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 (13)

• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• Introducing Cadabra: a symbolic computer algebra system for field theory problems
• The Invar Tensor Package
• xPand: An algorithm for perturbing homogeneous cosmologies
• The Invar tensor package: Differential invariants of Riemann
• Second and higher-order perturbations of a spherical spacetime
• A brief introduction to Cadabra: a tool for tensor computations in General Relativity
• Superfield integrals in high dimensions
• An Algorithm to Simplify Tensor Expressions
• Group-theoretic Approach for Symbolic Tensor Manipulation: II. Dummy Indices
• Spinors: a Mathematica package for doing spinor calculus in General Relativity
• Introduction to representation theory

Cited by in corpus (161)

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