SPACE seminar: Varun Kushwaha - "Area Scaling of Dynamical Degrees of Freedom in Regularised Scalar Field Theory"

Tuesday 10 Mar 2026, 12:00 → 13:00 Europe/Rome

Aula 4 (San Marcellino)

Speaker: Varun Kushwaha (LMU Munich)

Abstract: Holographic ideas suggest that the number of fundamental degrees of freedom in a region should scale with its boundary area, in tension with the volume–extensive kinematics of quantum field theory. Recent work by Cao et al. [2] and Friedrich et al. [3] has explored how effective field-theoretic behaviour may emerge from systems with fewer underlying resources, in which many apparent modes are built from a smaller set of fundamental ones.

In this talk, I present a complementary, dynamical perspective on this tension based on our recent work [1]. Rather than imposing redundancy kinematically, I ask how much compression is already enforced by ordinary Hamiltonian field dynamics.

Focusing on a regulated classical scalar field, I introduce the notion of minimal symplectic dimension: the smallest number of canonical degrees of freedom required to reproduce a trajectory using an autonomous Hamiltonian system. Using symplectic model order reduction and action–angle methods, I show that this dimension is controlled by the number of distinct normal-mode frequencies and exhibits area-type scaling in flat space, with controlled curvature corrections.

The resulting reduced dynamics naturally generates families of local-looking modes that are not independent, but share the same underlying canonical variables. This provides a concrete classical mechanism for redundancy and mode sharing, without modifying canonical structures by hand. The results isolate the maximal compression already enforced by field-theoretic dynamics and clarify which features of holographic-inspired constructions can arise prior to quantisation and independently of gravity. 

References:

1. Oliver Friedrich, Kristina Giesel, and Varun Kushwaha. Area scaling of dynamical degrees of freedom in regularised scalar field theory, 2026. [https://arxiv.org/abs/2602.09100]
2. ChunJun Cao, Wissam Chemissany, Alexander Jahn, and Zoltán Zimborás. Overlapping qubits from non-isometric maps and de Sitter tensor networks. Nature Communications, 16(1), January 2025. [https://arxiv.org/abs/2304.02673]
3. Oliver Friedrich, ChunJun Cao, Sean M. Carroll, Gong Cheng, and Ashmeet Singh. Holographic phenomenology via overlapping degrees of freedom. Classical and Quantum Gravity, 41(19):195003, October 2024. [https://arxiv.org/abs/2402.11016]
   

 

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