Covariant Field Research Articles

Parton distributions from nonlocal chiral SU(3) effective theory: Splitting functions

We present a new formulation of pseudoscalar meson loop corrections to nucleon parton distributions within a nonlocal covariant chiral effective field theory, including contributions from SU(3) octet and decuplet baryons. The nonlocal Lagrangian, constrained by requirements of local gauge invariance and Lorentz-invariant ultraviolet regularization, generates additional interactions associated with gauge links. We use these to compute the full set of proton $\to$ meson + baryon splitting functions, which in general contain on-shell and off-shell contributions, in addition to $\delta$-function terms at zero momentum, along with nonlocal contributions associated with the finite size of the proton. We illustrate the shapes of the various local and nonlocal functions numerically using a simple example of a dipole regulator.

A study of shell structure in normal to exotic nuclides within relativistic Hartree–Bogoliubov approximation

The purpose of this work is to study theoretically the shell structure of even–even isotopes in Si, S, Ar and Ca and isotones at neutron number N = 0, 28, 50 and 82. We employed Covariant Relativistic self-consistent mean field models analogous to Kohn–Sham density functional theory to construct the Nuclear Density Functionals from Lagrangian densities based on meson exchange and point coupling models. The pairing correlations of nucleons are considered by the relativistic Hartree–Bogoliubov functional based on quasi-particle operators of Bogoliubov transformations. The theoretical calculations of shell closure parameter [Formula: see text](N) and the differential variation of the two-neutron separation energy [Formula: see text](Z, N) provide recognizable signature of shell closure at N = 14 and 20 in case of Si, N = 14, 20 and 28 in S, Ar and Ca isotopes and are consistent with recent experimental investigations of new sub-shell gaps.

Horizontal spatial correlation of reverberation for rough sea-bottom interface

Correlation sonar, which estimates the velocity of vessel utilizing the principle of waveform invariance, can achieve the sampling of the horizontal spatial correlation of sea-bottom reverberation. The horizontal spatial correlation can be expressed as a correlation function and is affected by sea-bottom characteristics. The expression of the correlation function of the sea-bottom reverberation is derived, which is written as the convolution of the autocorrelation function of transmitted signal, the cross-correlation function of the backscattered impulse response from a plane interface, and the autocorrelation function of the probability density function of the sea-bottom roughness. The isotropic interface roughness of the sea-bottom leads to a circular planform of the correlation function whose width varies with roughness. The anisotropic interface roughness of the sea-bottom leads to an elliptical planform of the correlation function whose major axis is in the direction of weaker roughness. Simulation of submarine reverberation and correlation function verifies this conclusion. The model for the spatially covariant field is used to estimate the backscattering cross section which varies with azimuth angle under the condition of anisotropic seafloor roughness. It should be noted that the horizontal spatial correlation of reverberation is also related to sonar parameters and other sea-bottom characteristics.

A Classical Field Theory Formulation for the Numerical Solution of Time Harmonic Electromagnetic Fields

Finite element representations of Maxwell's equations pose unusual challenges inherent to the variational representation of the “curl-curl” equation for the fields. We present a variational formulation which solves for the four-potential instead, based on classical field theory. Borrowing from quantum electrodynamics, we modify the Lagrangian by adding an implicit gauge-fixing term. This reformulation explicitly accounts for Gauss' law through the coupling between φ and ρ, and enables the use of nodal basis functions instead of edge elements for time-harmonic problems. We demonstrate how this formulation, adhering to the deeper underlying symmetries of the four-dimensional covariant field description, provides a highly general, robust numerical framework.

New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity

We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the derivatives of the fields), it is singular and, hence, this is a gauge field theory with constraints. These constraints are obtained after applying a constraint algorithm to the field equations, both in the Lagrangian and the Hamiltonian formalisms. In order to do this, the covariant field equations must be written in a suitable geometrical way, using integrable distributions which are represented by multivector fields of a certain type. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalism. The gauge symmetries of the model are discussed in both formalisms and, from them, the equivalence with the Einstein-Hilbert model is established.

Non-commutative waves for gravitational anyons

We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2 + 1 dimensions, motivated by its role as a deformed Poincaré symmetry and symmetry algebra in (2 + 1)-dimensional quantum gravity. We express the unitary irreducible representations in terms of covariant, infinite-component fields on curved momentum space satisfying algebraic spin and mass constraints. Adapting and applying the method of group Fourier transforms, we obtain covariant fields on (2 + 1)-dimensional Minkowski space which necessarily depend on an additional internal and circular dimension. The momentum space constraints turn into differential or exponentiated differential operators, and the group Fourier transform induces a star product on Minkowski space and the internal space which is essentially a version of Rieffel’s deformation quantisation via convolution.

On Wick Polynomials of Boson Fields in Locally Covariant Algebraic QFT

This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fields are pictured as sections of natural vector bundles over globally hyperbolic spacetimes and quantized through the known functorial machinery in terms of local $^*$-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles, in addition to the Lorentzian metric. The mass and the coupling constants are in particular viewed as background fields. Wick powers of the quantized vector field are axiomatically defined imposing in particular local covariance, scaling properties and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is specialized to the case of general tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields. The notion of local smooth dependence on polynomial scalar invariants is made precise in the text.

Covariant open string field theory on multiple Dp-branes**Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A1A02017805)

We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in (p + 1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.

A small non-vanishing cosmological constant from the Krein–Gupta–Bleuler vacuum

We point out a potential relevance between the Krein–Gupta–Bleuler (KGB) vacuum leading to a fully covariant quantum field theory for gravity in de Sitter (dS) spacetime and the observable smallness of the cosmological constant. This may provide a formulation of linear quantum gravity in a framework amenable to developing a more complete theory determining the value of the cosmological constant.

A New Approach to Classical Electrodynamics: Covariant Second-Order Field Variations

This paper describes a formulation of classical electrodynamics without point charges and masses. Maxwell's equations are assumed to be valid at all scales, and the Lorentz force is replaced as a fundamental law of nature by equations derived by a second order variation on a covariant 'action' in which the usual term involving mass, , has been replaced by a covariant mass density associated with the fields. Fij and Tik are the usual field and energy-momentum tensors, and ui is the four-velocity associated with charge. Distributions having charge of a single sign are found to be stabilized by charge motion in the distribution's self-field, and they have finite extent, charge, and mass. The motion of these charged bodies in an imposed electromagnetic field is shown to obey the Lorentz force law, where the mass is equivalent to the total energy of the electromagnetic field integrated over all space. Ordinary classical electromagnetism is thus reproduced, and in addition, the classical structures of fundamental charged bodies are obtained. The singularities usual to dualistic theories disappear. Classical structures of the electron and proton are briefly discussed.

Composite graviton self-interactions in a model of emergent gravity

We consider a theory of scalars minimally coupled to an auxiliary background metric. The theory is generally covariant and subject to the constraint of vanishing energy-momentum tensor. Eliminating the auxiliary metric leads to a reparametrization invariant, non-polynomial, metric-independent action for the scalar fields. Working in the limit of a large number of physical scalars, a composite massless spin-2 state, the graviton, was identified in previous work, in a two-into-two scalar scattering process. Here, we further explore the possibility that dynamical emergent gravity is a natural feature of generally covariant quantum field theories, by studying the self-interactions of the emergent composite graviton. We show that the fine-tuning previously imposed to ensure the vanishing of the cosmological constant, as well as the existence of the massless spin-2 state, also assures that the emergent graviton's cubic self-interactions are consistent with those of Einstein's general relativity, up to higher-derivative corrections. We also demonstrate in a theory with more than one type of scalar that the composite graviton coupling is universal.

Casimir energy–momentum tensor for curved boundaries in de Sitter space-time

In the present paper, we study Casimir effect for a conformally coupled scalar field propagating on background of $$4+1$$ -dimensional de Sitter (dS) space-time. The field is supposed to obey Dirichlet boundary condition on two 4-dimensional curved boundaries. Technically, we accomplish our calculations using an indefinite field quantization scheme, which already has been successfully applied to the dS minimally coupled massless scalar field and the dS linear gravity to obtain a causal and fully covariant quantum field on dS space-time.

Entanglement entropy for open bosonic strings on Dp-branes

We study the entanglement entropy for open bosonic strings on multiple Dp-branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which Dp-branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of (p−1)-dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) region. However, the leading divergences are mainly due to tachyon contributions to the entanglement entropy, which may be absent in supersymmetric string theories. Apart from the divergences thanks to tachyons, the entanglement entropy for open bosonic strings on Dp-branes is finite for 2≤p≤dcritical−2 and logarithmically divergent for p=1,dcritical−1.

A multi-objective tool-axis optimization algorithm based on covariant field functional

In multi-axis machining, sudden change of tool-axis orientation has adverse effects on the machining quality and efficiency. In this paper, we proposed a mathematical framework to generate smooth tool-axis variation even on part surfaces lacking G2 and/or G1 continuities. An integral functional is formulated as the object function to represent the measurement of the rate of tool-axis change. The functional is covariant so that the result is independent of surface parameterization and applicable to non-Euclidean geometry. The minimization of the integral functional ensures minimal fluctuation of tool-axis. Other machining requirements, such as gouging-free, preferred (or greedy) direction, are incorporated into this optimization problem as constraints. The unified optimization problem is solved by a Finite Element Method (FEM) numerical method. The proposed algorithm is implemented in the planar sections of blade rough machining to produce tool path with smooth tool-axis variation. Machining results indicate that the presented algorithm can improve machining quality/efficiency and avoid gouging.

A unified universe

We present a unified evolution of the universe from very early times until the present epoch by including both the leading local correction R^2 and the leading non-local term Rfrac{1}{square ^2}R to the classical gravitational action. We find that the inflationary phase driven by R^2 term gracefully exits in a transitory regime characterized by coherent oscillations of the Hubble parameter. The universe then naturally enters into a radiation dominated epoch followed by a matter dominated era. At sufficiently late times after radiation–matter equality, the non-local term starts to dominate inducing an accelerated expansion of the universe at the present epoch. We further exhibit the fact that both the leading local and non-local terms can be obtained within the covariant effective field theory of gravity. This scenario thus provides a unified picture of inflation and dark energy in a single framework by means of a purely gravitational action without the usual need of a scalar field.

Quantum field theory with no zero-point energy

Traditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical quantization procedures. For identical classical theories, an alternative quantization procedure, called affine field quantization, leads to the desirable feature of having a vanishing zero-point energy. This procedure has been applied to renormalizable and nonrenormalizable covariant scalar fields, fermion fields, as well as general relativity. Simpler models are offered as an introduction to affine field quantization.

Remarks on entanglement entropy in string theory

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for Bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations". We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates the ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

Canonical quantization of the covariant fields on de Sitter space–times

The properties of the covariant quantum fields on de Sitter space–times are investigated focusing on the isometry generators and Casimir operators in order to establish the equivalence among the covariant representations and the unitary irreducible ones of the de Sitter isometry group. For the Dirac quantum field, it is shown that the spinor covariant representation, transforming the Dirac field under de Sitter isometries, is equivalent with a direct sum of two unitary irreducible representations of the [Formula: see text] group, transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down finding that the covariant representations are equivalent with unitary irreducible ones from the principal series whose canonical weights are determined by the fermion mass and spin.

Multisymplectic unified formalism for Einstein-Hilbert gravity

We present a covariant multisymplectic formulation for the Einstein-Hilbert model of general relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified Lagrangian-Hamiltonian formalism is particularly interesting when it is applied to these kinds of theories, since it simplifies the treatment of them, in particular, the implementation of the constraint algorithm, the retrieval of the Lagrangian description, and the construction of the covariant Hamiltonian formalism. In order to apply this algorithm to the covariant field equations, they must be written in a suitable geometrical way, which consists of using integrable distributions, represented by multivector fields of a certain type. We apply all these tools to the Einstein-Hilbert model without and with energy-matter sources. We obtain and explain the geometrical and physical meaning of the Lagrangian constraints and we construct the multimomentum (covariant) Hamiltonian formalisms in both cases. As a consequence of the gauge freedom and the constraint algorithm, we see how this model is equivalent to a first-order regular theory, without gauge freedom. In the case of the presence of energy-matter sources, we show how some relevant geometrical and physical characteristics of the theory depend on the type of source. In all the cases, we obtain explicitly multivector fields which are solutions to the gravitational field equations. Finally, a brief study of symmetries and conservation laws is done in this context.

Covariant fields on anti-de Sitter spacetimes

The covariant free fields of any spin on anti-de Sitter (AdS) spacetimes are studied, pointing out that these transform under isometries according to covariant representations (CRs) of the AdS isometry group, induced by those of the Lorentz group. Applying the method of ladder operators, it is shown that the CRs with unique spin are equivalent with discrete unitary irreducible representations (UIRs) of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations (reps.) may depend on the mass and spin of the covariant field. The conclusion is that on AdS spacetime, one cannot formulate a universal mass condition as in special relativity.