卷 59, 编号 11 (2017)

Within the framework of the Duffin–Kemmer–Petiau (DKP) formalism a consistent approach to derivation of the third-order wave equation is suggested. For this purpose, an additional algebraic object, the so-called q-commutator (q is a primitive cubic root of unity) and a new set of matrices η_μ instead of the original matrices β_μ of the DKP algebra are introduced. It is shown that in terms of these η-matrices, we have succeeded to reduce the procedure of the construction of cubic root of the third-order wave operator to a few simple algebraic transformations and to a certain operation of passage to the limit z → q, where z is some complex deformation parameter entering into the definition of the η_μ-matrices. A corresponding generalization of the result obtained to the case of interaction with an external electromagnetic field introduced through the minimal coupling scheme is performed. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.

An approach to the quantum description of the orientation of relativistic particles, generalizing the approach to nonrelativistic objects possessing orientation (in particular, a rotator) is proposed, based on the self-consistent use of two reference frames. The realization of such an approach is connected with the introduction of wave functions f (x, z) on the Poincaré group M(3,1), which depend on the coordinates x^μ of the Minkowski space M(3,1)/Spin(3,1) and orientational variables assigned by the elements z_β^α of the matrix Z ∈Spin(3,1).The field f (x, z) is the generating function for ordinary spin-tensor fields and admits a number of symmetries. Besides the Lorentz transformations (corresponding to the action of the Poincaré group from the left and interpretable as external symmetries), transformations of a reference frame associated with an orientable object (corresponding to the action of the Poincaré group from the right and interpretable as internal symmetries) are applicable to orientable objects. In addition to the six quantum numbers assigned by the Casimir operators and the left generators, quantum numbers arise here that are assigned by the right generators and are associated with internal symmetries. The assumption that the internal symmetries of the theory of orientable objects are local leads to gauge theories describing the electroweak and gravitational interactions.

We study the special features of vacuum particle creation in an external classical field for two simple external field models in standard QED. Our investigation is based on a kinetic equation that is a nonperturbative consequence of the fundamental QED equations of motion. We identify the special features of system evolution that apply qualitatively also for other systems and are therefore rather general. The common basis for a description of these systems is formed by kinetic equations for vacuum particle creation belonging to the class of integro-differential equations of non-Markovian type with fastly oscillating kernel. This allows us to characterize the processes of this type as belonging to the class of field-induced phase transitions. Examples range from condensed matter physics to cosmology.

Although the perturbation series in quantum electrodynamics has been studied for eighty years concerning its high-order behavior, our present understanding is still poorer than for many other field theories. An interesting case is Schwinger pair creation in a constant electric field, which may possibly provide a window to high loop orders; simple non-perturbative closed-form expressions have been conjectured for the pair creation rate in the weak field limit, for scalar QED in 1982 by Affleck, Alvarez, and Manton, and for spinor QED by Lebedev and Ritus in 1984. Using Borel analysis, these can be used to obtain non-perturbative information on the on-shell renormalized N-photon amplitudes at large N and low energy. This line of reasoning also leads to a number of nontrivial predictions for the effective QED Lagrangian in either four or two dimensions at any loop order, and preliminary results of a calculation of the three-loop Euler–Heisenberg Lagrangian in two dimensions are presented.

Effective theory of soft photons in slowly varying electromagnetic background fields is studied at one-loop order in QED. This is of relevance for the study of all-optical signatures of quantum vacuum nonlinearity in realistic electromagnetic background fields as provided by high-intensity lasers. The central result derived in this article is a new analytical expression for the photon polarization tensor in two linearly polarized counterpropagating pulsed Gaussian laser beams. Treating the peak field strengths of both laser beams as free parameters, this field configuration can be considered as interpolating between the limiting cases of a purely right- or left-moving laser beam (if one of the peak field strengths is set equal to zero) and the standing-wave type scenario with two counter-propagating beams of equal strength.

Due to the nonlinearity of QED, a static charge becomes a magnetic dipole if placed in a magnetic field, and a magnetic monopole on the background is a combination of constant electric and magnetic fields. Already without external field, the cubic Maxwell equation for the field of a point charge has a soliton solution with a finite field energy and finite potential, the energy-momentum vector of a moving soliton being the same as that of a point massive particle. Equations are given for self-coupling dipole moments. Any theoretically found value for a multipole moment of a baryon or a meson should be subjected to nonlinear renormalization.

In this article we summarize and discuss results presented in [1, 2] in the light of recent developments in holography [3–6].

The Casimir energy of a massive scalar field on a Riemann cap with the Dirichlet boundary conditions is calculated. The problem is considered in the quasi-stationary approximation. Formulas are derived which are suitable for numerical calculations.

A uniquely defined expression for the one-loop effective action of scalar bosons on a nonstationary background has been found.

Results of calculation of the light-by-light contribution from the lightest neutral pseudoscalar and scalar mesons and the dynamical quark loop to the muon anomalous magnetic moment are discussed in the framework of the nonlocal SU(3) × SU(3) chiral quark model. The model is based on four-quark interaction of the Nambu–Jona–Lasinio type and Kobayashi–Maskawa–‘t Hooft six-quark interaction. The full kinematic dependence of vertices with off-shell mesons and photons in intermediate states in the light-by-light scattering amplitude is taken into account. All calculations are elaborated in explicitly gauge-invariant manner. These results complete calculations of all hadronic light-by-light scattering contributions to aμ in the leading order in the 1/N_c expansion. The final result does not allow the discrepancy between the experiment and the Standard Model to be explained.

We introduce a model which may generate particle number asymmetry in an expanding Universe. The model includes charge parity (CP) violating and particle number violating interactions. The model consists of a real scalar field and a complex scalar field. Starting with an initial condition specified by a density matrix, we show how the asymmetry is created through the interaction and how it evolves at later time. We compute the asymmetry using non-equilibrium quantum field theory and as a first test of the model, we study how the asymmetry evolves in the flat limit.

High Energy Accelerator Research Organization (KEK [1]) is a world class accelerator-based research laboratory. The field of its scientific interests spreads widely from the study of fundamental properties of matter, particle physics, nuclear physics to materials science, life science, technical researches, and industrial applications. Research outcomes from the laboratory achieved making use of high-energy particle beams and synchrotron radiation. Two synchrotron facilities of KEK, the Photon Factory (PF) ring and the Photon Factory Advanced Ring (PF-AR) are the second biggest synchrotron light source in Japan. A very wide range of the radiated light, from visible light to X-ray, is provided for a variety of materials science, biology, and life science [2]. KEK strives to work closely with national and international research institutions, promoting collaborative research activities. Advanced research and facilities provision are key factors to be at the frontier of the accelerator science. In this review I am going to discuss KEK overall accelerator-based science, and to consider light sources research and development. The state of arts of the current projects with respect to the elementary particles physics in the external electromagnetic fields is also stressed here.

The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electric field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the calculation is performed within the strong field quantum electrodynamics formalism, requiring a solution of the Dirac equation in momentum space. The equation is solved using a split-operator numerical scheme on parallel computers, allowing for the investigation of several field configurations. The strength of the method is illustrated by computing the electron momentum density generated from a realistic laser pulse model. We observe quantum interference patterns reminiscent of Landau–Zener–Stückelberg interferometry.

A modification of the electroweak theory, where the fermions with the same electroweak quantum numbers are combined in multiplets and are treated as different quantum states of a single particle, is proposed. In this model, mixing and oscillations of particles arise as a direct consequence of the general principles of quantum field theory. The developed approach enables one to calculate the probabilities of the processes taking place in the detector at long distances from the particle source. Calculations of higher-order processes, including computation of the contributions due to radiative corrections, can be performed in the framework of the perturbation theory using the regular diagram technique. As a result, the analog to the Dirac–Schwinger equation of quantum electrodynamics describing neutrino oscillations and its spin rotation in dense matter can be obtained.

Parameters of the observed radiation of pulsars are identified with the help of numerical simulation within the framework of the nonlinear least squares problem. With the help of the obtained parameter values, we have constructed profiles of radiation and indicatrices of the angular distribution of the instantaneous radiated power for experimentally observed pulsars.

A review of the finite field-dependent Becchi–Rouet–Stora–Tyutin (BRST) and BRST-antiBRST transformations is presented. Exact rules for calculating the Jacobian of the corresponding change of variables in the partition function are given. Infrared peculiarities under R_ξ-gauges in the Yang–Mills theory and the Standard Model are examined in a gauge-invariant way with an appropriate horizon functional and unaffected N = 1, 2 BRST symmetries.

We consider the entropy-energy inequality for a three-level atom implemented on superconducting circuits with the Josephson junction. It is suggested to use the positivity of the relative entropy of the qutritquantum system for verification of tomography of quantum states of qudits. The relations obtained are considered in detail on the example of the temperature density matrix.