Area scaling of dynamical degrees of freedom in regularized scalar field theory
Friedrich O, Giesel K, Kushwaha V (2026)
Publication Type: Journal article
Publication year: 2026
Journal
Book Volume: 114
Article Number: 045020
Journal Issue: 4
DOI: 10.1103/TJC4-221Z
Abstract
How many canonical degrees of freedom are dynamically needed to reproduce the Hamiltonian evolution of a regulated field theory?We address this question for a UV/IR-regularized classical scalar field by identifying the minimal symplectic dimension required to reproduce a single trajectory by an autonomous Hamiltonian system. Using symplectic model order reduction as a structure-preserving diagnostic, we show that, for the free scalar field, this dimension is controlled not by the volume-extensive number of regulated field modes but by the smaller number of distinct normal-mode frequencies below the ultraviolet cutoff. In a flat cubic box, this gives an area-type scaling with the size of the region, up to slowly varying corrections. For geodesic balls in maximally symmetric curved spaces, positive curvature produces a superarea enhancement that remains subextensive, while negative curvature suppresses the scaling, with the flat result recovered smoothly in the small-curvature limit. Numerical experiments indicate that the same frequency-based mechanism persists in weakly interacting λϕ4 theory on quasi-integrable timescales. Beyond the counting result, the reduced dynamics has a characteristic algebraic structure: it decomposes into independent oscillator blocks, while reconstructed field modes are linear combinations of these blocks and have Poisson brackets governed by a projector rather than the identity. In this precise classical sense, overlapping degrees of freedom arise dynamically, without modifying the canonical structure by hand. The results provide a controlled setting in which area-type dynamical scaling and overlap structures can be studied before quantization and help separate ordinary Hamiltonian compression effects from genuinely gravitational mechanisms.
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Germany (DE)How to cite
APA:
Friedrich, O., Giesel, K., & Kushwaha, V. (2026). Area scaling of dynamical degrees of freedom in regularized scalar field theory. Physical Review D, 114(4). https://doi.org/10.1103/TJC4-221Z
MLA:
Friedrich, Oliver, Kristina Giesel, and Varun Kushwaha. "Area scaling of dynamical degrees of freedom in regularized scalar field theory." Physical Review D 114.4 (2026).
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