84436927
ORDER PARAMETERS FOR BROKEN ABELIAN SYMMETRIES
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).
16936199
Hopf algebra structure of a model quantum field theory
Recent elegant work[1] on the structure of Perturbative Quantum Field Theory (PQFT) has revealed an astonishing interplay between analysis( Riemann Zeta functions), topology (Knot theory), combinatorial graph theory (Feynman Diagrams) and algebra (Hopf structure). The difficulty inherent in the complexities of a fully-fledged field theory such as PQFT means that the essential beauty of the relationships between these areas can be somewhat obscured. Our intention is to display some, although not all, of these structures in the context of a simple zero-dimensional field theory; i.e. a quantum theory of non-commuting operators which do not depend on spacetime. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs [2, 3], analogous to the Feynman diagrams of PQFT, which we show possess a Hopf algebra structure[4]. Our approach is based on the partition function for a boson gas. In a subsequent note in these Proceedings we sketch the relationship between the Hopf algebra of our simple model and that of the PQFT algebra.
118438283
Spontaneous symmetry breaking and the Cabibbo angle
SummaryWe study the possibility that the magnitude and direction of the strong breaking ofSU3 may be obtained from a self-consistent response equation, symmetric inSU3 apart from driving terms. These driving terms may be eithera), direct: a relatively strong force corresponding to the fifth interaction, orb) indirect: small perturbations due to electromagnetic and appropriate weak interactions. In the latter case, choosing a model in which the nonleptonic decays have a characteristic angle twice that of the semi-leptonic decays, one obtains the value

$$\tfrac{1}{2}\cos ^{ - 1} (\sqrt 3 /2) = 15^ \circ $$

 for the Cabibbo angle.RiassuntoSi studia la possibilità di ottenere l’intensità e la direzione della rottura forte diSU3 da una equazione di risposta autocoerente, simmetrica inSU3 indipendentemente dai termini fondamentali. Questi termini fondamentali possono esere siaa) diretti: una forza relativamente forte corrispondente alla quinta interazione, ob) indiretti: piccole perturbazioni dovute ad interazioni elettromagnetiche deboli ed appropriate. Nell'ultimo caso, scegliendo un modello in cui i decadimenti non leptonici hanno un angolo caratteristico doppio di quello dei decadimenti semileptonici, si ottiene il valore di

$$\tfrac{1}{2}\cos ^{ - 1} (\sqrt 3 /2) = 15^ \circ $$

 per l’angolo di Cabibbo.РезюмеМы изучаем возможность, что величина и направление сильного нарушенияSU3 могут быть получены из само-согласованного характеристического уравнения, симметричного вSU3, за иа исключением главных членов. Эти главные члены могут быть либо a)прямыми: относительно сильная сила, соответствующая Пятому Взаимодействию, либо б) непрямыми: слабые возмущения, обусловленные электромагинтным и соответствующим слабым взаимодействиями. В последнем случае, выбирая модель, в которой нелептонные распады имеют характеристический угол в два раза болясий, чем для полу-лептонных распадов, получаем величину

$$\tfrac{1}{2}\cos ^{ - 1} (\sqrt 3 /2) = 15^ \circ $$

 для угла Кабиббо.
86533547
GROUP THEORY AND SUPERFLUID SYSTEMS
117176517
THE ISING ALGEBRA
Publisher Summary This chapter presents a Lie algebra connected with the solution of a classical problem in statistical mechanics, which is the Ising model. The model consists of a two-dimensional array of spins, each of which interacts with its nearest neighbours only. The standard treatments show that such two-dimensional lattice problems are reduced to one-dimensional form by the introduction of an elegant device called the transfer matrix T. The solution then involves diagonalization of this transfer matrix, the thermodynamic free energy being determined by the maximum eigenvalue of T. Generally T has the form of a product of exponentials. The chapter presents the equation of the transfer matrix.
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.