121983423
Global and Infinitesimal Nonlinear Chiral Transformations
The problem of determining arbitrary nonlinear representations of a given compact Lie group is studied with the object of constructing Lagrangians invariant under the group. To achieve this, expressions for the covariant derivatives are obtained and it is shown how previous treatments based on global and on infinitesimal considerations are related. The noncompact case, the relationship between non‐linearity and zero‐mass particles, and the possibility of embedding the representation manifold in a higher‐dimensional space are all discussed.
27515895
Generalized Holstein-Primakoff squeezed states for SU(n).
We show how to define multiphoton, many-mode squeezed states for SU(n), using a generalized Holstein-Primakoff realization. We prove that for the class of realizations given, the resulting squeezing reduces to that of SU(2), and exemplify with a specific calculation for SU(3).
84436927
ORDER PARAMETERS FOR BROKEN ABELIAN SYMMETRIES
119711153
Dynamical group model of the CDW state
Abstract The dynamical group for a one-dimensional model of a many-electron system exhibiting a charge-density wave is obtained. The corresponding Lie algebra in a physical model is U(2); it is used to obtain the spectrum and coherent ground state, and to define a corresponding order parameter.
121551361
Chiral symmetry and the goldstone theorem
1803
A multipurpose Hopf deformation of the Algebra of Feynman-like Diagrams
We construct a three parameter deformation of the Hopf algebra $\mathbf{LDIAG}$. This new algebra is a true Hopf deformation which reduces to $\mathbf{LDIAG}$ on one hand and to $\mathbf{MQSym}$ on the other, relating $\mathbf{LDIAG}$ to other Hopf algebras of interest in contemporary physics. Further, its product law reproduces that of the algebra of polyzeta functions.
119221920
Inflationary Instabilities of Einstein-Aether Cosmology
We examine the consequences of Lorentz violation during slow-roll inflation. We consider a canonical scalar inflaton coupled, through its potential, to the divergence of a fixed-norm timelike vector field, or "aether." The vector is described by Einstein-aether theory, a vector-tensor model of gravitational Lorentz violation. We derive and analyze the cosmological perturbation equations for the metric, inflaton, and aether. If the scale of Lorentz violation is sufficiently small compared to the Planck mass, and the strength of the scalar-aether coupling is suitably large, then the spin-0 and spin-1 perturbations grow exponentially and spoil the inflationary background. The effects of such a coupling on the CMB are too small to be visible to current or near-future CMB experiments; unusually, no isocurvature modes are produced at first order in a perturbative expansion around the aether norm. These results are discussed for both a general potential and a worked example, $m^2 \phi^2$ inflation with a quadratic scalar-aether coupling term.