On the structure of the free field equations

1980 ◽  
Vol 13 (12) ◽  
pp. 3619-3633
Author(s):  
J Rembielinski
Keyword(s):  
Free Field ◽  
Field Equations

Causal amplitudes and the Yang-Feldman formalism

1957 ◽  
Vol 53 (4) ◽  
pp. 843-847 ◽  
Author(s):  
J. C. Polkinghorne
Keyword(s):  
Field Theory ◽  
Green’S Functions ◽  
Free Field ◽  
Dispersion Relations ◽  
Matrix Elements ◽  
Field Equations ◽  
Commutation Relations ◽  
The Matrix ◽  
Free Fields ◽  
Set Up

ABSTRACTThe Yang-Feldman formalism vising the Feynman-like Green's functions is set up. The corresponding free fields have non-trivial commutation relations and contain information about the scattering. S-matrix elements are simply the matrix elements of anti-normal products of the field φF′(x). These are evaluated, and they give directly expressions used in the theory of causality and dispersion relations. It is possible to formulate field theory in a form in which the fields obey free field equations and the effects of interaction are contained in their commutation relations.

scholarly journals PARTICLE SPECTRUM OF NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (14) ◽  
pp. 1137-1161 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Field ◽  
Free Field ◽  
Gauge Fields ◽  
Particle Spectrum ◽  
Field Equations ◽  
Abelian Gauge ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Extended Field ◽  
Rank 2

We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

Group Properties of Free‐Field Equations

1963 ◽  
Vol 4 (4) ◽  
pp. 465-468 ◽  
Author(s):  
V. Amar ◽  
M. Lucchini ◽  
P. G. Sona
Keyword(s):  
Free Field ◽  
Field Equations

scholarly journals FREE FIELD EQUATIONS FOR SPACE–TIME ALGEBRAS WITH TENSORIAL MOMENTUM

2002 ◽  
Vol 17 (21) ◽  
pp. 1393-1406 ◽  
Author(s):  
R. MANVELYAN ◽  
R. MKRTCHYAN
Keyword(s):  
Einstein Equation ◽  
Gauge Invariance ◽  
Free Field ◽  
Space Time ◽  
Field Equations ◽  
Invariance Properties ◽  
Diffeomorphism Invariance ◽  
Rank Tensor

Free field equations, with various spins, for space–time algebras with second-rank tensor (instead of the usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. Special attention is paid to gauge invariance properties, in particular the spin-two equations with gauge invariance are constructed for dimensions 2+2 and 2+4, and the connection with Einstein equation and diffeomorphism invariance is established.

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