form 2, with locally L∞ connection coefficients 3. We correct these claims, and show how the field equations may be reformulated as a first order, quasi-linear, non-conservative, non-strictly hyperbolic system. We discuss existence and uniqueness of generalized solutions of this system using bounded functions of bounded variation (BV) 4, where the product of a BV function and the derivative of another BV function may be interpreted as a locally finite measure. The solutions obtained provide a dynamical extension to the future of the singularity.

Pair creation of neutral Dirac particle in (1 + 2)d noncommutative spacetime

2018 ◽  
Vol 33 (03) ◽  
pp. 1850017 ◽  
Author(s):  
B. Hamil
Keyword(s):  
Neutral Particle ◽  
Pair Creation ◽  
Dirac Particle ◽  
Bogoliubov Transformation ◽  
Quantum Fields ◽  
Field Equations ◽  
First Order ◽  
Noncommutative Spacetime

In this paper, we study the influence of the noncommutativity on the pairs creation of neutral particle–antiparticle in (1 + 2)d. Using the Seiberg–Witten maps, the modified Euler–Lagrange field equations up to first-order in the noncommutativity, parameter [Formula: see text] is obtained and the Nikishov method based on Bogoliubov transformation is applied to calculate the density number of created neutral fermions. It is shown that the noncommutativity amplifies the density number N. In addition, when [Formula: see text], we obtain the known results corresponding to the undeformed quantum fields.

scholarly journals On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations

2020 ◽  
Vol 404 ◽  
pp. 109088 ◽  
Author(s):  
Michael Dumbser ◽  
Francesco Fambri ◽  
Elena Gaburro ◽  
Anne Reinarz
Keyword(s):  
Order Reduction ◽  
Einstein Field Equations ◽  
Field Equations ◽  
First Order

scholarly journals A geometrical analysis of the field equations in field theory

2002 ◽  
Vol 29 (12) ◽  
pp. 687-699 ◽  
Author(s):  
A. Echeverría-Enríquez ◽  
M. C. Muñoz-Lecanda ◽  
N. Román-Roy
Keyword(s):  
Field Theory ◽  
Classical Field ◽  
Field Theories ◽  
Geometrical Analysis ◽  
Field Equations ◽  
First Order ◽  
Nonuniqueness Of Solutions ◽  
Lagrangian And Hamiltonian Formalisms ◽  
Classical Field Theories ◽  
Geometric Formulation

We give a geometric formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and nonuniqueness of solutions of these equations, as well as their integrability.

Exact solution of a static charged sphere in general relativity

1969 ◽  
Vol 47 (21) ◽  
pp. 2401-2404 ◽  
Author(s):  
S. J. Wilson
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Gravitational Constant ◽  
The Self ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
Field Equations ◽  
First Order ◽  
Self Energy ◽  
Spherically Symmetric Distribution

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordström metric at the boundary. The self-energy contributions to the total gravitational mass are computed retaining only the first order terms in the gravitational constant.

scholarly journals THE SEIBERG–WITTEN MAP FOR NON-COMMUTATIVE PURE GRAVITY AND VACUUM MAXWELL THEORY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350023 ◽  
Author(s):  
ELISABETTA DI GREZIA ◽  
GIAMPIERO ESPOSITO ◽  
MARCO FIGLIOLIA ◽  
PATRIZIA VITALE
Keyword(s):  
Explicit Construction ◽  
Einstein Equations ◽  
Electromagnetic Potential ◽  
Field Equations ◽  
Maxwell Theory ◽  
Commutative Field ◽  
Yang Mills ◽  
First Order ◽  
Pure Gravity ◽  
Vacuum Solutions

In this paper the Seiberg–Witten map is first analyzed for non-commutative Yang–Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg–Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space–time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, when the Seiberg–Witten map is eventually inserted. In the attempt of understanding whether or not this is a peculiar property of gravity, in the second part of the paper, the Seiberg–Witten map is considered in the simpler case of Maxwell theory in vacuum in the absence of charges and currents. Once more, no obvious solution of the non-commutative field equations is found, unless the electromagnetic potential depends in a very special way on the wave vector.

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