Strong coupling in the quantum field theory with nonlocal nonpolynomial interaction

In the relativistic quantum field theory the representation for theS-matrix elements is obtained for any coupling constantsg in the case of a one component scalar field (x) with nonlocal nonpolynomial interaction _I ()=gU() when the causal function is bounded in the Euclidean region 0D _c (x _E ² D _c (0)< and the function |U(u)|1 for realu. It is proved that the two point Green function is bounded in the physical region of momenta variablep ².     

Confinement of quarks in nonlocal quantum field theory

The model of quarks in the frame of nonlocal quantum field theory is demonstrated. Here all basic principles of quantum theory are conserved, quarks are automatically confined and the scaling behaviour of the amplitude of an inclusive process is manifested explicitly in lower orders of perturbation theory.On leave of absence from theDept. of Theoretical Physics, Comenius University, Bratislava, Czechoslovakia.     

Causality in local quantum field theory: Some general results

General asymptotic causality properties of chronologicalN-point functions and, in massive theories, ofN-particle collision amplitudes, are derived from locality and the spectral condition. Results include specified rates of exponential fall-off, with simple and direct physical content, for large non-causal separations of points or particles in Minkowski space-time depending on values of the energy-momenta and on the mass spectrum. Relevant mathematical results on rates of exponential fall-off of generalized Fourier transforms outside their microsupports are given.Laboratoire de la Direction des Sciences de la Matière du Commissariat à l'Energie Atomique     

Tuning the nonlocal spin-spin interaction between quantum dots with a magnetic field

We describe a device where the nonlocal spin-spin interaction between quantum dots (QDs) can be turned on and off with a small magnetic field. The setup consists of two QDs at the edge of two two-dimensional electron gases (2DEGs). The QDs' spins are coupled through a RKKY-like interaction mediated by the electrons in the 2DEGs. A magnetic field B(z) perpendicular to the plane of the 2DEG is used as a tuning parameter. When the cyclotron radius is commensurate with the interdot distance, the spin-spin interaction is amplified by a few orders of magnitude. The sign of the interaction is controlled by finely tuning B(z). Our setup allows for several dots to be coupled in a linear arrangement and it is not restricted to nearest-neighbor interaction.     

Scalar quantum field theory with a complex cubic interaction

In this Letter it is shown that an i phi(3) quantum field theory is a physically acceptable model because the spectrum is positive and the theory is unitary. The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.     

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:

1. The regularizedS ^δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
2. The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?^δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
3. The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ₁=δ₂=δ₃=0.
4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

Electron self-energy in nonlocal field theory

In the framework of quantum electrodynamics with the nonlocal interaction it is shown that the correspondence principle holds in the problem on the self-mass of an electron and a particle with arbitrary spin. It appears that the second order of perturbation theory in the limit ? → 0 gives just the classical expression for the electron self-energy, and all higher order corrections are zero.     

Causality between preparation and registration processes in relativistic quantum theory

A causality postulate is considered which is based on the conception of systems that are prepared in some finite region of space-time and recorded in some other region. If these regions are spacelike separated, the recording apparatus should react as if no preparing apparatus were present, i.e., it should respond with at most some vacuum rate. The causality postulate is mathematically formulated within the framework of statistical theories. The connections with algebraic field theory are discussed and the relation between causality and spectral conditions is studied. General methods for constructing systems satisfying the causality postulate are given and applied in several examples.     

Zitterbewegung in quantum field theory

Traditionally, the zitterbewegung （ZB） of the Dirac electron has just been studied at the level of quantum mechanics. Seeing the fact that an old interest in ZB has recently been rekindled by the investigations on spintronic, graphene, and superconducting systems, etc., this paper presents a quantum-field-theory investigation on ZB and obtains the conclusion that, the ZB of an electron arises from the influence of virtual electron-positron pairs （or vacuum fluctuations） on the electron.     

Duality in quantum field theory

We postulate a convergent version of operator product expansions on the vacuum and explore some of their consequences. They lead to structures much reminiscent of dual resonance models.     

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.On leave from Department of Physics, Princeton University. Research supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266     

Hyperfunction quantum field theory

The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not containC functions with compact support. In spite of this defect the support concept ofH-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory.     

Quaternionic quantum field theory

We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second order wave equation. The theory takes the form of either a functional integral with quaternion-imaginary Lagrangian, or a Schrödinger equation and transformation theory for quaternion-valued wave functions, with a quaternion-imaginary Hamiltonian. The connection between the two formulations is developed in detail, and many related issues, including the breakdown of the correspondence principle and the Hilbert space structure, are discussed.     

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x_μx^μ = τ². This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free—a feature characteristic of Dirac’s “point-form” of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincaré generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.