xTras: a field-theory inspired xAct package for Mathematica

Abstract

We present the tensor computer algebra package xTras, which provides functions and methods frequently needed when doing (classical) field theory. Amongst others, it can compute contractions, make Ansätze, and solve tensorial equations. It is built upon the tensor computer algebra system xAct, a collection of packages for Mathematica.

29 pages. The package can be downloaded from http://www.xact.es/xtras/

References in corpus (4)

• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• The Invar tensor package: Differential invariants of Riemann
• Second and higher-order perturbations of a spherical spacetime

Cited by in corpus (160)

• A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Generalized Parametrization Dependence in Quantum Gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Correlation functions on a curved background
• Lifshitz holography: The whole shebang
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity
• Ising and Gross-Neveu model in next-to-leading order
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• General theories of linear gravitational perturbations to a Schwarzschild Black Hole
• Lorentz symmetry is relevant
• Higher Derivative Mimetic Gravity
• Higher-derivative operators and effective field theory for general scalar-tensor theories
• Critical (Chiral) Heisenberg Model with the Functional Renormalisation Group
• Higher derivatives in Type II and M-theory on Calabi-Yau threefolds
• On conformal higher spin wave operators
• Effective action of bosonic string theory at order ${\alpha }^{\prime 2}$
• Infinite order quantum-gravitational correlations
• Duality constraints on effective actions
• Scalar-Tensor theories within Asymptotic Safety
• The Two-Loop Four-Graviton Scattering Amplitudes
• Cosmological perturbations in modified teleparallel gravity models: Boundary term extension
• Lifshitz Scale Anomalies
• Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action
• Beta functions of (3+1)-dimensional projectable Horava gravity
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• One-loop divergences for $f(R)$ gravity
• A cautionary case of casual causality
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Higher-curvature Gravities from Braneworlds and the Holographic c-theorem
• $R^4$ terms in supergravities via T-duality constraint
• Holographic Plasmon Relaxation with and without Broken Translations
• Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
• Canonical variational completion and 4D Gauss-Bonnet gravity
• Stealth dark energy in scordatura DHOST theory
• Minimal independent couplings at order ${\alpha }^{\prime 2}$
• Lifshitz Anomalies, Ward Identities and Split Dimensional Regularization
• Renormalization of generalized vector field models in curved spacetime
• Lessons from conformally reduced quantum gravity
• Minimal gauge invariant couplings at order ${\alpha }^{\prime 3}$: NS-NS fields
• FeynGrav : FeynCalc extension for gravity amplitudes
• Gravity in $d=2+\epsilon$ dimensions and realizations of the diffeomorphisms group
• On NS-NS couplings at order ${\alpha }^{\prime 3}$
• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• Scattering amplitudes in affine gravity
• On the weak-gravity bound for a shift-symmetric scalar field
• The shape of Scalar Gauss-Bonnet Gravity
• Metric- and frame-like higher-spin gauge theories in three dimensions
• Dual actions for massless, partially-massless and massive gravitons in (A)dS
• The Schwinger-Keldysh Coset Construction
• Consistent inflationary cosmology from quadratic gravity with dynamical torsion
• Inflation with multiple vector fields and non-Gaussianities
• On Swift Gravitons
• Non-linear partially massless symmetry in an SO(1,5) continuation of conformal gravity
• Gauge and global symmetries of the candidate partially massless bimetric gravity
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• Non-minimal Tinges of Unimodular Gravity
• FeynGrav 2.0
• Perturbations in higher derivative gravity beyond maximally symmetric spacetimes
• Classification of all 3 particle S-matrices quadratic in photons or gravitons
• A multicritical Landau-Potts field theory
• Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories
• Supercomputers against strong coupling in gravity with curvature and torsion
• Stable Cosmology in Generalised Massive Gravity
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism
• Anisotropic Mimetic Cosmology
• Complexity Growth in Flat Spacetimes
• Geometrized quantum Galileons
• Exorcising Ghosts in Induced Gravity
• Transverse Collective Modes in Interacting Holographic Plasmas
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes
• On power-counting renormalizability of Hořava gravity with detailed balance
• One-modulus Calabi-Yau fourfold reductions with higher-derivative terms
• $O(9,9)$ symmetry of NS-NS couplings at order ${\alpha }^{\prime 3}$
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• On variational principle and canonical structure of gravitational theory in double-foliation formalism
• Classical Lagrangians for the nonminimal spin-nondegenerate Standard-Model Extension at higher orders in Lorentz violation
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds
• On D-brane action at order ${\alpha }^{\prime 2}$
• Linearized Holographic Isotropization at Finite Coupling
• Higher-derivative field redefinitions in the presence of boundary
• Conformal anomalies in 6d 4-derivative theories: a heat-kernel analysis
• Second-order gravitational self-force in a highly regular gauge: Covariant and coordinate punctures
• Lower-dimensional Limits of Cubic Lovelock Gravity
• Generalised Proca Theories in Teleparallel Gravity
• xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica
• $O(25,25)$ symmetry of bosonic string theory at order ${\alpha }^{\prime 2}$
• Refined Gribov-Zwanziger theory coupled to scalar fields in the Landau gauge
• Conformally covariant operators of mixed-symmetry tensors and MAGs
• Charged rotating black strings in Einsteinian cubic gravity
• Effective action of string theory at order ${\alpha }^{\prime }$ in the presence of boundary
• Novel Hairy Black Hole Solutions in Einstein-Maxwell-Gauss-Bonnet-Scalar Theory
• On loop corrections to integrable $2D$ sigma model backgrounds
• S-dual Amplitude and D3-Brane Couplings
• O-plane couplings at order ${\alpha }^{\prime 2}$: one R-R field strength
• Couplings of order six in the gauge field strength and the second fundamental form on a D${}_p$-brane at order ${\alpha }^{\prime 2}$
• ${\alpha }^{\prime }$-corrections to DBI action via T-duality constraint
• Non-linearly ghost-free higher curvature gravity
• An off-shell D-brane action at order ${\alpha }^{\prime 2}$ in flat spacetime
• Higher derivative corrections to WZ action: One RR, one NSNS and one NS couplings
• Higher-derivative couplings and torsional Riemann curvature
• On the uniqueness of ghost-free special gravity
• Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity
• Higher spins from exotic dualisations
• Heat kernel coefficients for massive gravity
• Non-linear Electrodynamics from Massive Gravity
• Construction of higher-order metric fluctuation terms in spacetime symmetry-breaking effective field theory
• Short-range forces due to Lorentz-symmetry violation
• Analysis of Unitarity in Conformal Quantum Gravity
• Surface terms in effective action of O-plane at order ${\alpha }^{\prime 2}$
• Spin-2 twisted duality in (A)dS
• Irrelevant Operators and their Holographic Anomalies
• Lectures in Quantum Gravity
• FieldsX -- An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology
• Einstein-Grisaru-Zanon gravity
• A covariant approach to parameterised cosmological perturbations
• Two Ramond-Ramond corrections to type II supergravity via field-theory amplitude
• Higher derivative corrections to DBI action at ${\alpha }^{\prime 2}$ order
• Higher Derivative Theories for Interacting Massless Gravitons in Minkowski Spacetime
• T-duality of ${\alpha }^{\prime }$-correction to DBI action at all orders of gauge field
• $O(D,D)$-constraint on $D$-dimensional effective actions
• Shift-symmetric $SO(N)$ multi-Galileon
• Gauging the higher-spin-like symmetries by the Moyal product
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• The data on the boundary at order ${\alpha }^{\prime }$
• Covariantly Constant Anomalies on Conformal Manifolds
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Higher dualisations of linearised gravity and the $A_1^{+++}$ algebra
• Commutator technique for the heat kernel of minimal higher derivative operators
• RG and logarithmic CFT multicritical properties of randomly diluted Ising models
• Non-perturbative quantum Galileon in the exact renormalization group
• Higher dimensional charged static and rotating solutions in mimetic gravity
• Slow-roll inflation in $f\left(R,T,R_{ab}{T}^{ab}\right)$ gravity
• Gauge field corrections to 11-dimensional supergravity via dimensional reduction
• Six-Derivative Yang-Mills Couplings in Heterotic String Theory
• Unfolding $E_{11}$
• Hadamard Renormalization of a 2-Dimensional Dirac Field
• On T-duality of $R^2$-corrections to DBI action at all orders of gauge field
• Instability of BTZ black holes in parity-even massive gravity
• Heat kernel of non-minimal second-order operators
• T-duality of D-brane versus O-plane actions
• Holographic complexity of Born-Infeld gravity
• Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach
• Minimal gauge invariant couplings at order ${\ell }_p^6$ in M-theory
• EFT Corrections to Majumdar-Papapetrou Black Holes
• Quantizing non-projectable Hořava gravity with Lagrangian path integral
• On effective field theory of F-theory beyond leading order
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
• De Sitter scattering amplitudes in the Born approximation
• Electrically charged black hole solutions in semiclassical gravity and dynamics of linear perturbations
• Gravitational Couplings on D-brane Revisited
• Static spherically symmetric black holes in de Rham-Gabadadze-Tolley massive gravity in arbitrary dimensions
• Higher-derivative corrections to type II supergravity:Four Ramond-Ramond terms
• Aspects of three-dimensional higher-curvature gravities
• Positivity vs. Lorentz-violation: an explicit example