Covariant Field Research Articles

A study of nucleon-nucleon scattering in covariant chiral effective field theory at the two-loop level

A study of nucleon-nucleon scattering in covariant chiral effective field theory at the two-loop level

Background field method for nonlinear sigma models in nonrelativistic string theory

We continue the study of nonrelativistic string theory in background fields. Nonrelativistic string theory is described by a nonlinear sigma model that maps a relativistic worldsheet to a non-Lorentzian and non-Riemannian target space geometry, which is known to be string Newton-Cartan geometry. We develop the covariant background field method in this non-Riemannian geometry. We apply this background field method to compute the beta-functions of the nonlinear sigma model that describes nonrelativistic string theory on a string Newton-Cartan geometry background, in presence of a Kalb-Ramond two-form and dilaton field.

Alternative Lagrangians obtained by scalar deformations

We study mechanical systems that can be recast into the form of a system of genuine Euler–Lagrange equations. The equations of motions of such systems are initially equivalent to the system of Lagrange equations of some Lagrangian [Formula: see text], including a covariant force field. We find necessary and sufficient conditions for the existence of a differentiable function [Formula: see text] such that the initial system is equivalent to the system of Euler–Lagrange equations of the deformed Lagrangian [Formula: see text].

Remarks on the non-Riemannian sector in Double Field Theory

Taking mathbf {O}(D,D) covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, (n,bar{n}). Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over n and bar{n} dimensions respectively. Examples include, but are not limited to, Newton–Cartan, Carroll, or Gomis–Ooguri. Here we analyze the variational principle with care for a generic (n,bar{n}) non-Riemannian sector. We recognize a nontrivial subtlety for {nbar{n}ne 0} that infinitesimal variations generically include those which change (n,bar{n}). This seems to suggest that the various non-Riemannian gravities should better be identified as different solution sectors of Double Field Theory rather than viewed as independent theories. Separate verification of our results as string worldsheet beta-functions may enlarge the scope of the string landscape far beyond Riemann.

Study on the covariant chiral effective field theory of vector meson

Study on the covariant chiral effective field theory of vector meson

An Ultralocal Classical and Quantum Gravity Theory

An ultralocal form of any classical field theory eliminates all spatial derivatives in its action functional, e.g., in its Hamiltonian functional density. It has been applied to covariant scalar field theories and even to Einstein's general relativity, by Pilati, as an initial term in a perturbation series that aimed to restore all omitted derivatives. Previously, the author has quantized ultralocal scalar fields by affne quantization to show that these non-renormalizanle theories can be correctly quantized by affne quantization; the story of such scalar models is discussed in this paper. The present paper will also show that ultralocal gravity can be successfully quantized by affne quantization. The purpose of this study is that a successful affne quantization of any ultralocal field problem implies that, with properly restored derivatives, the classical theory can, in principle, be guaranteed a successful result using either a canonical quantization or an affne quantization. In particular, Einstein's gravity requires an affne quantization, and it will be successful.

Tensor fields associated with integrable systems of chiral

This article describes necessary conditions for chiral-type systems to admit Lax representation with values in simple compact Lie algebras. These conditions state that there exists a covariant constant tensor field with an additional property. It is proposed to construct in an invariant way some covariant tensor fields using the Lax representation of the system under consideration. These fields are constructed by taking linear differential forms with values in the Lie algebra that are constructed using the Lax representation of the system and substituting them into an arbitrary Ad-invariant form on the Lie algebra. The paper proves that such tensor fields are Killing tensor fields or covariant constant fields. The discovered necessary conditions for the existence of the Lax representation are obtained using a special case of such tensor fields associated with the Killing metric of the Lie algebra.

Relativistic Equations for Arbitrary Spin, Especially for the Spin s = 2

The further approbation of the equation for the particles of arbitrary spin introduced recently in our papers is under consideration. The comparison with the known equations suggested by Bhabha, Pauli–Fierz, Bargmann–Wigner, Rarita–Schwinger (for spin s =3/2) and other authors is discussed. The advantages of the new equations are considered briefly. The advantage of the new equation is the absence of redundant components. The important partial case of spin s =2 is considered in details. The 10-component Dirac-like wave equation for the spin s =(2,2) particle-antiparticle doublet is suggested. The Poincar´e invariance is proved. The three-level consideration (relativistic canonical quantum mechanics, canonical Foldy–Wouthuysen-type field theory, and locally covariant field theory) is presented. The procedure of our synthesis of arbitrary spin covariant particle equations is demonstrated on the example of spin s =(2,2) doublet.

A connection between the classical r-matrix formalism and covariant Hamiltonian field theory

We bring together aspects of covariant Hamiltonian field theory and of classical integrable field theories in 1+1 dimensions. Specifically, our main result is to obtain for the first time the classical r-matrix structure within a covariant Poisson bracket for the Lax connection, or Lax one form. This exhibits a certain covariant nature of the classical r-matrix with respect to the underlying spacetime variables. The main result is established by means of several prototypical examples of integrable field theories, all equipped with a Zakharov–Shabat type Lax pair. Full details are presented for: (a) the sine–Gordon model which provides a relativistic example associated to a classical r-matrix of trigonometric type; (b) the nonlinear Schrödinger equation and the (complex) modified Korteweg–de Vries equation which provide two non-relativistic examples associated to the same classical r-matrix of rational type, characteristic of the AKNS hierarchy. The appearance of the r-matrix in a covariant Poisson bracket is a signature of the integrability of the field theory in a way that puts the independent variables on equal footing. This is in sharp contrast with the single-time Hamiltonian evolution context usually associated to the r-matrix formalism.

On the Jacobi metric for a general Lagrangian system

An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system, and the corresponding geodesics are described in terms of an appropriate nonlinear connection and the associated curvature. In the limit of low kinetic energies, the trajectories of motion of any Lagrangian system are very well approximated by the geodesics of an energy dependent Randers metric or, equivalently, by the paths in configuration space of a representative point subject to electromagnetic- and gravitational-like force fields. For higher kinetic energy values, the trajectories of motion are instead the geodesics of a general energy dependent Finsler metric, corresponding also to the paths in configuration space of a representative point subject to a hierarchy of a potentially infinite number of covariant force fields that generalize the electromagnetic and gravitational ones. Some general implications of these findings are discussed.

Gauge fields with vanishing scalar invariants

We consider extension of some established techniques of study of tensor fields on Lorentzian manifolds of arbitrary dimension to non-Abelian gauge covariant fields. These are then applied to study of gauge fields with vanishing scalar curvature invariants and universal Yang–Mills fields, for which all possible higher-order corrections to the Yang–Mills equation identically vanish.

Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity

We employ stochastic quantization for a self-interacting nonminimal massive scalar field in curved spacetime. The covariant background field method and local momentum space representation are used to obtain the Euclidean correlation function and evaluate multi-loop quantum corrections through simultaneous expansions in the curvature tensor and its covariant derivatives and in the noise fields. The stochastic correlation function for a quartic self-interaction reproduces the well-known one-loop result by Bunch and Parker and is used to construct the effective potential in curved spacetime in an arbitrary dimension D up to the first order in curvature. Furthermore, we present a sample of numerical simulations for D=3 in the first order in curvature. We consider the model with spontaneous symmetry breaking and obtain fully nonperturbative solutions for the vacuum expectation value of the scalar field and compare them with one- and two-loop solutions.

Thermal Quantum Spacetime

The intersection of thermodynamics, quantum theory and gravity has revealed many profound insights, all the while posing new puzzles. In this article, we discuss an extension of equilibrium statistical mechanics and thermodynamics potentially compatible with a key feature of general relativity, background independence; and we subsequently use it in a candidate quantum gravity system, thus providing a preliminary formulation of a thermal quantum spacetime. Specifically, we emphasise an information-theoretic characterisation of generalised Gibbs equilibrium that is shown to be particularly suited to background independent settings, and in which the status of entropy is elevated to being more fundamental than energy. We also shed light on its intimate connections with the thermal time hypothesis. Based on this, we outline a framework for statistical mechanics of quantum gravity degrees of freedom of combinatorial and algebraic type, and apply it in several examples. In particular, we provide a quantum statistical basis for the origin of covariant group field theories, shown to arise as effective statistical field theories of the underlying quanta of space in a certain class of generalised Gibbs states.

Construction of p-Adic Covariant Quantum Fields in the Framework of White Noise Analysis

In this article we construct a large class of interacting Euclidean quantum field theories, over a p-adic space time, by using white noise calculus. We introduce p-adic versions of the Kondratiev and Hida spaces in order to use the Wick calculus on the Kondratiev spaces. The quantum fields introduced here fulfill all the Osterwalder-Schrader axioms, except the reflection positivity.

Variational Discretizations of Gauge Field Theories Using Group-Equivariant Interpolation

We describe a systematic mathematical approach to the geometric discretization of gauge field theories that is based on Dirac and multi-Dirac mechanics and geometry, which provide a unified mathematical framework for describing Lagrangian and Hamiltonian mechanics and field theories, as well as degenerate, interconnected, and nonholonomic systems. Variational integrators yield geometric structure-preserving numerical methods that automatically preserve the symplectic form and momentum maps, and exhibit excellent long-time energy stability. The construction of momentum-preserving variational integrators relies on the use of group-equivariant function spaces, and we describe a general construction for functions taking values in symmetric spaces. This is motivated by the geometric discretization of general relativity, which is a second-order covariant gauge field theory on the symmetric space of Lorentzian metrics.

Light-cone reduction of Witten\u2019s open string field theory

We elucidate some exact relations between light-cone and covariant string field theories on the basis of the homological perturbation lemma for A∞. The covariant string field splits into the light-cone string field and trivial excitations of BRST quartets: the latter generates the gauge symmetry and covariance. We first show that the reduction of gauge degrees can be performed by applying the lemma, which gives a refined version of the no-ghost theorem of covariant strings. Then, we demonstrate that after the reduction, gauge-fixed theory can be regarded as a kind of effective field theory and it provides an exact gauge-fixing procedure taking into account interactions. As a result, a novel light-cone string field theory is obtained from Witten’s open string field theory.

Minimal gauge invariant and gauge fixed actions for massive higher-spin fields

Inspired by the rich structure of covariant string field theory, we propose a minimal gauge invariant action for general massive integer spin n field. The action consists of four totally symmetric tensor fields of order respectively n, n − 1, n − 2 and n − 3, and is invariant under the gauge transformation represented by two also totally symmetric fields of order n − 1 and n − 2. This action exactly has the same gauge structure as for the string field theory and we discuss general covariant gauge fixing procedure using the knowledge of string field theory. We explicitly construct the corresponding gauge fixed action for each of general covariant gauge fixing conditions.

The Dual Graviton in Duality Covariant Theories

AbstractWe review (and elaborate on) the ‘dual graviton problem’ in the context of duality covariant formulations of M‐theory (exceptional field theories). These theories require fields that are interpreted as components of the dual graviton in order to build complete multiplets under the exceptional groups E, . Circumventing no‐go arguments, consistent theories for such fields have been constructed by incorporating additional covariant compensator fields. The latter fields are needed for gauge invariance but also for on‐shell equivalence with and type IIB supergravity. Moreover, these fields play a non‐trivial role in generalized Scherk‐Schwarz compactifications, as for instance in consistent Kaluza‐Klein truncation on AdS4 × S7.

Polygonal shell elements with assumed transverse shear and membrane strains

In this study, a new polygonal shell element is developed to provide greater flexibility in mesh design of complex shell structures. Wachspress coordinates are used to construct shape functions for polygonal shell elements. An assumed covariant shear strain field with respect to the element natural coordinate system is defined by employing the mixed interpolation of tensorial components approach to avoid transverse shear locking in polygonal shell elements. Moreover, an assumed covariant membrane strain field is constructed by using characteristic geometry and displacement vectors defined on quadrilateral subdomains of polygonal shell elements to alleviate membrane locking due to the element curvature. Some benchmark shell problems are solved to evaluate the performance of the proposed polygonal shell elements. Numerical experiments show that they converge much better than triangular shell elements and comparable to quadrilateral shell elements.

Unambiguous phase spaces for subregions

The covariant phase space technique is a powerful formalism for understanding the Hamiltonian description of covariant field theories. However, applications of this technique to problems involving subregions, such as the exterior of a black hole, have heretofore been plagued by ambiguities arising at the boundary. We provide a resolution of these ambiguities by directly computing the symplectic structure from the path integral, showing that it may be written as a contour integral around a partial Cauchy surface. We comment on the implications for gauge symmetry and entanglement.