arXiv subjects

James T. Wheeler

Publications and source records attributed to James T. Wheeler.

At least 19 recordsLinked to original sources

arXiv2026

Dirac Sources for Nonmetricity and Torsion in Metric-affine Gravity

Metric-affine gravity (GL(4) gauge theory) in 4-dimensions is coupled to a spacetime Dirac source field using the isomorphisms of the Lie algebra gl(4) to the Clifford algebras Cl(3,1) and Cl(2,2). A simple transformation relates the generators of Cl(3,1) to a real representation of Cl(2,2), while the real representation of Cl(2,2) serves directly as a basis for the Lie algebra gl(4). Therefore, although GL(4) does not contain a spinor representation of the Lorentz group, expanding its Lie algebra in the Cl(2,2) basis gives a Clifford valued connection with well-defined coupling to Dirac spinors. Variation of the expansion coefficients gives new Dirac sources for both torsion and nonmetricity, separated by identifying the so(3,1) basis within the gl(4) basis.

gr-qc↗

arXiv2025

Poincare gauge gravity from nonmetric gravity

We consider general linear gauge theory, with independent solder form and connection. These spaces have both torsion and nonmetricity. We show that the Cartan structure equations together with the defining equation for nonmetricity allow the mixed symmetry components of nonmetricity to be absorbed into an altered torsion tensor. Field redefinitions reduce the structure equations to those of Poincare gauge theory, with local Lorentz symmetry and metric compatibility. In order to allow recovery the original torsion and nonmetric fields, we replace the definition of nonmetricity by an additional structure equation and demand integrability of the extended system. We show that the maximal Lie algebra compatible with the enlarged set is isomorphic to the conformal Lie algebra. From this Lorentzian conformal geometry, we establish that the difference between the field strength of special conformal transformations and the torsion and is given by the mixed symmetry nonmetricity of an equivalent asymmetric system.

gr-qc↗

arXiv2025

Geometry from geodesics: fine-tuning Ehlers, Pirani, and Schild

Ehlers, Pirani, and Schild argued that measurements of null and timelike geodesics yield Weyl and projective connections, respectively, with compatibility in the lightlike limit giving an integrable Weyl connection. Their conclusions hold only for a 4-dim representation of the conformal connection on the null cone, and by restricting reparameterizations of timelike geodesics to yield a torsion-free, affine connection. An arbitrary connection gives greater freedom. A linear connection for the conformal symmetry of null geodesics requires the SO(4,2) representation. The enlarged class of projective transformations of timelike geodesics changes Weyl's projective curvature, and we find invariant forms of the torsion and nonmetricity, along with a new, invariant, second rank tensor field generalizing the dilatational curvature without requiring a metric. We show that either projective or conformal connections require a monotonic, twice differentiable function on a spacetime region foliated by order isomorphic, totally ordered, twice differentiable timelike curves in a necessarily Lorentzian geometry. We prove that the conditions for projective and conformal Ricci flatness imply each other and gauge choices within either can reduce the geometry to the original Riemannian form. Thus, measurements of null and timelike geodesics lead to an SO(4,2) connection, with no requirement for a lightlike limit. Reduction to integrable Weyl symmetry can only follow from the field equations of a gravity theory. We show that the simplest quadratic spacetime action leads to this reduction.

gr-qc↗

arXiv2023

Internal symmetry in Poincare gauge gravity

We find a large internal symmetry within 4-dimensional Poincare gauge theory. In the Riemann-Cartan geometry of Poincare gauge theory the field equation and geodesics are invariant under projective transformation, just as in affine geometry. However, in the Riemann-Cartan case the torsion and nonmetricity tensors change. By generalizing the Riemann-Cartan geometry to allow both torsion and nonmetricity while maintaining local Lorentz symmetry the difference of the antisymmetric part of the nonmetricity Q and the torsion T is a projectively invariant linear combination $S = T - Q$ with the same symmetry as torsion. The structure equations may be written entirely in terms of S and the corresponding Riemann-Cartan curvature. The new description of the geometry has manifest projective and Lorentz symmetries, and vanishing nonmetricity. Torsion, S and Q lie in the vector space of vector-valued 2-forms. Within the extended geometry we define rotations with axis in the direction of S. These rotate both torsion and nonmetricity while leaving S invariant. In n dimensions and (p, q) signature this gives a large internal symmetry. The four dimensional case acquires SO(11,9) or Spin(11,9) internal symmetry, sufficient for the Standard Model. The most general action up to linearity in second derivatives of the solder form now includes combinations quadratic in torsion and nonmetricity, torsion-nonmetricity couplings, and the Einstein-Hilbert action. Imposing projective invariance reduces this to dependence on S and curvature alone. The new internal symmetry decouples from gravity in agreement with the Coleman-Mandula theorem.

hep-th↗

arXiv2023

Sources of torsion in Poincare gauge theory

We study sources for torsion in Poincare gauge theory of any dimension, signature, and spin. We find that symmetric kinetic terms for non-Yang-Mills bosonic fields of arbitrary rank drive torsion. Our detailed discussion of spin-3/2 Rarita-Schwinger fields shows that they source all independent parts of the torsion. We develop systematic notation for spin-(2k+1)/2 fields and find the spin tensor for arbitrary k in n > 2k dimensions. For k > 0 there is a novel direct coupling between torsion and spinor fields. We also cast the well-known gauge relation between the canonical and Belinfante-Rosenfield energy tensors in terms of different choices of independent variables.

hep-th↗

arXiv2022

Abelian symmetry and the Palatini variation

Independent variation of the metric and connection in the Einstein-Hilbert action, called the Palatini variation, is generally taken to be equivalent to the usual formulation of general relativity in which only the metric is varied. However, when an abelian symmetry is allowed for the connection, the Palatini variation leads to an integrable Weyl geometry, not Riemannian. We derive this result using two possible metric/connection pairs: (1) the metric and general coordinate connection and (2) the solder form and local Lorentz spin connection of Poincarè gauge theory. Both lead to the same conclusion. Finally, we relate our work to other treatments in the literature.

gr-qc↗

arXiv2021

Yang-Mills sources in biconformal gravity

Biconformal gravity, based on gauging of the conformal group to 2n dimensions, reproduces n-dim scale-covariant general relativity on the co-tangent bundle in any dimension. We generalize this result to include Yang-Mills matter sources formulated as SU\left(N\right) gauge theories with a twisted action on the full 2n-dimensional biconformal space. We show that the coupling of the sources to gravity does not stop the reduction of effective dimension 2n\rightarrow n of the gravity theory, and instead forces the Yang-Mills source to reduce to ordinary n-dimensional Yang-Mills theory on the gravitating cotangent bundle, with the usual Yang-Mills energy tensor as gravitational source. The results apply as well to gravity with sources on Kähler manifolds and in double field theories.

hep-th↗

arXiv2018

Weyl geometry

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature tensor is the conformally invariant part of the Riemann curvature, and shows the explicit change in the Ricci and Schouten tensors required to insure conformal invariance. We include a proof of the well-known condition for the existence of a conformal transformation to a Ricci-flat spacetime. We generalize this to a derivation of the condition for the existence of a conformal transformation to a spacetime satisfying the Einstein equation with matter sources. Then, enlarging the symmetry from Poincaré to Weyl, we develop the Cartan structure equations of Weyl geometry, the form of the curvature tensor and its relationship to the Riemann curvature of the corresponding Riemannian geometry. We present a simple theory of Weyl-covariant gravity based on a curvature-linear action, and show that it is conformally equivalent to general relativity. This theory is invariant under dilatations, but not the full conformal group.

gr-qc↗

arXiv2016

Dynamical spacetime symmetry

According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dim Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected SO(n) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an SO(n-1,1) connection on the spacetime. The principal fiber bundle character of the original SO(n) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.

hep-th↗

arXiv2014

Weyl gravity as general relativity

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.

gr-qc↗

arXiv2010

The existence of time

Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures - the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.

gr-qc↗

arXiv2006

Yang-Mills gravity in biconformal space

We write a gravity theory with Yang-Mills type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of slowly changing fields. In addition, we systematically extend arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena for studying flat space Yang-Mills theories. By applying the biconformal extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we establish a 1-1, onto mapping between a set of gravitational gauge theories and 4-dim, flat space gauge theories.

hep-th↗

arXiv2005

Not so Classical Mechanics - Unexpected Symmetries of Classical Motion

A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force motion; a general discussion of higher-order Lagrangians and Hamiltonians with examples from Bohmian quantum mechanics, the Korteweg-de Vries equation and the logistic equation; gauge theories of Newtonian mechanics; classical spin, Grassmann numbers, and pseudomechanics.

physics.class-ph↗

arXiv2005

Quantum mechanics as a measurement theory on biconformal space

Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive standard quantum mechanics, and show how the need for probability amplitudes arises from the use of a standard of measurement. Additionally, we show that a postulate for unique, classical motion yields Hamiltonian dynamics with no measurable size changes, while a postulate for probabilistic evolution leads to physical dilatations manifested as measurable phase changes. Our results lead to the Feynman path integral formulation, from which follows the Schroedinger equation. We discuss the Heisenberg uncertainty relation and fundamental canonical commutation relations.

hep-th↗

arXiv2003

Biconformal supergravity and the AdS/CFT conjecture

Biconformal supergravity models provide a new gauging of the superconformal group relevant to the Maldacena conjecture. Using the group quotient method to biconformally gauge SU(2,2|N), we generate a 16-dim superspace. We write the most general even- and odd-parity actions linear in the curvatures, the bosonic sector of which is known to descend to general relativity on a 4-dim manifold.

hep-th↗

arXiv2003

Gauging Newton's Law

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton's law with the simplest measurement theory leads to Lagrangian mechanics, while use of conformal measurement theory leads to Hamilton's equations.

hep-th↗

arXiv2000

Extended Conformal Symmetry

We show that the grading of fields by conformal weight, when built into the initial group symmetry, provides a discrete, non-central conformal extension of any group containing dilatations. We find a faithful vector representation of the extended conformal group and show that it has a scale-invariant scalar product and satisfies a closed commutator algebra. The commutator algebra contains the infinite Heisenberg and Virasoro algebras. In contrast to the classical treatment of scale invariance, covariant derivatives and gauge transformations automatically incorporate the correct conformal weights when the extended symmetry is gauged.

hep-th↗

arXiv2000

Actions for Biconformal Matter

We extend 2n-dim biconformal gauge theory by including Lorentz-scalar matter fields of arbitrary conformal weight. For a massless scalar field of conformal weight zero in a torsion-free biconformal geometry, the solution is determined by the Einstein equation on an n-dim submanifold, with the stress-energy tensor of the scalar field as source. The matter field satisfies the n-dim Klein-Gordon equation.

hep-th↗