Spacetime Dependent Lagrangians and Weak-Strong Duality : Sine Gordon and Massive Thirring Models

The formalism of spacetime dependent lagrangians developed in Ref.1 is applied to the Sine Gordon and massive Thirring models.It is shown that the well-known equivalence of these models (in the context of weak-strong duality) can be understood in this approach from the same considerations as described in [1] for electromagnetic duality. A further new result is that all these can be naturally linked to the fact that the holographic principle has analogues at length scales much larger than quantum gravity. There is also the possibility of {\it noncommuting coodinates} residing on the boundaries. PACS: 11.15.-q: 11.10/EfComment: Latex, 16 pages, article shortened, references added, minor typos correcte

Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-Mills Quantum Field Theory in Four Dimensions

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function $E(x,y)$ of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as $$E(x,y) \sim |x - y|^{-2 - 2 d_G},$$ \noindent for $|x-y|>>0,$ where $d_G$ is a positive integer depending on the gauge group $G.$ In the case where $G=SU(n),$ we conjecture that $$d_G = {\rm dim}SU(n) - {\rm dim}S(U(n-1) \times U(1)),$$ \noindent so that the rate of decay of correlations increases as $n \to \infty.$Comment: Minor corrections of notation, style and arithmetic errors; correction of minor gap in the proof of Proposition 1.4 (the statement of the Proposition was correct); further remark and references adde

Vacuum Decay in Theories with Symmetry Breaking by Radiative Corrections

The standard bounce formalism for calculating the decay rate of a metastable vacuum cannot be applied to theories in which the symmetry breaking is due to radiative corrections, because in such theories the tree-level action has no bounce solutions. In this paper I derive a modified formalism to deal with such cases. As in the usual case, the bubble nucleation rate may be written in the form $A e^{-B}$. To leading approximation, $B$ is the bounce action obtained by replacing the tree-level potential by the leading one-loop approximation to the effective potential, in agreement with the generally adopted {\it ad hoc} remedy. The next correction to $B$ (which is proportional to an inverse power of a small coupling) is given in terms of the next-to-leading term in the effective potential and the leading correction to the two-derivative term in the effective action. The corrections beyond these (which may be included in the prefactor) do not have simple expressions in terms of the effective potential and the other functions in the effective action. In particular, the scalar-loop terms which give an imaginary part to the effective potential do not explicitly appear; the corresponding effects are included in a functional determinant which gives a manifestly real result for the nucleation rate.Comment: 39 pages, CU-TP-57

Roles of Critical Valence Fluctuations in Ce- and Yb-Based Heavy Fermion Metals

The roles of critical valence fluctuations of Ce and Yb are discussed as a key origin of several anomalies observed in Ce- and Yb-based heavy fermion systems. Recent development of the theory has revealed that a magnetic field is an efficient control parameter to induce the critical end point of the first-order valence transition. Metamagnetism and non-Fermi liquid behavior caused by this mechanism are discussed by comparing favorably with CeIrIn5, YbAgCu4, and YbIr2Zn20. The interplay of the magnetic order and valence fluctuations offers a key concept for understanding Ce- and Yb-based systems. It is shown that suppression of the magnetic order by enhanced valence fluctuations gives rise to the coincidence of the magnetic-transition point and valence-crossover point at absolute zero as a function of pressure or magnetic field. The interplay is shown to resolve the outstanding puzzle in CeRhIn5 in a unified way. The broader applicability of this newly clarified mechanism is discussed by surveying promising materials such as YbAuCu4, beta-YbAlB4, and YbRh2Si2.Comment: 17 pages, 8 figures, invited paper in special issue on strongly correlated electron system

Regularized Green's Function for the Inverse Square Potential

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.Comment: 10 pages. The final section was expande

Vacuum decay and internal symmetries

We study the effects of internal symmetries on the decay by bubble nucleation of a metastable false vacuum. The zero modes about the bounce solution that are associated with the breaking of continuous internal symmetries result in an enhancement of the tunneling rate into vacua in which some of the symmetries of the initial state are spontaneously broken. We develop a general formalism for evaluating the effects of these zero modes on the bubble nucleation rate in both flat and curved space-times.Comment: LaTex, 11 pages, No figures, one minor chang

Semiconductor superlattice photodetectors

A superlattice photomultiplier and a photodetector based on the real space transfer mechanism were studied. The wavelength for the first device is of the order of a micron or flexible corresponding to the bandgap absorption in a semiconductor. The wavelength for the second device is in the micron range (about 2 to 12 microns) corresponding to the energy of the conduction band edge discontinuity between an Al/(sub x)Ga(sub 1-x)As and GaAs interface. Both devices are described

Semiconductor superlattice photodetectors

Two novel types of superlattice photodetectors were studied. The first was a superlattice photomultiplier and the second a photodetector based on the real space transfer mechanism. A summary of the results is presented

Semiconductor superlattice photodetectors

Superlattice photodetectors were investigated. A few major physical processes in the quantum-well heterostructures related to the photon detection and electron conduction mechanisms, the field effect on the wave functions and the energy levels of the electrons, and the optical absorption with and without the photon assistance were studied