Chiral fermions on the lattice and index relations

Comparing recent lattice results on chiral fermions and old continuum results for the index puzzling questions arise. To clarify this issue we start with a critical reconsideration of the results on finite lattices. We then work out various aspects of the continuum limit. After determining bounds and norm convergences we obtain the limit of the anomaly term. Collecting our results the index relation of the quantized theory gets established. We then compare in detail with the Atiyah-Singer theorem. Finally we analyze conventional continuum approaches.Comment: 34 pages; a more detaild introduction and a subsection with remarks on literature adde

A Perturbative Study of a General Class of Lattice Dirac Operators

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. We study one-loop fermion contributions to the self-energy of the gauge field, which are related to the fermion contributions to the one-loop $\beta$ function and to the Weyl anomaly. We first explicitly demonstrate that the Ward identity is satisfied by the self-energy tensor. By performing careful analyses, we then obtain the correct self-energy tensor free of infra-red divergences, as a general consideration of the Weyl anomaly indicates. This demonstrates that our general operators give correct chiral and Weyl anomalies. In general, however, the Wilsonian effective action, which is supposed to be free of infra-red complications, is expected to be essential in the analyses of our general class of Dirac operators for dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in press

Domain wall fermion and CP symmetry breaking

We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables $q$ and $\bar q$ together with Pauli-Villars fields $Q$ and $\bar Q$ are utilized. It is shown that this domain wall representation in the infinite flavor limit $N=\infty$ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing $a$. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in press

On the continuum limit of fermionic topological charge in lattice gauge theory

It is proved that the fermionic topological charge of SU(N) lattice gauge fields on the 4-torus, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac operator, reduces to the continuum topological charge in the classical continuum limit when the parameter $m_0$ is in the physical region $0<m_0<2$.Comment: latex, 18 pages. v2: Several comments added. To appear in J.Math.Phy

First-order super-radiant phase transitions in a multi-qubit--cavity system

We predict the existence of novel first-order phase transitions in a general class of multi-qubit-cavity systems. Apart from atomic systems, the associated super-radiant phase transition should be observable in a variety of solid-state experimental systems, including the technologically important case of interacting quantum dots coupled to an optical cavity mode.Comment: To appear in Phys. Rev. Let

Grand unification in the minimal left-right symmetric extension of the standard model

The simplest minimal left-right symmetric extension of the standard model is studied in the high energy limit, and some consequences of the grand unification hypothesis are explored assuming that the parity breaking scale is the only relevant energy between the electro-weak scale and the unification point. While the model is shown to be compatible with the observed neutrino phenomenology, the parity breaking scale and the heavy boson masses are predicted to be above 10^7 TeV, quite far from the reach of nowadays experiments. Below that scale only an almost sterile right handed neutrino is allowed with a mass M \approx 100 TeV

Hot Topics in Ultra-Peripheral Collisions

Ultra-peripheral collisions of relativistic heavy ions involve long-ranged electromagnetic interactions at impact parameters too large for hadronic interactions to occur. The nuclear charges are large; with the coherent enhancement, the cross sections are also large. Many types of photonuclear and purely electromagnetic interactions are possible. We present here an introduction to ultra-peripheral collisions, and present four of the most compelling physics topics. This note developed from a discussion at a workshop on ``Electromagnetic Probes of Fundamental Physics,'' in Erice, Italy, Oct. 16-21, 2001.Comment: 7 pages, with 3 figures. This developed from a discussion at the workshop on "Electromagnetic Probes of Fundamental Physics," Oct. 16-21, Erice, Ital

Large collective Lamb shift of two distant superconducting artificial atoms

Virtual photons can mediate interaction between atoms, resulting in an energy shift known as a collective Lamb shift. Observing the collective Lamb shift is challenging, since it can be obscured by radiative decay and direct atom-atom interactions. Here, we place two superconducting qubits in a transmission line terminated by a mirror, which suppresses decay. We measure a collective Lamb shift reaching 0.8% of the qubit transition frequency and exceeding the transition linewidth. We also show that the qubits can interact via the transmission line even if one of them does not decay into it.Comment: 7+5 pages, 4+2 figure