13202889
Optimal signal-to-quantum noise ratio for nonclassical number states
Abstract We analyze the properties of nonclassical number states, specifically squeezed number states D ( α ) S ( z )| n 〉, and find their maximum signal-to-quantum noise ratio. It is shown that the optimal signal-to-quantum noise ratio for these states decreases as 1/(2 n +1) 2 , where n is the photon number, from the optimal value as derived by Yuen [Phys. Lett. A 56 (1976) 105].
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.
84436927
ORDER PARAMETERS FOR BROKEN ABELIAN SYMMETRIES
12865240
An interface between physics and number theory
We extend the Hopf algebra description of a simple quantum system given previously, to a more elaborate Hopf algebra, which is rich enough to encompass that related to a description of perturbative quantum field theory (pQFT). This provides a mathematical route from an algebraic description of non-relativistic, non-field theoretic quantum statistical mechanics to one of relativistic quantum field theory. Such a description necessarily involves treating the algebra of polyzeta functions, extensions of the Riemann Zeta function, since these occur naturally in pQFT. This provides a link between physics, algebra and number theory. As a by-product of this approach, we are led to indicate inter alia a basis for concluding that the Euler gamma constant γ may be rational.
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.
9242923
INTERPRETING THE EVOLUTION OF THE SIZE-LUMINOSITY RELATION FOR DISK GALAXIES FROM REDSHIFT 1 TO THE PRESENT
A sample of very high resolution cosmological disk galaxy simulations is used to investigate the evolution of galaxy disk sizes back to redshift 1 within the ΛCDM cosmology. Artificial images in the rest-frame B band are generated, allowing for a measurement of disk scale lengths using surface brightness profiles as observations would, and avoiding any assumption that light must follow mass as previous models have assumed. We demonstrate that these simulated disks are an excellent match to the observed magnitude-size relation for both local disks and for disks at z = 1 in the magnitude/mass range of overlap. We disentangle the evolution seen in the population as a whole from the evolution of individual disk galaxies. In agreement with observations, our simulated disks undergo roughly 1.5 mag arcsec^(–2) of surface brightness dimming since z = 1. We find evidence that evolution in the magnitude-size plane varies by mass, such that galaxies with M_* ≥ 10^9 M_⊙ undergo more evolution in size than luminosity, while dwarf galaxies tend to evolve potentially more in luminosity. The disks grow in such a way as to stay on roughly the same stellar-mass-size relation with time. Finally, due to an evolving stellar-mass-star-formation-rate (SFR) relation, a galaxy at a given stellar mass (or size) at z = 1 will reside in a more massive halo and have a higher SFR, and thus a higher luminosity, than a counterpart of the same stellar mass at z = 0.