Zero modes in the light-front coupled-cluster method

The light-front coupled-cluster (LFCC) method is a technique for solving Hamiltonian eigenvalue problems in light-front-quantized field theories. Its primary purpose is to provide a systematic sequence of solvable approximations to the original eigenvalue problem without the truncation of Fock space. Here we discuss the incorporation of zero modes, modes of zero longitudinal momentum, into the formalism of the method. Without zero modes, the light-front vacuum is trivial, and the vacuum expectation value of the field is always zero. The LFCC method with zero modes provides for vacuum structure, in the form of a generalized coherent state of zero modes, as is illustrated here in two-dimensional model field theories.     

Superconductivity in Restricted Chromo-Dynamics (RCD) in SU(2) and SU(3) Gauge Theories

Characterizing the dyonically condensed vacuum by the presence of two massive modes (one determining how fast the perturbative vacuum around a colour source reaches the condensation and the other giving the penetration length of colored flux) in SU(2) theory, it has been shown that due to the dynamical breaking of magnetic symmetry the vacuum of RCD acquires the properties similar to those of relativistic superconductor. Analysing the behaviour of dyons around RCD string, the solutions of classical field equations have been obtained and it has been shown that magnetic constituent of dyonic current is zero at centre of the string and also at the points far away from the string. Extending RCD in the realistic color gauge group SU(3), it has been shown that the resulting Lagrangian leads to dyonic condensation, color confinement and the superconductivity with the presence of two scalar modes and two vector modes.     

Evidence for fine tuning of fermionic modes in lattice gluodynamics

We consider properties of zero and near-zero fermionic modes in lattice gluodynamics. The modes are known to be sensitive to the topology of the underlying gluonic fields in the quantum vacuum state of the gluodynamics. We find evidence that these modes are fine-tuned; that is, they exhibit sensitivity to both physical (one can say, hadronic) scale and to the ultraviolet cutoff. Namely, the density of the states is in physical units, while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. We briefly discuss the possible theoretical implications and also include some general, review-type remarks.     

Exact Perturbations for Inflation with Smooth Exit

Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently from a decaying vacuum cosmology, which evolves smoothly from nearly de Sitter inflation to radiation domination. We find exact solutions for super-horizon perturbations (scalar and tensor), and for sub-horizon perturbations in the vacuum- and radiation-dominated eras. The standard conserved quantity for super-horizon scalar perturbations is exactly constant for the growing modes, and zero for the decaying modes.     

A family of Jordan-Brans-Dicke Kerr solutions

A family of solutions of the vacuum Jordan-Brans-Dicke or scalar-tensor gravitational field equations is given. This family reduces to the Kerr rotating solution of the vacuum Einstein equations when the scalar field is constant. The family does not have spherical symmetry when the rotation is zero and the scalar field is not constant. The method used to generate the new solutions can also be used to obtain vacuum Jordan-Brans-Dicke solutions from any given vacuum stationary, axisymmetric solution.     

Constant gauge fields and their quantum fluctuations

We analyze the vacuum fluctuations generated by translation-invariant gauge fields and show that these fields are unstable unless they are (anti-)self-dual and abelian. Self-dual constant fields support infinitely many zero modes analogous to instantons. The quantum corrections to the classical action are worked out in the one-loop approximation.     

Dual Superconductivity in Restricted Chromo-Dynamics (RCD)

Characterizing the dyonically condensed vacuum by the presence of two massive modes (one determining how fast the perturbative vacuum around a colour source reaches the condensation and the other giving the penetration length of colored flux), it has been shown that due to the dynamical breaking of magnetic symmetry the vacuum of RCD acquires the properties similar to those of relativistic superconductor. Originally present global SU(2) symmetry in RCD has been broken to U(1) reducing the four dimensional action to two dimensional one by using an Ansatz which incorporates a non-trivial coordinate dependent phase between the components of SU(2) doublet. Analyzing the behaviour of dyons around RCD string, the solutions of classical field equations have been obtained and it has been shown that magnetic constituent of dyonic current is zero at centre of the string and also at the points far away from the string. The conditions for this current to be maximum at a transverse distance from the string have also been obtained.     

两模在单双模组合压缩真空态中同等程度地被压缩

从SG相位算符的正规编序形式出发,我们得到了双模的SG相位算符在单双模组合压缩真空态中无相位差.这说明,在单-双模组合压缩真空态中两模同等程度地被压缩.这对探索新的压缩机制具有一定的启发作用.     

Batalin-Vilkovisky field-antifield quantisation of fluctuations around classical field configurations

The Lagrangian field-antifield formalism of Batalin and Vilkovisky (BV) is used to investigate the application of the collective coordinate method to soliton quantisation. In field theories with soliton solutions, the Gaussian fluctuation operator has zero modes due to the breakdown of global symmetries of the Lagrangian in the soliton solutions. It is shown how Noether identities and local symmetries of the Lagrangian arise when collective coordinates are introduced in order to avoid divergences related to these zero modes. This transformation to collective and fluctuation degrees of freedom is interpreted as a canonical transformation in the symplectic field-antifield space which induces a time-local gauge symmetry. Separating the corresponding Lagrangian path integral of the BV scheme in lowest order into harmonic quantum fluctuations and a free motion of the collective coordinate with the classical mass of the soliton, we show how the BV approach clarifies the relation between zero modes, collective coordinates, gauge invariance and the center-of-mass motion of classical solutions in quantum fields. Finally, we apply the procedure to the reduced nonlinear O(3) σ-model.     

Dyson pairs and zero mass black holes

It has been argued by Dyson in the context of QED in flat space-time that perturbative expansions in powers of the electric charge e cannot be convergent because if e is purely imaginary then the vacuum should be unstable to the production of charged pairs. We investigate the spontaneous production of such Dyson pairs in electrodynamics coupled to gravity. They are found to consist of pairs of zero rest mass black holes with regular horizons. The properties of these zero rest mass black holes are discussed. We also consider ways in which a dilaton may be included and the relevance of this to recent ideas in string theory. We discuss accelerating solutions and find that, in certain circumstances, the “no strut” condition may be satisfied giving a regular solution describing a pair of zero rest mass black holes accelerating away from one another. We also study wormhole and tachyonic solutions and how they affect the stability of the vacuum.     

Insight into the role of instantons and their zero modes from lattice QCD

Evidence from lattice QCD calculations is presented showing that instantons and their associated zero modes play a major role in the physics of light hadrons and the propagation of ight quarks in the QCD vacuum.     

Spin effects in instanton models

Nonperturbative nolocal structure of QCD vacuum is well described by instanton model. Specific helicity and flavor structure of zero modes of quarks, in instanton field allows simultaneously to explain some important features of low-and high-energy hadron phenomemology. The basic characteristics of hadron spectrum, partonic sum rules, heavyquark potential etc within the instanton liquid model are briefly discussed.     

Topological confinement in bilayer graphene

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics.     

柱环腔中的量子电动力学效应

研究以同轴不同半径柱面围成的导体柱环腔体中电磁场真空零点振动模式所给出的宏观量子效应.零点振动模式通过求解柱环空腔边界条件下无源的Maxwell方程组获得.得到了双柱面同心柱环中单位长度和单位面积的且是有限的真空能量，即Casimir能量.这有限的Casimir能量可以分解为独立而且收敛的三部分，它们分别来自内柱面、外柱面和柱环之中.对多柱面同心柱环，Casimir能量可分解为独立的（2n—1）部分（n为柱面数）.柱环是类似于平行板的几何结构.但柱环所给出的Casimir能量和Casimir势能系数是随着 关键词： Casimir效应 柱环腔体 零点能 量子电动力学     

Do semiclassical zero temperature black holes exist?

The semiclassical Einstein equations are solved to first order in epsilon = Planck's over 2pi/M2 for the case of a Reissner-Nordstr?m black hole perturbed by the vacuum stress energy of quantized free fields. Massless and massive fields of spin 0, 1/2, and 1 are considered. We show that in all physically realistic cases, macroscopic zero temperature black hole solutions do not exist. Any static zero temperature semiclassical black hole solutions must then be microscopic and isolated in the space of solutions; they do not join smoothly onto the classical extreme Reissner-Nordstr?m solution as epsilon-->0.     

What Can the Quantum Liquid Say on the Brane Black Hole, the Entropy of an Extremal Black Hole, and the Vacuum Energy?

Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum life-time is long enough to consider the horizon as the quasistationary object. Using this analogy we calculate the Bekenstein entropy of the near-extremal and extremal black holes, which comes from the fermionic microstates in the region of the horizon—the fermion zero modes. We also discuss how the cancellation of the large cosmological constant follows from the thermodynamics of the vacuum.     

Varying vacuum energy of a self-interacting scalar field

Understanding mechanisms capable of altering the vacuum energy is currently of interest in field theories and cosmology. We consider an interacting scalar field and show that the vacuum energy naturally takes any value between its maximum and zero because interaction affects the number of operating field modes, the assertion that involves no assumptions or postulates. The mechanism is similar to the recently discussed temperature evolution of collective modes in liquids. The cosmological implication concerns the evolution of scalar field ?$?$ during the inflation of the Universe. ?$?$ starts with all field modes operating and maximal vacuum energy in the early inflation-dominated epoch. As a result of inflation, ?$?$ undergoes a dynamical crossover and arrives in the state with one long-wavelength longitudinal mode and small positive vacuum energy predicted to be asymptotically decreasing to zero in the late epoch. Accordingly, we predict that the currently observed cosmological constant will decrease in the future, and comment on the possibility of a cyclic Universe.     

A Comment on the Light-Cone Vacuum in 1+1 Dimensional Super-Yang–Mills Theory

The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious zero-mode problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the gauge zero mode. It is shown that the inclusion of the zero modes of the adjoint scalars and fermions is crucial for probing the phase properties of the vacua. We find that the ground-state energy is zero and thus consistent with unbroken supersymmetry and conclude that the light-cone Fock vacuum is unchanged with or without the presence of matter fields.     

Solution of the five-dimensional vacuum Einstein equations in Kaluza-Klein theory

In a recent paper Ross obtained the five-dimensional vacuum Einstein equations in Kaluza-Klein theory with energy-momentum tensor equal to zero and solved the equations for a particular case. Here we obtain the complete set of solutions of these equations.     

Refraction of a surface polariton by an interface

We have calculated the transmission and reflection coefficients for a surface polariton that is incident normally on the interface between two different surface active dielectric media characterized by real, scalar, frequency dependent dielectric functions. Numerical solutions are obtained by matching the boundary conditions for the electromagnetic fields at the interface between the media and between each medium and the vacuum above it. The energy carried away by the vacuum modes is also calculated.