String field theory in the Siegel gauge

We specialize the gauge-fixing procedure for the Witten action of the open bosonic string, given in a preceding paper, choosing the Siegel gauge. We find that the BRST-invariant gauge-fixed action is the gauge invariant one with ghost number unrestricted plus a gauge-fixing term. The BRST invariance of the measure in the functional integral is briefly discussed. As a technical tool the Hodge dual of a string functional is defined.     

Reducible gauge algebra of BRST-invariant constraints

We show that it is possible to formulate the most general first-class gauge algebra of the operator formalism by only using BRST-invariant constraints. In particular, we extend a previous construction for irreducible gauge algebras to the reducible case. The gauge algebra induces two nilpotent, Grassmann-odd, mutually anti-commuting BRST operators that bear structural similarities with BRST/anti-BRST theories but with shifted ghost number assignments. In both cases we show how the extended BRST algebra can be encoded into an operator master equation. A unitarizing Hamiltonian that respects the two BRST symmetries is constructed with the help of a gauge-fixing boson. Abelian reducible theories are shown explicitly in full detail, while non-Abelian theories are worked out for the lowest reducibility stages and ghost momentum ranks.     

A new “dual” symmetry structure of the KP hierarchy

A new infinite set of commuting additional (“ghost”) symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to a new double-KP hierarchy embedding “ghost” and original KP-type Lax hierarchies connected to each other via a “duality” mapping exchanging the isospectral and “ghost” “times”. A new representation of the 2D Toda lattice hierarchy as a special Darboux-Bäcklund orbit of the double-KP hierarchy is found and parametrized entirely in terms of (adjoint) eigenfunctions of the original KP subsystem.     

Ghost counting in supergravity

The elimination of unphysical degrees of freedom from a quantized massless Rarita-Schwinger field interacting with a (quantized or classical) gravitational field is analyzed on the one-loop level. It is shown that, beside the ordinary Faddeev-Popov ghosts, an extra ghost is needed to remove the effects of unphysical modes. The new ghost only couples to the S-matrix if the gauge-fixing of the Rarita-Schwinger field involves the gravitational field, but it is necessary in the partition function for other gauge choices.     

Fully gauge-invariant field theory of free superstrings

Gauge invariant actions are discussed for free open superstrings in the BRST formalism. While the Neveu-Schwarz sector is analogous to the bosonic string, the Ramond sector has a complication in the commuting zero modes of the superconformal ghost. It is shown how consistency determines the inner product of the zero-mode states. On this basis, a fully gauge-invariant action for free open superstrings is derived. It is also shown that by consistent truncation this action precisely reproduces the “minimal” one with a smaller gauge invariance discussed by other authors.     

The relationship between the gauged BRST symmetry and the ghost number symmetry

A general method of gauging the BRST algebra by combining a (local) ghost number symmetry with the standard (global) BRST algebra, is displayed. This method enables us to construct an automatically nilpotent local BRST algebra and to obtain in a straightforward way the corresponding versions of the action and the eventual anomalies. To illustrate the procedure we study the Yang-Mills and the free bosonic string theories (including the “conformal” Beltrami parametrization) and show that it reproduces the results discussed in the literature. Two major outcomes of this scheme are briefly discussed: a possible connection between ghost number and BRST currents, arising from the Slavnov identities and the implications of the ghost number anomaly for the BRST localization program in theories such as string theory.     

Space-time supersymmetry of the covariant superstring

We explicitly derive the ghost oscillator contribution to the gauge covariant fermion emission vertex. This vertex is used to construct the space-time supersymmetry transformation laws which are shown to be an invariance of the free gauge covariant action of the superstring. We develop methods to deal with the quadratic exponentials which appear in the fermion emission vertex, in order to study the closure of the supersymmetry algebra. As a by-product, we complete the proof of the equivalence between the “old” and “new” formulations of the superstring.     

针对多散斑图的差分压缩鬼成像方案研究

鬼成像方案实现所需设备、成像的质量以及成像所花的时间是决定鬼成像技术可实用化的重要因素. 本文提出一种针对多散斑图的差分压缩鬼成像方案. 该方案通过连续探测多个独立的散斑图, 降低了热光鬼成像方案对探测器高时间分辨力的要求; 通过采用差分方法, 抑制了背景噪声和其他噪声源的干扰; 通过使用压缩感知重建算法, 有效地降低了鬼成像所需时间并同时提升成像的质量. 数值仿真结果表明, 对于二灰度“N” 图, 本方案在8000次的采样情形下与多散斑图鬼成像方案35000次采样的结果相比, 均方误差降低了96.9%、峰值信噪比提升15.1 dB. 对于八灰度“Pepper”图, 本方案与多散斑图鬼成像方案相比, PSNR提升11.4 dB. 本方案可降低探测设备的要求、提高成像质量、降低重建时间, 具有广阔的应用前景.     

Rigid rotor as a toy model for Hodge theory

We apply the superfield approach to the toy model of a rigid rotor and show the existence of the nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations, under which, the kinetic term and the action remain invariant. Furthermore, we also derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST symmetry transformations, under which, the gauge-fixing term and the Lagrangian remain invariant. The anticommutator of the above nilpotent symmetry transformations leads to the derivation of a bosonic symmetry transformation, under which, the ghost terms and the action remain invariant. Together, the above transformations (and their corresponding generators) respect an algebra that turns out to be a physical realization of the algebra obeyed by the de Rham cohomological operators of differential geometry. Thus, our present model is a toy model for the Hodge theory.     

One-loop renormalisation of superfield Yang-Mills theories

We calculate the one-loop ultraviolet and infrared divergences in superfield Yang-Mills theories to fourth order in the gauge field. The ultraviolet divergences require a non-linear field renormalisation, and graphs with external ghost fields show that a non-linear renormalisation of the gauge-fixing function is also needed. These observations are confirmed by calculations incorporating matter fields, which are used to extend the result to all orders for the special case of SU(2). On the other hand the infrared divergences, which occur in general gauges, are apparently impossible to remove in any acceptable way.     

Anomalies and gauge symmetry

Anomalies are known to have an intrinsic geometrical meaning. Using a formalism where the gauge condition is never made explicit we reanalyze the gauge theory anomaly problem. By requiring simultaneously the BRS and anti-BRS invariances, we do not need to use in our study the gauge dependent anti-ghost equation of motion. Then all equations definining the anomaly are independent of all parameters specifying the lagrangian. Not only does this stress explicitly the geometrical nature of the anomaly problem, but it allows for a single analysis for all possible BRS and anti-BRS invariant gauges, including those with four-ghost interactions. Our method for solving the anomaly equations is as a new sign of the relevance of the formalism in which the ghost components are unified with those of the classical gauge field, the ghost fields playing the role of a “connection” along unphysical directions. We recover the ABJ anomaly directly from the structure of BRS equations, as a straightforward application of the Chern-Weil theorem in some enlarged space. The method can be formally extended to higher space-time dimensions, and a general formula for “anomalies” in any even dimension is given.     

Stochastic quantization and gauge-fixing of the linearized gravitational field

Due to the indefiniteness of the euclidean gravitational action the Parisi-Wu stochastic quantization scheme fails in the case of the gavitational field. Therefore we apply a recently proposed modification of stochastic quantization that works in Minkowski space and preserves all the advantages of the original Parisi-Wu method; in particular no gauge-fixing is required. Additionally stochastic gauge-fixing may be introduced and is also studied in detail. The graviton propagators obtained with and without stochastic gauge-fixing all exhibit a noncausal contribution, but apart from this effect the gauge-invariant quantities are the same as those of standard quantization.     

String couplings from meromorphic differentials

The “Neumann-function method” which allows one to determine oscillator representation of multiple string vertices is put on firm basis. The Neumann coefficients are related to the Laurent coefficients of certain meromorphic differentials. A systematic procedure of constructing the differentials is developed. The method is exemplified by the “covariantized” light-cone vertex. Our results on the ghost part of this vertex are in disagreement with various proposals in the literature,     

Cluster-variational calculations for extended nuclear systems

The energy as a function of density is calculated for neutron matter and for symmetrical nuclear matter, based on Jastrow trial wave functions. The energy expectation value is truncated in low cluster order. A detailed analysis of the two- and three-body cluster contributions and a special portion of the four-body contribution is given. Variation of a parameterized two-body correlation function is subjected to constraints designed to confine the trial wave function to the domain corresponding to rapid cluster convergence. Results are presented for a variety of model central potentials containing hard cores, for different sets of constraints, and for two- and three-parameter correlation functions. Calculations constrained by the “average Pauli condition” are found to yield results very close to those constrained by the “normalization” or “unitarity” condition, and the two-parameter correlation function appears to be quite adequate. The convergence of the cluster expansion, as reflected in the low orders, is good except at the highest densities considered. The three-body cluster contribution displays, in all cases, a remarkable internal cancellation between its “two-correlation-line” addends.     

Gauge fixing for gravity-coupled theories and the super-Higgs effect beyond the unitary gauge

A straightforward gauge-fixing procedure is presented for a general gauge theory coupled to gravity, which relies on the geometrical nature of the BRS symmetry. It promotes the Stueckelberg “auxiliary” field (and its generalizations) to the level of a fundamental quantum field, like ghosts and antighosts. In this way, the Nielsen-Kallosh phenomenon is fully clarified, and a complete derivation of the quantum lagrangian of N = 1, D = 4 “new minimal” supergravity is given. As an output we analyze the super-Higgs effect beyond the unitary gauge and find a particularly simple gauge analogous to the 't Hooft-Feynman one for spontaneously broken Yang-Mills theories.     

Källen's theorem and the unphysical nature of abelian external fields in Yang-Mills theory

Yang-Mills theory is considered in an abelian external field with a covariant background gauge-fixing condition. The failure mechanism of Källen's inequality for the charge renormalization constant is studied, and indicates that a uniform external electric field should decay predominantly into negative norm gluon ghost states. Explicit calculation verifies this conjecture. This result is interpreted as evidence of the unphysical nature of abelian field configurations in Yang-Mills quantum theory.     

Gauge fields,BRS symmetry and the Casimir effect

The canonical quantization of the photon field in covariant gauge is studied in the presence of static boundaries, on which the field satisfies either “bag” or superconductor boundary conditions. The inclusion of the Fadeev-Popov ghost fields is found to be essential for agreement with Coulomb gauge calculations of the Casimir energy.     

Generalized Slavnov-Taylor,BRST and covariance identities from the geometry of the gauge surface

We establish the equivalence between the extended BRST invariances, and the conventional Slavnov-Taylor transformations together with a new “dual” analogue. However, the latter (a non-local gauge transformation, generating anA-dependent translation of the gauge-fixing surface) isnot an invariance of the Faddeev-Popov determinant, contrary to the published claim.     

The physics of 2 ≠ 1 + 1

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as “ghost” interference and “ghost” imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 ≠ 1 + 1.