Ghost Fields Research Articles

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

Perturbative Yang–Mills theory without Faddeev–Popov ghost fields

A modified Faddeev–Popov path integral density for the quantization of Yang–Mills theory in the Feynman gauge is discussed, where contributions of the Faddeev–Popov ghost fields are replaced by multi-point gauge field interactions. An explicit calculation to O(g2) shows the equivalence of the usual Faddeev–Popov scheme and its modified version.

BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields

We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. We discuss four different cases: abelian, nonabelian, relativistic, and nonrelativistic situations and extend the system to the whole phase space including ghost fields. In addition, we obtain the BRST charge of the field system and check its nilpotence of the BRST transformation which plays an important role such as in topological quantum field theory and string theory.

Testing the efficiency of rover science protocols for robotic sample selection: A GeoHeuristic Operational Strategies Test

The GHOST field tests are designed to isolate and test science-driven rover operations protocols, to determine best practices. During a recent field test at a potential Mars 2020 landing site analog, we tested two Mars Science Laboratory data-acquisition and decision-making methods to assess resulting science return and sample quality: a linear method, where sites of interest are studied in the order encountered, and a “walkabout-first” method, where sites of interest are examined remotely before down-selecting to a subset of sites that are interrogated with more resource-intensive instruments. The walkabout method cost less time and fewer resources, while increasing confidence in interpretations. Contextual data critical to evaluating site geology was acquired earlier than for the linear method, and given a higher priority, which resulted in development of more mature hypotheses earlier in the analysis process. Combined, this saved time and energy in the collection of data with more limited spatial coverage. Based on these results, we suggest that the walkabout method be used where doing so would provide early context and time for the science team to develop hypotheses-critical tests; and that in gathering context, coverage may be more important than higher resolution.

The Chern‐Simons Current in Systems of DNA‐RNA Transcriptions

AbstractA Chern‐Simons current, coming from ghost and anti‐ghost fields of supersymmetry theory, can be used to define a spectrum of gene expression in new time series data where a spinor field, as alternative representation of a gene, is adopted instead of using the standard alphabet sequence of bases . After a general discussion on the use of supersymmetry in biological systems, we give examples of the use of supersymmetry for living organism, discuss the codon and anti‐codon ghost fields and develop an algebraic construction for the trash DNA, the DNA area which does not seem active in biological systems. As a general result, all hidden states of codon can be computed by Chern‐Simons 3 forms. Finally, we plot a time series of genetic variations of viral glycoprotein gene and host T‐cell receptor gene by using a gene tensor correlation network related to the Chern‐Simons current. An empirical analysis of genetic shift, in host cell receptor genes with separated cluster of gene and genetic drift in viral gene, is obtained by using a tensor correlation plot over time series data derived as the empirical mode decomposition of Chern‐Simons current.

Renormalization of Supersymmetric QCD on the Lattice

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green’s functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

Viable tensor-to-scalar ratio in a symmetric matter bounce

Matter bounces refer to scenarios wherein the universe contracts at early times as in a matter dominated epoch until the scale factor reaches a minimum, after which it starts expanding. While such scenarios are known to lead to scale invariant spectra of primordial perturbations after the bounce, the challenge has been to construct completely symmetric bounces that lead to a tensor-to-scalar ratio which is small enough to be consistent with the recent cosmological data. In this work, we construct a model involving two scalar fields (a canonical field and a non-canonical ghost field) to drive the symmetric matter bounce and study the evolution of the scalar perturbations in the model. We find that the model can be completely described in terms of a single parameter, viz. the ratio of the scale associated with the bounce to the value of the scale factor at the bounce. We evolve the scalar perturbations numerically across the bounce and evaluate the scalar power spectra after the bounce. We show that, while the scalar and tensor perturbation spectra are scale invariant over scales of cosmological interest, the tensor-to-scalar ratio proves to be much smaller than the current upper bound from the observations of the cosmic microwave background anisotropies by the Planck mission. We also support our numerical analysis with analytical arguments.

Quantizing the Palatini action using a transverse traceless propagator

We consider the first order form of the Einstein-Hilbert action and quantize it using the path integral. Two gauge fixing conditions are imposed so that the graviton propagator is both traceless and transverse. It is shown that these two gauge conditions result in two complex Fermionic vector ghost fields and one real Bosonic vector ghost field. All Feynman diagrams to any order in perturbation theory can be constructed from two real Bosonic fields, two Fermionic ghost fields and one real Bosonic ghost field that propagate. These five fields interact through just five three point vertices and one four point vertex.

Anomaly on Superspace of Time Series Data

AbstractWe apply the G-theory and anomaly of ghost and antighost fields in the theory of supersymmetry to study a superspace over time series data for the detection of hidden general supply and demand equilibrium in the financial market. We provide proof of the existence of a general equilibrium point over 14 extradimensions of the new G-theory compared with the M-theory of the 11 dimensions model of Edward Witten. We found that the process of coupling between nonequilibrium and equilibrium spinor fields of expectation ghost fields in the superspace of time series data induces an infinitely long exact sequence of cohomology from a short exact sequence of moduli state space model. If we assume that the financial market is separated into two topological spaces of supply and demand as the D-brane and anti-D-brane model, then we can use a cohomology group to compute the stability of the market as a stable point of the general equilibrium of the interaction between D-branes of the market. We obtain the result that the general equilibrium will exist if and only if the 14thBatalin–Vilkovisky cohomology group with the negative dimensions underlying 14 major hidden factors influencing the market is zero.

Tweaking one-loop determinants in AdS3

We revisit the subject of one-loop determinants in AdS3 gravity via the quasi-normal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS3 that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.

Supersymmetric QCD on the lattice: An exploratory study

We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric ${\cal N}{=}1$ QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves the Wilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use na\"ive discretization. The gauge group that we consider is $SU(N_c)$, while the number of colors, $N_c$, the number of flavors, $N_f$, and the gauge parameter, $\alpha$, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant ($Z_g$) and of the quark ($Z_\psi$), gluon ($Z_u$), gluino ($Z_\lambda$), squark ($Z_{A_\pm}$), and ghost ($Z_c$) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.

String-Localized Free Vector and Tensor Potentials for Massive Particles with Any Spin: I. Bosons

It is well-known that a (point-localized) free quantum field for massive particles with spin $s$ acting in a Hilbert space has at best scaling dimension $s+1$, which excludes its use in the perturbative construction of renormalizable interacting models for higher spin ($s\geq 1$). Up to date, such models have been constructed only in the context of gauge theory, at the cost of introducing additional unphysical (ghost) fields and an unphysical (indefinite metric) state space. The unphysical degrees of freedom are divided out by requiring gauge (or BRST) invariance. We construct free quantum fields for higher spin particles which have the same good UV behaviour as the scalar field (scaling dimension one), and at the same time act on a Hilbert space without ghosts. They are localized on semi-infinite strings extending to space-like infinity, but are linearly related to their point-local counterparts. We argue that this is sufficient locality for a perturbative construction of interacting models of the gauge theory type, with a string-independent S-matrix and point-localized interacting observable fields. The usual principle of gauge-invariance is here replaced by the (deeper) principle of locality.

Noncommutative geometry and the BV formalism: Application to a matrix model

We analyze a U(2)-matrix model derived from a finite spectral triple. By applying the BV formalism, we find a general solution to the classical master equation. To describe the BV formalism in the context of noncommutative geometry, we define two finite spectral triples: the BV spectral triple and the BV auxiliary spectral triple. These are constructed from the gauge fields, ghost fields and anti-fields that enter the BV construction. We show that their fermionic actions add up precisely to the BV action. This approach allows for a geometric description of the ghost fields and their properties in terms of the BV spectral triple.

Four-loop renormalization of QCD with a reducible fermion representation of the gauge group: anomalous dimensions and renormalization constants

We present analytical results at four-loop level for the renormalization constants and anomalous dimensions of an extended QCD model with one coupling constant and an arbitrary number of fermion representations. One example of such a model is the QCD plus gluinos sector of a supersymmetric theory where the gluinos are Majorana fermions in the adjoint representation of the gauge group.The renormalization constants of the gauge boson (gluon), ghost and fermion fields are analytically computed as well as those for the ghost-gluon vertex, the fermion-gluon vertex and the fermion mass. All other renormalization constants can be derived from these. Some of these results were already produced in Feynman gauge for the computation of the β-function of this model, which was recently published [1]. Here we present results for an arbitrary ξ-parameter.

One-loop β function of noncommutative scalar QED4

In this paper, we consider the $\beta$ function at one-loop approximation for noncommutative scalar QED. The renormalization of the full theory, including the basic vertices, and the renormalization group equation are fully established. Next, the complete set of the one-loop diagrams corresponding to the first-order radiative corrections to the basic functions is considered: gauge, charged scalar and ghost fields self-energies, and three- and four-point vertex functions $\left<\phi^\dag \phi A\right>$ and $\left<\phi^\dag \phi A A\right>$, respectively. We pay special attention to the noncommutative contributions to the renormalization constants. To conclude, the one-loop $\beta$ function of noncommutative scalar QED is then computed and comparison to known results is presented.

Cyclic mixmaster universes

We investigate the behaviour of bouncing Bianchi type IX `Mixmaster' universes in general relativity. This generalises all previous studies of the cyclic behaviour of closed spatially homogeneous universes with and without entropy increase. We determine the behaviour of models containing radiation by analytic and numerical integration and show that increase of radiation entropy leads to increasing cycle size and duration. We introduce a null energy condition violating ghost field to create a smooth, non-singular bounce of finite size at the end of each cycle and compute the evolution through many cycles with and without entropy increase injected at the start of each cycle. In the presence of increasing entropy we find that the cycles grow larger and longer and the dynamics approach flatness, as in the isotropic case. However, successive cycles become increasingly anisotropic at the expansion maxima which is dominated by the general-relativistic effects of anisotropic 3-curvature. However, it becomes positive after expansion drives the dynamics close enough to isotropy for the curvature to become positive and for gravitational collapse to ensue. In the presence of a positive cosmological constant, radiation and a ghost field we show that, for a very wide range of cosmological constant values, the growing oscillations always cease and the dynamics subsequently approach those of the isotropic de Sitter universe at late times. This model is not included in the scope of earlier cosmic no-hair theorems because the 3-curvature can be positive. In the case of negative cosmological constant, radiation and an ultra-stiff field (to create non-singular bounces) we show that a sequence of chaotic oscillations also occurs, with sensitive dependence on initial conditions. In all cases, we follow the oscillatory evolution of the scale factors, the shear, and the 3-curvature from cycle to cycle.

On four-point interactions in massless higher spin theory in flat space

We consider a minimal interacting theory of a single tower of spin j = 0, 2, 4,… massless Fronsdal fields in flat space with local Lorentz-covariant cubic interaction vertices. We address the question of constraints on possible quartic interaction vertices imposed by the condition of on-shell gauge invariance of the tree-level four-point scattering amplitudes involving three spin 0 and one spin j particle. We find that these constraints admit a local solution for quartic 000j interaction term in the action only for j = 2 and j = 4. We determine the non-local terms in four-vertices required in the j ≥ 6 case and suggest that these non-localities may be interpreted as a result of integrating out a tower of auxiliary ghost-like massless higher spin fields in an extended theory with a local action, up to possible higher-point interactions of the ghost fields. We also consider the conformal off-shell extension of the Einstein theory and show that the perturbative expansion of its action is the same as that of the non-local action resulting from integrating out the trace of the graviton field from the Einstein action. Motivated by this example, we conjecture the existence of a similar conformal off-shell extension of a massless higher spin theory that may be related to the above extended theory. It may then have the same infinite-dimensional symmetry as the higher-derivative conformal higher spin theory and may thus lead to a trivial S matrix.

Adiabatic regularization for gauge fields and the conformal anomaly

We construct the adiabatic regularization method for a $U(1)$ gauge field in a conformally flat spacetime by quantizing in the canonical formalism the gauge fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields. We show that the adiabatic expansion for the mode functions and the adiabatic vacuum can be defined in a similar way using WKB-type solutions as the scalar fields. As an application of the adiabatic method, we compute the trace of the energy momentum tensor and reproduces the known result for the conformal anomaly obtained by the other regularization methods. The availability of the adiabatic expansion scheme for gauge field allows one to study the renormalization of the de-Sitter space maximal superconformal Yang-Mills theory using the adiabatic regularization method.

Complete renormalization of QCD at five loops

We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.

Quantum Gauge Symmetry of Reducible Gauge Theory

We derive the gaugeon formalism of the Kalb-Ramond field theory, a reducible gauge theory, which discusses the quantum gauge freedom. In gaugeon formalism, theory admits quantum gauge symmetry which leaves the action form-invariant. The BRST symmetric gaugeon formalism is also studied which introduces the gaugeon ghost fields and gaugeon ghosts of ghosts fields. To replace the Yokoyama subsidiary conditions by a single Kugo-Ojima type condition the virtue of BRST symmetry is utilized. Under generalized BRST transformations, we show that the gaugeon fields appear naturally in the reducible gauge theory.