arXiv subjects

Sam Bateman

Publications and source records attributed to Sam Bateman.

3 recordsLinked to original sources

arXiv2026

On divergences in a four-derivative scalar field theory

We perform a detailed diagrammatic analysis of the renormalisation of a family of asymptotically free, shift-symmetric four-derivative scalar field theories introduced by Holdom in arXiv:2303.06723 and arXiv:2402.09223. We extend the renormalisation of the theory from one to three loops using both an $R^*$ method and an asymptotic expansion in momenta. We prove that the Euclidean correlators (or off-shell amplitudes) are IR finite, to all orders in perturbation theory, and derive a non-renormalisation theorem describing the all-order structure of the renormalisation constants. In particular, a purely cubic interaction is RG invariant and a perfect square Lagrangian density is preserved under renormalisation. The latter result is due to a Ward identity in a related $\textit{ gravitational}$ theory $-$ the conformally flat limit of quadratic gravity (CFQG). We show that the beta function for the perfect square theory maps exactly to that of an $O(2)$-symmetric, two-derivative, massless $\phi^4$ theory at negative coupling. We verify this relationship explicitly up to three loops and thus determine the beta function and anomalous dimension for both the perfect square theory and CFQG to six loops.

hep-th↗

arXiv2026

Escape from Ostrogradsky via Hidden Ghost Parity

We present a counterexample to Ostrogradsky's famous "no go" theorem as usually interpreted in quantum field theory (QFT), namely a four-derivative, UV-complete QFT with a consistent perturbative expansion which describes high energy scattering processes. We carefully quantize the theory on an $\textit{indefinite}$ space of states - a Krein space - using covariant methods which ensure perturbative causality and unitarity (in the form of the optical theorem) to all orders. We generalize the Born rule to Krein spaces and prove that all tree level transition probabilities are positive in spite of the presence of ghosts. A key role in the proof is played by a hidden "ghost parity" symmetry which becomes explicit when the theory is embedded in a two-derivative, two-field $O(1,1)$-symmetric perturbative field theory.

hep-th↗

arXiv2005

Film Growth and Surface Roughness with Fluctuating Covalent Bonds in Evaporating Aqueous Solution of Reactive Hydrophobic and Polar Groups: A Computer Simulation Model

A computer simulation model is proposed to study film growth and surface roughness in aqueous ($A$) solution of hydrophobic ($H$) and hydrophilic ($P$) groups on a simple three dimensional lattice of size $L_x \times L_y \times L_z$ with an adsorbing substrate. Each group is represented by a particle with appropriate characteristics occupying a unit cube (i.e., eight sites). The Metropolis algorithm is used to move each particle stochastically. The aqueous constituents are allowed to evaporate while the concentration of $H$ and $P$ is constant. Reactions proceed from the substrate and bonded particles can hop within a fluctuating bond length. The film thickness ($h$) and its interface width ($W$) are examined for hard-core and interacting particles for a range of temperature ($T$). Simulation data show a rapid increase in $h$ and $W$ is followed by its non-monotonic growth and decay before reaching steady-state equilibrium ($h_s, W_s$) in asymptotic time step limit. The growth can be described by power-laws, e.g., $h \propto t^γ, W \propto t^β$ with a typical value of $γ\approx 2, β\approx 1$ in initial time regime followed by $γ\approx 1.5, β\approx 0.8$ at $T = 0.5$. For hard-core system, the equilibrium film thickness ($h_s$) and surface roughness ($w_s$) seem to scale linearly with the temperature, i.e., $h_s = 6.206 + 0.302 T, W_s = 1,255 + 0.425 T$ at low $T$ and $h_s = 6.54 + 0.198 T, W_s = 1.808 + 0.202 T$ at higher $T$. For interacting functional groups in contrast, $h_s$ and $W_s$ decay rapidly followed by a slow increase on raising the temperature.

cond-mat.soft↗