Fermion number creation via electromagnetism

Let an external current, whose support is confined to the space-like slab |x ⁰| < T in two-dimensional spacetime, build up a localized charge density which vanishes for times |x ⁰| > T. We show that the zero mass Dirac quantum field reacts to this current by a c-number shift of the fermion number, i.e. Q _out=Q _in+Q, with , where q(x ⁰) denotes the total external charge. For the shift of the axial charge we obtain an extension of existing results.     

Absence of the efimov effect in a homogeneous magnetic field

A system of three identical particles in a homogeneous magnetic field is studied. It is shown that the Hamiltonian of this system with short-range potentials after the separation of the center of mass motion has a finite discrete spectrum for each fixed type m of the rotational (SO(2)) symmetry.Supported by the Erwin Schrödinger Institute, Austria, International Science Foundation Grant No. 9400 and Russian Grant of the State Committee for High Education RF-94-27-1022.     

On the finiteness of the discrete spectrum of Hamiltonians for quantum systems of three one- or two-dimensional particles

The system of three particles (acting in K dimensions (K=1, 2)) without stable two-particle subsystems is studied. For short-range potentials V _ij (r _ij ), the finiteness of the discrete spectrum is proved for any type of permutational symmetry.     

Nonrelativistic calculation of the Lamb shift without applying the dipole approximation

By applying a method which exploits the O(4) symmetry of the nonrelativistic hydrogen atom, the Lamb shift is calculated without making the dipole approximation. Similar calculations in the dipole approximation have been previously carried out by Lieber. The advantage of our calculations is that, without introducing a cutoff-frequency, analytical and numerical results for energy-level (Lamb) shifts, in which the self-energy of the free electron is completely separated, are obtained. Since the obtained results are finite, the significance of the retardation effects is clearly demonstrated. Furthermore, a comparison is also made with the results obtained by other authors.     

Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound

The kinetic energy inequality is alternatively proved which yields Lieb's boundN < 2Z + 1 on the maximum negative ionization of an atom with nucleus chargeZ andN electrons when the kinetic energy operator is the nonrelativistic or relativistic magnetic Schrödinger operator. It is seen to follow from the free case where the vector potential vanishes. The proof applies to the Weyl quantized relativistic magnetic Schrödinger operator as well.Research partially supported by Grant-in-Aid for Scientific Research Nos. 04640141 and 05640165, Ministry of Education, Science and Culture, Japanese Government.     

Theoretical basis for a new subnatural spectroscopy via correlation interferometry

A new line-narrowing effect in coincidence interferometry yielding subnatural resolution of atomic transition frequencies is proposed and analyzed. The approach utilizes second-order photon correlation properties of the radiation field. This is in contrast to the first-order measurements associated with time delay spectroscopy, which is known to yield subnatural resolution. Connections between the two techniques are investigated.Dedicated to the memory of Professor Julian Schwinger, a role model for us all     

Resonance fluorescence of strongly driven two-level system coupled to multiple dissipative reservoirs

We present a theoretical formalism for resonance fluorescence radiating from a two-level system (TLS) driven by any periodic driving and coupled to multiple reservoirs. The formalism is derived analytically based on the combination of Floquet theory and Born–Markov master equation. The formalism allows us to calculate the spectrum when the Floquet states and quasienergies are analytically or numerically solved for simple or complicated driving fields. We can systematically explore the spectral features by implementing the present formalism. To exemplify this theory, we apply the unified formalism to comprehensively study a generic model that a harmonically driven TLS is simultaneously coupled to a radiative reservoir and a dephasing reservoir. We demonstrate that the significant features of the fluorescence spectra, the driving-induced asymmetry and the dephasing-induced asymmetry, can be attributed to the violation of detailed balance condition, and explained in terms of the driving-related transition quantities between Floquet-states and their steady populations. In addition, we find the distinguished features of the fluorescence spectra under the biharmonic and multiharmonic driving fields in contrast with that of the harmonic driving case. In the case of the biharmonic driving, we find that the spectra are significantly different from the result of the RWA under the multiple resonance conditions. By the three concrete applications, we illustrate that the present formalism provides a routine tool for comprehensively exploring the fluorescence spectrum of periodically strongly driven TLSs.     

Weakly coupled states on branching graphs

We consider a Schrödinger particle on a graph consisting of N links joined at a single point. Each link supports a real locally integrable potential V _j ; the self-adjointness is ensured by the type boundary condition at the vertex. If all the links are semi-infinite and ideally coupled, the potential decays as x ^–1– along each of them, is nonrepulsive in the mean and weak enough, the corresponding Schrödinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the coupling constant may be interpreted in terms of a family of squeezed potentials.     

Search for lepton flavor violation in supersymmetric models via meson decays

Considering the constraints from the experimental data on μ→eγ$\mu \to e\gamma$, μ→3e$\mu \to 3e$, μ–e$\mu \text{–}e$ conversion, etc., we analyze the lepton flavor violating decays ?(J/Ψ,?(1S))→e⁺μ⁻(μ⁺τ⁻)$?(J/\Psi ,?(1S))\to e^{+}{\mu }^{-}({\mu }^{+}{\tau }^{-})$ in the scenarios of the minimal supersymmetric extensions of Standard Model with seesaw mechanism. Numerically, there is parameter space that the LFV processes of J/Ψ(?)→μ⁺τ⁻$J/\Psi (?)\to {\mu }^{+}{\tau }^{-}$ can reach the upper experimental bounds, meanwhile the theoretical predictions on μ→eγ$\mu \to e\gamma$, μ→3e$\mu \to 3e$, μ–e$\mu \text{–}e$ conversion satisfy the present experimental bounds. For searching of new physics, lepton flavor violating processes J/Ψ(?)→μ⁺τ⁻$J/\Psi (?)\to {\mu }^{+}{\tau }^{-}$ may be more promising and effective channels.     

Driven systems with one bound state

Schwinger's quantum action principle is used to calculate transition amplitudes in systems with a single bound state that are driven by a time-dependent force. Applications to the study of multiphoton processes in the negative hydrogen ion are hinted at.     

A Remark on the Estimate of a Determinant by Minami

In the context of the Anderson model, Minami proved a Wegner type bound on the expectation of 2 × 2 determinant of Green’s functions. We generalize it so as to allow for a magnetic field, as well as to determinants of higher order.      

q-Gravity

Since general relativity may be regarded as a non-Abelian gauge theory obtained by gauging the Lorentz group, one may obtain its q-deformation by gauging the q-Lorentz group. The q-dependent action resulting from this construction describes interacting gravitational and spinor fields. This action is invariant under nonlocal q-transformations.     

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941     

A new limit for the noncommutative space–time parameter

The spectrum of the hydrogen atom in the framework of noncommutative quantum mechanics is studied and the related phenomenology is presented. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in the atom. To the first order in the noncommutative parameter, it is equivalent to an electron in the fields of a Coulomb potential and an electric dipole and this allows us to get a bound for this parameter. In a second step, we compute noncommutative corrections of the energy levels and find that they are at the second order in the parameter of noncommutativity. By comparing our results to those obtained from experimental spectroscopy, we get another limit for this parameter.     

Scattering theory for a model of an atom in a quantized field

We compute the scattering operator for a simplified model of an atom interacting a with a quantized field. The field is restricted to the vacuum and one-particle sectors, and the atom has only two states. We also solve the inverse scattering problem for the same model. The methods used rely on the particular form of the interaction, which is chosen to mimic the interaction between radiation and matter.This work was partially supported by NSF Grant DMS-8922941.     

Failure of saturated ferromagnetism for the Hubbard model with two holes

We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small.     

Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics

A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral of a family of self-adjoint operators acting in the Hilbert space , where is the Hilbert space of the quantum radiation field. The fiber operator is called the Hamiltonian of the Dirac polaron with total momentum . The main result of this paper is concerned with the non-relativistic (scaling) limit of . It is proven that the non-relativistic limit of yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics.     

Frame-like action and unfolded formulation for massive higher-spin fields

Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS$(A)\mathit{dS}$ spaces are presented. Manifestly gauge invariant action for a spin s?2$s?2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.     

Dyons in topological field theories

We examine a class of topological field theories defined by Lagrangians that under certain conditions can be written as the sum of two characteristic numbers or winding numbers. Therefore, the action or the energy is a topological invariant and stable under perturbations. The sufficient conditions required for stability take the form of first-order field equations, analogous to the self-duality and Bogomol'nyi equations in Yang-Mills(-Higgs) theory. Solutions to the first-order equations automatically satisfy the full field equations. We show the existence of nontrivial, nonsingular, minimum energy spherically symmetric dyon solutions and that they are stable. We also discuss evidence for a dual field theory to Yang-Mills-Higgs in topological field theory. The existence of dual field theories and electric monopoles is predicted by Montonen and Olive.