Towards Lambda-nucleon coupling constants in relativistic mean field theory

New parameter sets for Λ-nucleon coupling in relativistic mean field theory are proposed based on nucleon-nucleon effective interaction PK1. Hypernuclear properties are described well through a systematical study. Effects of hyperon tensor coupling term on spin-orbit splitting are also investigated self-consistently.     

Towards Lambda-nucleon coupling constants in relativistic mean field theory

New parameter sets for Λ-nucleon coupling in relativistic mean field theory are proposed based on nucleon-nucleon effective interaction PK1. Hypernuclear properties are described well through a systematical study. Effects of hyperon tensor coupling term on spin-orbit splitting are also investigated self-consistently.     

A new formulation of the initial value problem for nonlocal theories

There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of nonlocality leads to improved UV behavior, novel cosmological dynamics and is a generic prediction of string theory. On the other hand, fundamentally nonlocal models are fraught with complications, including instabilities and complications in setting up the initial value problem. We study the structure of the initial value problem in an interesting class of nonlocal models. We advocate a novel new formulation wherein the Cauchy surface is “smeared out” over the underlying scale of nonlocality, so that the usual notion of initial data at t=0$t=0$ is replaced with an “initial function” defined over −M−1?t?0$-M^{-1}?t?0$ where M is the underlying scale of nonlocality. Focusing on some specific examples from string theory and cosmology, we show that this mathematical re-formulation has surprising implications for the well-known stability problem. For D-brane decay in a linear dilaton background, we are able to show that the unstable directions in phase space cannot be accessed starting from a physically sensible initial function. Previous examples of unstable solutions in this model therefore correspond to unphysical initial conditions, an observation which is obfuscated in the old formulation of the initial value problem. We also discuss implication of this approach for nonlocal cosmological models.     

非线性耦合标量场方程的新双周期解(Ⅱ)

基于具有双周期解的常微分方程，提出了一种构造非线性微分方程双周期解的新方法，在计算机符号软件帮助下方法可实现机械化.应用此方法于非线性耦合标量场方程，得到了该方程的大量的新精确解. 关键词： 非线性耦合标量场方程 双周期解 精确解     

The real scalar field in extreme RNdS space

The real scalar field equation between the outer black hole horizon and the cosmological horizon is solved in the extreme Reissner-Nordström de Sitter (RNdS) space. We use an accurate approximation, the polynomial approximation, to approximate the tortoise coordinate x(r) in order to get the inverse function r = r(x) and then to solve the wave equation. The case where the two horizons are very close to each other is discussed in detail. We find that the wave function is harmonic only in the very small regions near the horizons, and the amplitude decreases remarkably near the potential peak because of the effect of the potential. Furthermore, it is found that the height of the potential increases as the cosmological constant Λ decreases, and the wave amplitude will decrease more remarkably with less Λ.     

Resonant frequencies of massless scalar field in rotating black-brane spacetime

This paper investigates the resonant frequencies of the massless scalar field in the near extremal Kerr-like black-brane spacetime. It is shown that the different angular quantum number will present different resonant frequencies. It is also shown that the real part of the resonant frequencies increases as the compact dimensions parameter μi increases, but the magnitude of the imaginary part decreases as μi increases.     

非线性耦合标量场方程的新双周期解(Ⅰ)

对于具有丰富物理意义和众多应用价值的非线性耦合标量场方程，利用sinh-Gordon方程展开法，导出了五种新的双周期解，同时在退化的情形得到了新的孤波解和三角函数解.结果说明该方程具有丰富的解的结构，方程描述的物理模型所具有的物理现象仍将是物理学家和数学家进一步探讨的对象. 关键词： 非线性耦合标量场方程 sinh-Gordon方程展开法 双周期解 精确解     

Notes on nonlocal projective measurements in relativistic systems

In quantum mechanical bipartite systems, naive extensions of von Neumann’s projective measurement to nonlocal variables can produce superluminal signals and thus violate causality. We analyze the projective quantum nondemolition state-verification in a two-spin system and see how the projection introduces nonlocality without entanglement. For the ideal measurements of “R-nonlocal” variables, we argue that causality violation can be resolved by introducing further restrictions on the post-measurement states, which makes the measurement “Q-nonlocal”. After we generalize these ideas to quantum mechanical harmonic oscillators, we look into the projective measurements of the particle number of a single mode or a wave-packet of a relativistic quantum field in Minkowski space. It turns out that the causality-violating terms in the expectation values of the local operators, generated either by the ideal measurement of the “R-nonlocal” variable or the quantum nondemolition verification of a Fock state, are all suppressed by the IR and UV cutoffs of the theory. Thus relativistic quantum field theories with such projective measurements are effectively causal.     

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy, respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.     

洛仑兹破缺标量场的霍金隧穿辐射

把洛仑兹破缺的标量场方程推广到弯曲时空中,并通过Aether-like项对标量场方程进行修正,该项所产生的效应也会影响到黑洞时空视界附近处的物理效应.接着,进一步在半经典近似下得到了修正的Hamilton-Jacobi方程,然后用这一修正的Hamilton-Jacobi方程研究了史瓦西黑洞的隧穿辐射特征,并讨论了洛仑兹破缺对黑洞霍金辐射和黑洞熵的影响.结果表明,u~α=δ_t~αu~t,δ_r~αu~r形式的Aether-like项的效应可能使黑洞温度增加,而黑洞熵降低.该工作可以帮助我们更深刻地理解弯曲时空中的洛仑兹破缺效应的物理性质.     

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g?⁴classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.     

Real scalar field scattering in the nearly extremal Schwarzschild-de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild-de Sitter (SdS) space.The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a Pshl-Teller one.Meanwhile,the Schrdinger-like wave equation is transformed into a solvable form.Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x,while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.     

Effective Hamiltonian for scalar theories in the Gaussian approximation

We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the O(1) and O(2) scalar models. For the O(2)-theory we first explicitly calculate the massless Goldstone excitation and then show that the one-loop corrections of the effective Hamiltonian do not generate a mass.     

Real scalar field scattering in the nearly extremal Schwarzschildben de Sitter space

Reasonable approximations are introduced to investigate the real scalar field scattering in the nearly extremal Schwarzschild--de Sitter (SdS) space. The approximations naturally lead to the invertible x(r) and the global replacement of the true potential by a P?shl--Teller one. Meanwhile, the Schr?dinger-like wave equation is transformed into a solvable form. Our numerical solutions to the wave equation show that the wave is characteristically similar to the harmonic under the tortoise coordinate x, while the wave piles up near the two horizons and the wavelength tends to its maximum as the potential approaches to the peak under the radial coordinate r.     

单极子荷电黑洞时空背景中有质量标量场的衰减

通过对在单极子荷电黑洞背景中有质量标量场后期演化的研究,发现振荡反幂函数的衰减方式支配了有质量标量场的后期衰减.有质量标量场在单极子荷电黑洞时空背景中的后期衰减比在无整体单极子的ReissnerNordstrm时空度规下的后期衰减更快     

Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Recently,considerable progress has been made in understanding the early universe by loop quantum cosmology.Modesto et al.investigated the loop quantum black hole(LQBH)using improved semiclassical analysis and they found that the LQBH has two horizons,an event horizon and a Cauchy horizon,just like the Reissner-Nordstr¨om black hole.This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background.By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method,we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly.However,the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value.We also find that the loop quantum gravity area gap parameter a 0 causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer.In the complex ω plane,the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.     

New observables in topological instantonic field theories

Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type for the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on the linking of points.     

Dynamics of scalar fields in an expanding/contracting cosmos at finite temperature

This study extends the investigation of quantum dissipative effects of a cosmological scalar field by taking into account cosmic expansion and contraction.Cheung,Drewes,Kang,and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field in a recent work,where analytical expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interactions,and the work was conducted using Minkowski-space propagators in loop diagrams.In this work,we incorporate the Hubble expansion and contraction of the cosmic background and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly.Given that the Hubble parameter,H,attains a small but non-zero value,we carry out calculations to the first order in H.If we set H=0,all results match those in flat spacetime.Interestingly,we must integrate over the resonances,which in turn leads to an amplification of the effects of a non-zero H.This is an intriguing phenomenon,which cannot be uncovered in flat spacetime.The implications on particle creations in the early universe will be studied in a forthcoming study.     

Conformal field theories in six-dimensional twistor space

This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space–time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the six-dimensional case in which twistor space is the 6-quadric Q$Q$ in CP⁷${\mathbb{C}\mathbb{P}}^7$ with a view to applications to the self-dual (0,2)$(0,2)$-theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These yield an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space (H²$H^2$ and H³$H^3$) in which the H³$H^3$s arise as obstructions to extending the H²$H^2$s off Q$Q$ into CP⁷${\mathbb{C}\mathbb{P}}^7$.