Equations of Motion in Classical Nonlinear Field Theories

Abstract In a companion paper [1], we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)

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ASPECTS OF Q-MATTER STABILITY

International Journal of Modern Physics A ◽

10.1142/s0217751x92003306 ◽

1992 ◽

Vol 07 (28) ◽

pp. 7169-7184 ◽

Cited By ~ 6

Author(s):

MINOS AXENIDES

Keyword(s):

Order Parameter ◽

Mass Matrix ◽

Equations Of Motion ◽

Finite Energy ◽

Field Theories ◽

Strong Interactions ◽

Mass Relation ◽

Bosonic Field ◽

Meson Octet ◽

Continuous Symmetries

Relativistic bosonic field theories in 3+1 dimensions with exact global continuous symmetries and conserved charges Q may admit stable, finite energy, time dependent configurations (Q-balls) as solutions to their equations of motion. Previous work established their existence for both Abelian and non-Abelian symmetries. In the present work we elaborate on some more issues of stability and uniqueness that arise in the SO(3) and SU(3) renormalizable models. We consider the effect of explicit symmetry breaking in the spectrum of the SU(3) model, by identifying its order parameter with the meson octet and by choosing a mass matrix consistent with the Gell-Mann-Okubo mass relation. We demonstrate the existence of “isospin” and “strange” balls whose stability is due to the presence of residual global symmetries which are identified with the exact symmetries of isospin and strangeness of strong interactions.

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Quantization of Fields in Accordance with Modular Statistics

Australian Journal of Physics ◽

10.1071/ph750115 ◽

1975 ◽

Vol 28 (2) ◽

pp. 115 ◽

Cited By ~ 8

Author(s):

HS Green

Keyword(s):

Correspondence Principle ◽

Quantum Statistics ◽

Field Theories ◽

Nonlinear Field ◽

Dynamical State ◽

Fermi Statistics ◽

Integral Spin ◽

New Statistics

A new generalization of quantum statistics is described, which is different from parastatistics, though it includes Fermi statistics and parafermi statistics of order two. It can be applied to the quantization of nonlinear field theories, without violating the correspondence principle. Like parastatistics, it allows the occupation of a given dynamical state by more than one particle of half-odd-integral spin. A special feature is that quark-like particles are naturally associated in modules, which have many of the characteristics of baryons and mesons. The group theoretical properties of the new statistics, and the implied classification of states, are briefly examined.

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