Divergence cancellations in the renormalization of electroweak couplings

Cancellations of nonuniversal ultraviolet divergent contributions to the renormalization of couplingsvlW,vvZ,llZ (in the lowest nontrivial order) in theunitary (U) gauge of the Weinberg-Salam model are reconsidered. The expansion ofU-gauge Feynman diagrams into a set of simpler “secondary” graphs devised some time ago by Kummer and Lane is employed. It is shown that this approach reveals details of the cancellation mechanism which have not been discussed in previous treatments. The connection of cancellations in question with underlying gauge symmetry and the corresponding Higgs mechanism thus becomes more transparent.     

Feynman formulas for the diffusion of particles with position-dependent mass

In the present paper, Feynman formulas are obtained for Schrödinger semigroups generated by self-adjoint operators which are perturbations of self-adjoint extensions of the second-order Hamiltonian operator ?Δ _g,0/2+V (throughout the paper, the coefficient ?1/2 at Δ _g,0 is omitted to simplify the formulas) which describe the diffusion of a quasiparticle with position-dependent mass varying jump-like on a line. Every extension of this kind is defined by some invertible operator and is characterized by matching conditions at a jump point. The Schrödinger semigroups generated by self-adjoint Laplace operators and defined by the corresponding boundary conditions define solutions of initial-boundary value problems. In turn, the term “Feynman formulas” is applied (in the present case) to an explicit representation of the Schrödinger semigroup \(e^{t\hat H^T } \) in the form of a limit of integrals of finite multiplicity over Cartesian powers of some configuration space. In essence, the Feynman-Kac formula is a “probabilistic interpretation” of the Feynman formulas. Namely, the multiple integrals in the Feynman formulas approximate integrals against some measures on the space of trajectories (functions defined on an interval of the real line and ranging in the configuration space). Thus, the Feynman formulas enable one to evaluate integrals over spaces of trajectories. A crucial role in the proof of the Feynman formulas is played by the Chernoff theorem, which is a generalization of the famous Trotter formula. The result proved in the present paper is a demonstration of a part of the results recently announced by O. G. Smolyanov and H. von Weizäcker (“Feynman Formulas Generated by Self-Adjoint Extensions of the Laplacian,” Dokl. Ross. Akad. Nauk 426 (2), 162–165 (2009) [Doklady Mathematics, 2009 79 (3), 335–338 (2009)]). The formulations of the results in question are inessentially modified here.     

Feynman disentangling of noncommuting operators in quantum mechanics

Feynman’s disentangling theorem is applied to noncommuting operators in the problem of quantum parametric oscillator, which is mathematically equivalent to the problem of SU(1, 1) pseudospin rotation. The number states of the oscillator correspond to unitary irreducible representations of the SU(1, 1) group. Feynman disentangling is combined with group-theoretic arguments to obtain simple analytical formulas for the matrix elements and transition probabilities between the initial and final states of the oscillator. Feynman disentangling of time evolution operators is also discussed for an atom or ion interacting with a laser field and for a model Hamiltonian possessing the “ hidden” symmetry of the hydrogen atom.     

S-matrix,Feynman zigzag and Einstein correlation

An inherent binding between Einstein correlations and the S-matrix formalism entails full relativistic covariance, complete time symmetry, and spacelike connexions via Feynman zigzags. The relay is in the past for predictive correlations between future measurements, and in the future for retrodictive correlations between past preparations (Pflegor and Mandel).An analogy and a partial binding exist between intrinsic symmetry together with factlike asymmetry of (1) “blind statistical” prediction and retrodiction (retarded and advanced waves, information as cognizance and as will) and (2) positive and negative frequencies (particles and antiparticles). As advanced waves are required for completeness of expansions, “antiphysics” obeying blind statistical retrodiction should show up in appropriate contexts, “parapsychology” being submitted as one of them.     

Mode-locking of high power lasers by a combination of intensity and time dependent Q-switching

A new method for simultaneous mode-looking and Q-switching of high power lasers by a combination of intensity and time dependent Q-switching is described. The two Q-switching mechanisms are achieved by equipping the laser with a device, here called the “Electro-Opto-Optical Modulator” (EOOM). The modulator, which is driven by the optical field which it modulates in addition to an external electric field, contains nonlinear media which exhibit a large optical as well as dc Kerr effect. The advantages of this combined Q-switching compared with a pure intensity dependent Q-switching are that the generation of the model-locked pulses can be predetermined in time and that the length of the Kerr active medium can be decreased.     

Measure permutation formulas in Feynman’s operational calculi

In Jefferies-Johnson’s theory of Feynman’s operational calculi for noncommuting operators, the two operators T _{µ 1,µ 2} f(Ã, \(\tilde B\)) and T _{µ 2},µ₁ f(Ã, \(\tilde B\)) are not equal. Relationships between these two operators are given, i.e., “measure permutation formulas” in Feynman’s operational calculi are developed; they correspond to the “index permutation formula” in Maslov’s discretized version of Feynman’s operational calculus.     

“Massive” perturbative QCD, Regular in the IR limit

The goal of the research is to devise a modification of the perturbative QCD (pQCD) that should be regular in the low-energy region and could serve as a practical means for the analysis of data below 1 GeV down to the IR limit. Recent observation of the four-loop pQCD series “blow-up” in the region below 1 GeV for the Bjorken Sum Rule gave an impetus to this attempt. The proposed “massive” analytic pQCD has two sources. It can be treated as the common logarithmic pQCD with only one parameter added, the effective “glueball mass” m _gl ? 1 GeV, serving as an IR regulator. At the same time, it looks like a modification of Analytic Perturbation Theory (APT) comprising nonpower perturbative expansion that makes it compatible with linear integral transformations. Figuratively (with minor reservations), the proposed MAPT differs from the minimal APT by simple ansatz Q ² → Q ² + m _g1 ² .     

Investigation of slow surface states on a real germanium surface by the optical excitation technique

The slow states (SS) charging ΔQ_s under the action of light quanta of different energy (2 ? hv ? 4.6 eV) has been investigated on a real germanium surface. The considerable influence on the optical SS charging of the preparation method as well as of adsorption-desorption processes has been revealed. On the basis of the spectral dependencies ΔQ_s(hv) the conclusion has been made about the existence of the adsorption-sensitive system of “fluctuation” electron states near the edges of energy bands of the oxide layer. The photocharging method has been shown the construction of the whole energy scheme of the semiconductor-dielectric heterojunction (including the band gap of the dielectric layer). The possible origin of the deep traps in oxide layer which are responsible for the optical charging of a real germanium surface, has been discussed.     

A new interpretation of the special theory of relativity

Assuming the “Big Bang” theory as well as the usual axioms in the Special Theory of Relativity, the time dilations and length contractions are treated as real physical effects. This becomes possible by relating everything to the hypothetical frame,S _a , at rest relative to the “Big Bang” event. This frame in many senses plays the role of the classical aether frame. A clock's real ryhthm, as opposed to its rhythm observed by restricted methods, is then a function of its velocity relative toS _a (assuming a uniform gravitational field). It is further assumed that gravitational radiation is composed of “electromagnetic-like” waves. Therefore when a clock changes its velocity in a uniform gravitational field it must receive a different total energy due to the average frequency shift (Doppler effect), the time dilations are then caused by the change in energy due to this frequency shift. That is, not wo clocks can be in the “same” gravitational field unless they have no relative velocity, and therefore the Special Theory of Relativity is a special case of the General Theory from this viewpoint. Two feasible experimental tests, using the Mössbauer effect, are described that would decide on these viewpoints. The principle of equivalence and the “twin paradox” are also discussed.     

Raman spectral of low-lying longitudinal mode of KH2PO4 and KD2PO4 in ferroelectric phase

The origin of the low-lying modes of KH₂PO₄ and KD₂PO₄ in the ferroelectric phase has been clarified by the z(xy)z? Raman scattering experiments. The “S-mode”, which has been usually assigned to the proton tunneling mode in KH₂PO₄ at T<T_c, has been found in the z(xy)z? spectrum of KD₂PO₄ in contrast to the x(xy)y spectrum. It has been found that the frequency of the “S-mode” of KD₂PO₄ is higher than that of KH₂PO₄. These results have shown that the “S-mode” is far from the proton tunneling mode nor the proton/deuteron mode at all. From the present Raman spectroscopy, it is concluded that the “S-mode” is assigned to the libration mode of the PO₄ tertahedrons.     

Finite-temperature quantum field theory in Minkowski space

We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z₂ symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z₂ symmetry.     

Resonant electron tunneling in GaN/Ga1−x AlxN(0001) strained structures with spontaneous polarization and piezoeffect

Electron tunneling through the GaN/Ga_1?x Al_xN(0001) wurtzite strained structures is investigated by the pseudopotential and scattering matrix methods. It is shown that the results of multiband calculations at low aluminum concentrations (x<0.3) are adequately described within the single-valley model in the envelope wave function method accounting for the dependences of the effective mass on the energy and strain. Upon electron tunneling through two-barrier structures, sharp resonance peaks are observed at a barrier thickness of several monolayers and the characteristic collision time in the resonance region is equal to ～1 ps. The internal electric fields associated with spontaneous and piezoelectric polarizations lead to a “red” or “blue” shift in the resonance energy according to the thickness and location of barriers with respect to the polar axis. In the (GaN)_n(Ga_1?x Al_xN)_m superlattices, the internal fields can form the Stark ladder of electronic states at a small number of ultrathin layers even in the absence of external fields.     

Brownian motion with restoring drift: The petit and micro-canonical ensembles

Letf(Q) be odd and positive near +∞. Then the non-linear wave equation ?² Q/?t ²??² Q/?x ²?f(Q)=0, considered on the circle 0≤x<L, can be written in Hamiltonian formQ ^⊙ =?H/?P, P ^⊙ =??H/?Q with $$P = Q^\cdot and H = \tfrac{1}{2}\mathop \smallint \limits_0^L (Q')^2 + \mathop \smallint \limits_0^L F(Q) + \tfrac{1}{2}\mathop \smallint \limits_0^L P^2 ;$$ the corresponding flow preserves the (suitably interpreted) “petit ensemble”e ^?H d ^∞ Qd ^∞ P; and forL↓∞,Q settles down to the stationary diffusion with infinitesimal operator 1/2 ?²/?Q ²+m(Q)?/?Q,m being the logarithmic derivative of the ground state of ?d ²/dQ ² ‖F(Q). This diffusion is the “Brownian motion with restoring drift”; see McKean-Vaninsky [1993(1)]. For reasons suggested by the paper of Lebowitz-Rose-Speer [1988] on NLS, it is interesting to study the “micro-canonical ensemble” obtained by restricting to the sphere $\int\limits_0^L {Q^2 } = N$ and makingL↓∞ with fixedD=N/L. Now, forF(Q)/Q ²→∞, the same type of diffusion appears, but with drift arising from the modified potentialF(Q)+cQ ²,c being chosen so that the mean ofQ ² is the assigned numberD. The proof employs Döblin's method of “loops” [1937] and steepest descent. The same is true forF(Q)=m ² Q ², only now the proof is elementary. The outcome is also the same ifF(Q)/Q ²→0, providedD is smaller than the petit canonical mean ofQ ²; forD larger than this mean, the matter is more subtle and the outcome is unknown.     

Tunneling paths in multi-dimensional semiclassical dynamics

In light of the fundamental importance and renewed interest of the tunnel phenomena, we review the recent development of semiclassical tunneling theory, particularly from the view point of “tunneling path”, beginning from a simple one-dimensional formula to semiclassical theories making use of the analytic continuation, in time, coordinates, or momentum, which are the stationary solutions of semiclassical approximations to the Feynman path integrals. We also pay special attention to the instanton path and introduce various conventional and/or intuitive ideas to generate tunneling paths, to which one-dimensional tunneling theory is applied. Then, we review the recent progress in generalized classical mechanics based on the Hamilton–Jacobi equation, in which both the ordinary Newtonian solutions and the instanton paths are regarded as just special cases. Those new complex-valued solutions are generated along real-valued paths in configuration space. Such non-Newtonian mechanics is introduced in terms of a quantity called “parity of motion”. As many-body effects in tunneling, illustrative numerical examples are presented mainly in the context of the Hamilton chaos and chemical reaction dynamics, showing how the multidimensional tunneling is affected by the system parameters such as mass combination and anisotropy of potential functions.     

QCD at lowQ 2—A correspondence relation for moments of structure functions

The precocious validity of QCD predictions in deep inelastic lepton nucleon scattering ande ⁺ e ^? annihilation is interpreted as a signal for an underlying “correspondence principle” relating perturbative and nonperturbative physics on theQ ² average. Correspondence relations for nonsinglet moments of deep inelastic structure functions are formulated, discussed and successfully tested against experiment. The relations provide an independent determination of the QCD ?-parameter from lowQ ² data in perfect agreement with results from largeQ ² analyses.     

The first-to-zero-sound transition in non-superfluid liquid 4He

Neutron inelastic scattering from ⁴He at T = 2.3 K shows that for Q ? 2 nm^?1 “sound-wave” excitations propagate with the characteristics of ordinary or first sound while for Q ? 3 nm^?1 they propagate with the characteristics of zero sound.     

Atomic tunneling states with dissipation in glasses: temperature-dependent two-level systems

By taking account of the influence of dissipation on atomic tunneling states in glasses, we introduce a density of states of two-level systems which is non-linearly temperature dependent. Based on this model, we can explain the “excess T³” anomaly in the specific heat and the “plateau” in the thermal conductivity of glasses.