arXiv subjects

Callum Bell

Publications and source records attributed to Callum Bell.

6 recordsLinked to original sources

arXiv2026

Towards a Connection Formulation of Action-Dependent Palatini Gravity

Previous work has shown that first-order Palatini gravity may be cast as a non-conservative Herglotz Lagrangian field theory, which excludes the conformal mode from its space of dynamical variables. In the present work, we analyse the role of the $SO(1,3)$ gauge connection in the construction of this action-dependent theory. The connection may be algebraically decomposed into complementary sectors which we interpret as `shape' and `scale' components. Only the former is retained within the Herglotz theory, while the latter is incorporated into the action-dependent sector. It is shown that the choice of connection decomposition is a space that can be smoothly parameterised. Such an observation leads to the finding that there exists a `moduli space of frictional field theories', in which each point corresponds to a distinct algebraic splitting of the connection into shape and scale pieces. Movement within the moduli space transitions between Herglotz Lagrangians whose on-shell dynamics all reproduce first-order Palatini gravity. The distinction lies in how the reproduction of the scale dynamics of the original theory is partitioned between action dependence and dynamical torsion.

gr-qc↗

arXiv2026

Classical General Relativity as a Non-Conservative Action-Dependent Field Theory

Previous work has provided the mathematical framework within which to analyse dynamical similarities for classical theories of fields. This formalism has been extended to those theories which, in addition to scaling symmetries, also possess gauge degrees of freedom. In this article, we apply these ideas to the analysis of the first-order Palatini formulation of General Relativity. It is shown that the conformal mode of the spacetime metric may be identified as the generator of a dynamical similarity. Further, we demonstrate that the dynamical content of the Hilbert-Palatini action may be reformulated in terms of an action-dependent field theory, which makes no reference to the conformal mode. Finally, we consider the linearised limit of the equations of motion derived from the scale-reduced action. We find that, in the harmonic gauge, the first-order metric perturbations satisfy a free wave equation, as expected. However, the elimination of the conformal factor requires a qualitative reinterpretation of the physics at second order. Conventionally, one considers the second-order perturbations to be sourced by quadratic combinations of first-order terms. These are packaged into an object identified as an `effective stress-energy tensor'. This interpretation must be amended for the action-dependent theory, where the presence of terms that couple the action sector with the geometrical degrees of freedom shows that our construction is inherently non-conservative.

gr-qc↗

arXiv2026

Constrained Symplectic and Contact Hamiltonian Systems: A Review

Singular theories, characterised by the presence of degeneracies in their Lagrangian or Hamiltonian descriptions, require the systematic implementation of constraints in order to obtain well-defined dynamics. While the symplectic framework provides the standard geometrical setting for conservative mechanical systems, those theories which exhibit dissipative effects are most appropriately discussed within the context of contact geometry. In this review, we present the geometrical structure underlying pre-symplectic and pre-contact manifolds, and develop the corresponding constraint algorithms that determine the admissible subset of phase space upon which consistent Hamiltonian evolution exists. We then close the discussion of each of the constraint algorithms with an example.

math-ph↗

arXiv2025

Gauge Symmetries, Contact Reduction, and Singular Field Theories

The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings leads to a dynamically-equivalent theory, which is frictional in nature. In this article, we extend the formalism to physical models, of both particles and fields, described by singular Lagrangians. In order to work with a finite-dimensional (velocity) phase space, our construction requires that we treat classical field theories within the De Donder-Weyl formalism, in which a multisymplectic structure is introduced on the first jets of the bundle of fields. The results obtained are subsequently applied to a number of physically-motivated examples, as well as a discussion presented on the implications of our work for classical General Relativity.

gr-qc↗

arXiv2025

Dynamical Similarity in Multisymplectic Field Theory

Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant degrees of freedom may physically be identified with empirically-inaccessible measures of global scale. In this article, we present a mathematical framework which extends the symmetry reduction procedure to theories of classical fields, in both the Lagrangian and Hamiltonian settings. In order to maintain Lorentz covariance, while simultaneously working with a finite-dimensional phase space, we employ the De Donder-Weyl formalism, for which the natural description is formulated in terms of the fibered manifolds of multisymplectic geometry. We subsequently analyse a number of simple examples, and provide a discussion of the broader implications of our construction.

hep-th↗

arXiv2025

Dynamical Similarity in Higher-Order Classical Symplectic Systems

Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a reduction process to be carried out, eliminating a single degree of freedom from the system, which we associate with an overall scale. This process of `contact reduction' leads to theories of a frictional nature, in which the physically-observable quantities form an autonomous subsystem, that evolves in a predictable manner. We demonstrate that this procedure has a natural generalisation to theories of higher order; detailed examples are provided, and physical implications discussed.

math-ph↗