Phenomenological field theories for layered materials: Equations of motion and continuity conditions

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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Goldstones with extended shift symmetries

International Journal of Modern Physics D ◽

10.1142/s0218271814430019 ◽

2014 ◽

Vol 23 (13) ◽

pp. 1443001 ◽

Cited By ~ 25

Author(s):

Kurt Hinterbichler ◽

Austin Joyce

Keyword(s):

Scalar Field ◽

Lower Order ◽

Degrees Of Freedom ◽

Equations Of Motion ◽

Higher Order ◽

Field Theories ◽

Relativistic Case ◽

Goldstone Bosons

We consider scalar field theories invariant under extended shift symmetries consisting of higher order polynomials in the spacetime coordinates. These generalize ordinary shift symmetries and the linear shift symmetries of the galileons. We find Wess–Zumino Lagrangians which transform up to total derivatives under these symmetries, and which possess fewer derivatives per field and lower order equations of motion than the strictly invariant terms. In the nonrelativistic context, where the extended shifts are purely spatial, these theories may describe multi-critical Goldstone bosons. In the relativistic case, where the shifts involve the full spacetime coordinate, these theories generally propagate extra ghostly degrees of freedom.

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Complete factorization of equations of motion for generalized scalar field theories

EPL (Europhysics Letters) ◽

10.1209/0295-5075/119/61002 ◽

2017 ◽

Vol 119 (6) ◽

pp. 61002 ◽

Cited By ~ 1

Author(s):

D. Bazeia ◽

Diego R. Granado ◽

Elisama E. M. Lima

Keyword(s):

Scalar Field ◽

Equations Of Motion ◽

Field Theories ◽

Complete Factorization

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Higher spin theories in flat space–time

International Journal of Modern Physics A ◽

10.1142/s0217751x18450070 ◽

2018 ◽

Vol 33 (34) ◽

pp. 1845007

Author(s):

Loriano Bonora

Keyword(s):

Equations Of Motion ◽

Flat Space ◽

Space Time ◽

Local Fields ◽

Field Theories ◽

Gauge Transformations ◽

Yang Mills ◽

Higher Spin ◽

Chern Simons

It is shown that, contrary to a widespread prejudice, massless higher spin (HS) field theories can be defined in flat space–time. Examples of Yang–Mills-like theories with infinite many local fields of any spin are constructed explicitly in any dimension, along with Chern–Simons-like models in any odd dimension. These theories are defined via actions invariant under HS gauge transformations and their equations of motion are derived. It is also briefly explained why these theories circumvent well-known no-go theorems.

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Field theories with high derivatives

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100024014 ◽

1948 ◽

Vol 44 (1) ◽

pp. 76-86 ◽

Cited By ~ 26

Author(s):

T. S. Chang

Keyword(s):

Energy Momentum Tensor ◽

Equations Of Motion ◽

Hamiltonian Formulation ◽

Functional Derivative ◽

Momentum Tensor ◽

Field Theories ◽

Field Equations ◽

Gauge Invariant ◽

Image Position ◽

Derivatives Of

The relativistic field theories of elementary particles are extended to cases where the field equations are derived from Lagrangians containing all derivatives of the field quantities. Expressions for the current, the energy-momentum tensor, the angular-momentum tensor, and the symmetrized energy-momentum tensor are given. When the field interacts with an electromagnetic field, we introduce a subtraction procedure, by which all the above expressions are made gauge-invariant. The Hamiltonian formulation of the equations of motion in a gauge-invariant form is also given.After considering the Lagrangian L as a scalar in a general relativity transformation and thus a function of gμν and their derivatives, the functional derivative ofwith respect to gμν (x) at a point where the space time is flat is worked out. It is shown that this differs from the symmetrized energy-momentum tensor given in the above sections by a term which vanishes when certain operators Sij are antisymmetrical or when the Lagrangian contains the first derivatives of the field quantities only and whose divergence to either μ or ν vanishes.

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UNDERSTANDING SOLITONS ALGEBRAICALLY

Modern Physics Letters A ◽

10.1142/s0217732392002809 ◽

1992 ◽

Vol 07 (36) ◽

pp. 3403-3410 ◽

Cited By ~ 9

Author(s):

ZVONIMIR HLOUSEK ◽

DONALD SPECTOR

Keyword(s):

Equations Of Motion ◽

Field Theories ◽

Topological Solitons ◽

Model Independent ◽

Central Result

We describe techniques we have developed to analyze the physics of topological solitons in a model-independent way. Our central result is to show that topological solitons in generic field theories exhibit Bogomol’nyi bounds and Bogomol’nyi equations. Our methods turn the derivation of these Bogomol’nyi relationships into algebraic calculations and do not depend on the particular equations of motion. We present a discussion of the O(3) nonlinear σ-model as an example of our techniques.

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