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Joshua Y. L. Jones

Publications and source records attributed to Joshua Y. L. Jones.

5 recordsLinked to original sources
arXiv2026

Spectral Spacetime Entropy for Quasifree Theories

Motivated by the necessity to UV-regularise entanglement entropy, we present a spectral method for calculating the entropy of quasifree states, for both bosonic and fermionic field theories. This construction is defined in spacetime rather than on a hypersurface, enabling the covariant regularisation of entropies, and its calculation in generic spacetime regions. We derive these formulae, which have previously appeared in the literature, in a new manner and highlight certain aspects of them, such as their connection to the density matrix and its eigenvalues. The spacetime nature of the formulation makes it particularly apt in the context of semiclassical and quantum gravity and in connection to black hole entropy. Another useful property of the formulation is its application to settings where no notion of a Cauchy surface exists, such as in the causal set theory approach to quantum gravity. We show example applications of the formulae which demonstrate their ability to reproduce known results. We also show a calculation in a causal set in $1+1$ dimensions which makes use of several of the unique and useful features of the formalism. In this last example, we obtain a novel result of a slightly modified entanglement entropy scaling coefficient, giving a possible signature of spacetime discreteness.

hep-th↗
arXiv2026

Spectral Density of the Causal Propagator

The causal propagator (or Pauli-Jordan function), which multiplied by $i$ is the spacetime commutator of the field $[ϕ(x),ϕ(x')]$, plays an essential role in scalar quantum field theory. We discuss the role of the causal propagator and its spectrum in recent developments in defining quantum field theory in a more explicitly covariant manner, as well as in causal set theory. We then present a conjecture for its asymptotic spectral density in a free theory, and give examples that lend evidence to the conjectured scaling. Our work has implications for Lorentzian spectral geometry in much the same way as Weyl's asymptotic law has for Riemannian spectral geometry.

gr-qc↗
arXiv2025

Efficient evaluation of real-time path integrals

The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals is still extremely expensive and numerically delicate due to its high-dimensional and oscillatory nature. We propose an efficient method for the numerical evaluation of the real-time world-line path integral for theories where the potential is dominated by a quadratic at infinity. This is done by rewriting the high-dimensional oscillatory integral in terms of a series of low-dimensional oscillatory integrals, that we efficiently evaluate with Picard-Lefschetz theory or approximate with the eikonal approximation. Subsequently, these integrals are stitched together with a series of fast Fourier transformations to recover the lattice regularized Feynman path integral. Our method directly applies to problems in quantum mechanics, the word-line quantization of quantum field theory, and quantum gravity.

quant-ph↗
arXiv2022

Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory

A more complete understanding of entanglement entropy in a covariant manner could inform the search for quantum gravity. We build on work in this direction by extending previous results to disjoint regions in $1+1$D. We investigate the entanglement entropy of a scalar field in disjoint intervals within the causal set framework, using the spacetime commutator and correlator, $i\mathbfΔ$ and $\mathbf{W}$ (or the Pauli-Jordan and Wightman functions), respectively. A new truncation scheme for disjoint causal diamonds is presented, which follows from the single diamond truncation scheme. We investigate setups including two and three disjoint causal diamonds, as well as a single causal diamond that shares a boundary with a larger global causal diamond. In all the cases that we study, our results agree with the expected area laws. In addition, we study the mutual information in the two disjoint diamonds setup. The ease of our calculations indicate our methods to be a useful tool for numerically studying such systems. We end with a discussion of some of the strengths and future applications of the spacetime formulation we use in our entanglement entropy computations, both in causal set theory and in the continuum.

hep-th↗