204014568
Allowed Domains for Chiral-Symmetry- and Isospin-Breaking Parameters
In addition to the chiral-symmetry-breaking terms ${\ensuremath{\epsilon}}_{0}{\ensuremath{\sigma}}_{0}+{\ensuremath{\epsilon}}_{8}{\ensuremath{\sigma}}_{8}$ an isospin - breaking term ${\ensuremath{\epsilon}}_{3}{\ensuremath{\sigma}}_{3}$ is included in the study of the (3,\ifmmode\bar\else\textasciimacron\fi{}3)\ensuremath{\bigoplus}(\ifmmode\bar\else\textasciimacron\fi{}3,3) model. By assuming that the intermediate symmetry is either ${\mathrm{SU}}_{2}$\ensuremath{\bigotimes}${\mathrm{SU}}_{2}$ or ${\mathrm{SU}}_{3}$, allowed domains for the chiral-symmetry- and isospin-breaking parameters are derived. A $\ensuremath{\sigma}$-model Lagrangian is then constructed. The positivity condition for the masses reproduces the general features of the domain structure.
14771278
Nonadiabatic geometric phase for the cyclic evolution of a time-dependent Hamiltonian system
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic timeperiodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states is expressed as a superposition of an infinite number of squeezed states. Their geometric phases are found to be independent of \, and equal to 2(n11/2) times the classical nonadiabatic Hannay angle. @S1050-2947~98!03311-3# The Berry phase is one of the most important findings on the fundamental problem of quantum mechanics in recent years @1#. It reveals the gauge structure associated with a phase shift in adiabatic processes in quantum mechanics. This quantal phase is connected with a classical angle, namely, the Hannay angle, by a simple and elegant expression in the semiclassical limit @2#. The next important advance was the relaxation of the adiabatic approximation @3,4#. Aharanov and Anandan studied the phase associated with a cyclic evolution in quantum mechanics, which occurs when a state returns to its initial condition. They showed that the phase is a geometrical property of the curve in the projective Hilbert space which is naturally associated with the motion @3#. For the special case of an adiabatic evolution, this phase factor is a gauge-invariant generalization of the Berry phase. The significance of Aharanov and Anandan’s generalization lies in the following: ~i! the cyclic evolution of a physical system is of the most interest in physics both experimentally and theoretically; ~ii! the universal existence of the cyclic evolution is guaranteed for any quantum system. The second point can be easily recognized by considering the eigenvectors of the unitary evolution operator for a quantum system. An explicit example is a time-periodic Hamiltonian system where the Floquet theorem applies. The eigenfunctions of the Floquet operator, which are the socalled Bloch wave functions in condensed-matter physics, are obviously cyclic solutions and are of great interest in physics. However, unlike the adiabatic case, in the nonadiabatic case calculating the eigenvectors and extracting the nonadiabatic geometric phase from the quasienergy term for a time-dependent Hamiltonian is far from a trivial task, except in the special case of the spin particle in a magnetic field. Recent works of Ge and Child@5# made a further step in this direction. They found a special cyclic state of the Gaussian wave packet’s form for a generalized harmonic oscillator. The nonadiabatic geometric phase is explicitly calculated and found to be one-half of the classical nonadiabatic Hannay angle. In this paper, we would like to suggest an alternative approach—the squeezed-state approach to study the general cyclic evolutions of the generalized harmonic oscillator. In particular, we shall construct a class of quantum states based on the superposition of an infinite number of squeezed states. We find that the condition for them to be cyclic evolutions is nothing but the quantization rule without Maslov-Morse correction. The nonadiabatic geometric phases are obtained analytically, and found to be related to the classical Hannay angle by an explicit expression.
122878082
Induced Topological Terms, Hidden Local Symmetry, and Anyon Superconductivity
We show how the topological Chern-Simons term in three dimensions and the θ-term, in four dimensions can be dynamically generated due to quantum fluctuations in Nambu-Jona-Lasinio models. These results give a vivid demonstration of hidden local symmetry at work. The fluctuation-induced Chern-Simons term provides a natural way to incorporate fractional statistics and thus a more direct connection with anyon superconductivity. Possible phenomenological implications of this approach in particle physics are also discussed.
117912244
Galilean structure of the Poincaré group on the light-cone
SummaryIt is observed that the isomorphism between the Poincaré subgroup in the L.C. (light-cone) co-ordinates and the two-dimensional Galilean group can be trivially extended to higher dimensions. The case of five dimension is explicitly shown, and the generalization to any finite dimensionn (> 2) is immediate.RiassuntoSi osserva che l’isomorfismo fra il sottogruppo di Poincaré nelle coordinate del cono di luce (L.C.) ed il gruppo galileano bidimensionale può essere esteso in modo banale a dimensioni superiori. Si presenta esplicitamente il caso delle cinque dimensioni, e la generalizzazione a qualunque dimensione finitan (>2) è immediata.РеэюмеОтмечается, что иэоморфиэм между подгруппой Пуанкаре в координата светового конуса и двумерной группой Галилея может быть тривиально распространен на случай больщего числа иэмерений. Явным обраэом исследуется пятимерный случай. Обобшение на случай любого числа иэмеренийп (>2) получается непосредственно.
209934211
Anomalous dimensions of tensor operators in 4-epsilon dimensions
120428117
Crossover phenomena in the multifractal behavior of invariant circles
Abstract The singularity spectrum f(α) and the generalized dimension Dq of the critical invariant circle in an area-preserving twist map with a variable degree of inflection z is studied. The scaling behavior is found to depend on z, and there is a crossover from the simple fixed point to the standard fixed point when z varies from 2 to 3. Thus z plays a role quite similar to that of dimensionality in phase transition, with z = 2 and 3 corresponding to the lower and upper critical dimensions respectively.
119185851
Timelike vector field dynamics in the early universe
We study the dynamics of a timelike vector field when the background spacetime is in an accelerating phase in the early universe. With a timelike vector field, an inflationary phase is shown to be difficult to realize, so we investigate the evolution of a vector field within a scalar field-driven inflation model. Also, we calculate the power spectrum of the vector field without considering the metric perturbations. While the time component of the vector field perturbations provides a scale invariant spectrum when ζ = 0, where ζ is a nonminimal coupling parameter, both the longitudinal and the transverse perturbations give a scale invariant spectrum when ζ = 1/6 in the absence of the coupling terms. The deviation of the power spectrum due to the coupling terms is calculated by use of the Greens’ function.
17221851
Vacuum fluctuations and moving atoms / detectors: From Casimir-Polder to Unruh effect
In this note we review some recent results on corrections to the Casimir?Polder retardation force due to atomic motion and present a preliminary critique on one recently proposed cavity QED scheme for detection of the Unruh?Davies?DeWitt?Fulling effect. These two well-known effects arise from the interaction between a moving atom or detector and a quantum field under some boundary conditions introduced by a conducting mirror/cavity or dielectric wall. The Casimir?Polder force is a retardation force on the atom due to the dressing of the atomic ground state by the vacuum electromagnetic field in the presence of a conducting mirror or dielectric wall. We have recently provided an improved calculation by treating the mutual influence of the atom and the (constrained) field in a self-consistent way. For an atom moving adiabatically, perpendicular to a mirror, our result finds a coherent retardation correction up to twice the stationary value. The Unruh?Davies?DeWitt?Fulling effect refers loosely to the fact that a uniformly accelerated detector feels hot. Two prior schemes have been proposed for the detection of 'Unruh radiation', based on charged particles in linear accelerators and storage rings. Here we are interested in a third scheme proposed recently by Scully et al involving the injection of accelerated atoms into a microwave or optical cavity. We analyse two main factors instrumental to the purported success in this scheme, the cavity factor and the sudden switch-on factor. We conclude that the effects engendered from these factors are unrelated to the Unruh?Davies?DeWitt?Fulling effect.
14650080
Moving charges, detectors, and mirrors in a quantum field with backreaction
This is a progress report on our current work on moving charges[1, 2], detectors[3], and moving mirrors[4, 5] in a quantum field treated in a fully relativistic way via the Feynman-Vernon influence functional method[6], which preserves maximal quantum coherence of the system with selfconsistent back-reaction from the field.
20833106
New analytical methods for gravitational radiation and reaction in binaries with arbitrary mass ratio and relative velocity
or small mass ratio for its formulation. This case should encompass the inspiral and possibly the plunge and merger phases of binaries with otherwise general parameters (e.g., mass ratio and relative velocity) though more investigation is needed to substantiate it. In the second part, we discuss how the mass ratio can be treated as a perturbation parameter in the post-Newtonian eective
118426631
Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields
Using the full radiation transfer function, we numerically calculate the CMB angular bispectrum seeded by the compensated magnetic scalar density mode. We find that, for the string inspired primordial magnetic fields characterized by index nB = −2.9 and mean-field amplitude Bλ = 9nG, the angular bispectrum is dominated by two primordial magnetic shapes. The first magnetic shape looks similar to the one from local-type primordial curvature perturbations, so both the amplitude and profile of the Komatsu-Spergel estimator (reduced bispectrum) seeded by this shape are almost the same as those of the primary CMB anisotropies. However, for different parameter sets (l1,l2), this ``local-type'' reduced bispectrum oscillates around different asymptotic values in the high-l3 regime because of the effect of the Lorentz force, which is exerted by the primordial magnetic fields on the charged baryons. This feature is different from the standard case where all modes approach to zero asymptotically in the high-l limit. On the other hand, the second magnetic shape appears only in the primordial magnetic field model. The amplitude of the Komatsu-Spergel estimator sourced by the second shape diverges in the low-l regime because of the negative slope of shape. In the high-l regime, this amplitude is approximately equal to that of the first estimator, but with a reversal phase.