scholarly journals Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank

2005 ◽  
Vol 461 (2059) ◽  
pp. 2181-2195 ◽  
Author(s):  
Göran Bergqvist ◽  
Paul Lankinen
Keyword(s):  
Field Equation ◽  
Free Field ◽  
Massless Spin ◽  
Complete Set ◽  
Higher Rank ◽  
Necessary And Sufficient ◽  
Differential Condition

We present a study of Rainich-like conditions for symmetric and trace-free tensors T . For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel–Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.

METHOD OF MEAN VALUE OPERATORS FOR RADON TRANSFORMS IN THE SPACE OF MATRICES

2008 ◽  
Vol 19 (03) ◽  
pp. 245-283 ◽  
Author(s):  
E. OURNYCHEVA ◽  
B. RUBIN
Keyword(s):  
Radon Transform ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Inversion Method ◽  
Radon Transforms ◽  
Inversion Formulas ◽  
Higher Rank ◽  
Necessary And Sufficient

We extend the Funk–Radon–Helgason inversion method of mean value operators to the Radon transform [Formula: see text] of continuous and Lpfunctions which are integrated over matrix planes in the space of real rectangular matrices. Necessary and sufficient conditions of existence of [Formula: see text] for such f and explicit inversion formulas are obtained. New higher-rank phenomena related to this setting are investigated.

scholarly journals Bulk Local Operators, Conformal Descendants, and Radial Quantization

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Zhao-Long Wang ◽  
Yi Yan
Keyword(s):  
Field Theory ◽  
Field Equation ◽  
Prior Knowledge ◽  
Free Field ◽  
Finite Energy ◽  
Energy Scale ◽  
Quantization Formalism ◽  
Local Operators

We establish a construction of the bulk local operators in AdS by considering CFT at finite energy scale. Without assuming any prior knowledge about the bulk, the solution to the bulk free field equation automatically appears in the field theory arguments. In the radial quantization formalism, we find a properly regularized version of our initial construction. Possible generalizations beyond pure AdS are also discussed.

A two-parameter eigenvalue problem involving complex potentials

1990 ◽  
Vol 116 (1-2) ◽  
pp. 177-191
Author(s):  
M. Faierman
Keyword(s):  
Hilbert Space ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Complex Potentials ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Parameter System ◽  
Complete Set ◽  
Necessary And Sufficient ◽  
Two Parameter

SynopsisWe consider a two-parameter system of ordinary differential equations of the second order involving complex potentials and show that, unlike the case of real potentials, the eigenfunctions of the system do not necessarily form a complete set in the usual Hilbert space associated with the problem. We also give a necessary and sufficient condition for the eigenfunctions to be complete. Finally, we establish some results concerning the eigenvalues of the system.

scholarly journals Massless Spin Two Field, Covariant Quantization in a General Covariant Gauge: The Free Field Case

1978 ◽  
Vol 59 (2) ◽  
pp. 579-589
Author(s):  
L. Fernandez ◽  
A. Foussats ◽  
R. Laura ◽  
J. Lewis ◽  
O. Zandron
Keyword(s):  
Free Field ◽  
Covariant Quantization ◽  
Field Case ◽  
Massless Spin ◽  
Covariant Gauge

scholarly journals A Cylindrical Formulation of Force Free Magnetic Fields

2001 ◽  
Vol 203 ◽  
pp. 270-272
Author(s):  
E. A. Evangelidis ◽  
G. J. J. Botha
Keyword(s):  
Field Equation ◽  
Magnetic Fields ◽  
Free Field ◽  
Cylindrical Coordinates ◽  
Force Free Field

A new solution of the force free field equation is presented in cylindrical coordinates.

Exact regions of oscillation for a neutral differential equation

2000 ◽  
Vol 130 (2) ◽  
pp. 277-286
Author(s):  
S. S. Cheng ◽  
Y. Z. Lin
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Necessary And Sufficient Conditions ◽  
All Solutions ◽  
Constant Coefficients ◽  
Complete Set ◽  
Necessary And Sufficient

This paper is concerned with a neutral differential equation with four constant coefficients, one delay and one advancement. By means of the theory of envelopes, we consider all possible values of the parameters involved in the equation and obtain a complete set of necessary and sufficient conditions for all solutions to be oscillatory.

scholarly journals Conjugate spinor field equation for massless spin-3/2 field in de Sitter ambient space

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 465
Author(s):  
S. Falahi ◽  
S. Parsamehr
Keyword(s):  
Field Equation ◽  
Lagrange Equation ◽  
Ambient Space ◽  
Quantum Field ◽  
De Sitter ◽  
Comprehensive Description ◽  
Sitter Group ◽  
Gauge Invariant ◽  
Massless Spin ◽  
Spinor Field Equation

The quantum field theory in de Sitter ambient space provide us with a comprehensive description of massless gravitational field. Using the gauge-covariant derivative in the de Sitter ambient space, the gauge invariant Lagrangian density has been found.In this paper, the equation of the conjugate spinor for massless spin-$\frac{3}{2}$ field is obtained by Euler-Lagrange equation. Then the field equation is written in terms of the Casimir operator of the de Sitter group. Finally, the gauge invariant field equation is presented.

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