arXiv subjects

Peter Lowdon

Publications and source records attributed to Peter Lowdon.

At least 19 recordsLinked to original sources

arXiv2026

Resonances at finite temperature from the lattice

The properties of hadronic resonances at finite temperature constitute an important probe of the thermal QCD medium. In this work we use the concept of thermoparticles, which characterise thermally-modified but stable particle-like states, to define the notion of two-particle scattering at finite temperature, and establish a unitarity relation for the thermal scattering amplitude. We derive a finite-temperature generalisation of the vacuum two-particle quantisation condition via a skeleton expansion of the finite-volume correlation function. Solving this condition at the finite-volume energy levels of the system constrains the form of the thermal scattering amplitude, and hence the properties of resonances. In contrast to the vacuum case, the kinematic function containing the leading finite-volume corrections is finite at all energies, reflecting the fact that thermoparticles have broadened spectral peaks due to their interactions with the thermal medium. Since all lattice simulations involve a finite temporal extent, our approach can also be used to study finite-temporal size effects in vacuum analyses.

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arXiv2026

Towards a consistent perturbation theory at finite temperature

The standard approach to perturbation theory for finite-temperature quantum field theories has several issues, including the appearance of ill-defined on-shell contributions in the real-time formulation, and infrared diverges in massless theories. Earlier studies indicate that these issues all stem from the inconsistent thermal generalisation of the Gell-Mann-Low relation, which forms the foundation of perturbation theory in vacuum. This inconsistency arises from the use of free scattering states in the relation, which are known not to exist in interacting thermal theories. In this work, we propose a generalisation of the Gell-Mann-Low relation for scalar theories based on non-perturbative spectral insights, namely that finite-temperature scattering states can be described by damped but stable particle-like excitations, so-called thermoparticles. The perturbative expansion of this generalised relation gives rise to contributions with exactly the same topology as the standard finite-temperature approach, except that now the propagators appearing in this expansion are not those of a free field but of thermoparticles, which depend on the dynamics of the theory. We demonstrate that thermoparticle perturbation theory resolves the known problems of the standard approach. Furthermore, by comparing imaginary-time calculations at two-loop level with numerical lattice simulations of two-point correlation functions in massive $\phi^{4}$ theory, we explicitly show that this framework gives rise to precise predictions, as in the vacuum case, in stark contrast to the standard approach.

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arXiv2025

Goldstone bosons across thermal phase transitions

Temperature has a significant effect on the properties of quantum field theories (QFTs) with a spontaneously broken symmetry, in particular on the massless Goldstone bosons that exist in the vacuum state. It has recently been shown using lattice calculations for a $\mathrm{U}(1)$ complex scalar field theory that the Goldstone mode persists even when the symmetry is restored above the critical temperature $T_{c}$, and has the properties of a screened excitation, a so-called thermoparticle. In this work, we continue the investigation of this theory by determining explicitly how the Goldstone mode evolves as the temperature is increased both below and above $T_{c}$. We find that the two phases of the theory are entirely characterised by the thermal dissipative effects experienced by the Goldstone mode, with the broken and symmetry-restored phases associated with weak and strong damping, respectively. These findings are consistent with the non-perturbative constraints imposed by spontaneous symmetry breaking, and provide a new way in which to characterise thermal phase transitions in QFTs.

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arXiv2025

Goldstone bosons at non-zero temperature

Spontaneous symmetry breaking in quantum field theories at non-zero temperature still holds fundamental open questions, in particular what happens to vacuum Goldstone bosons when the temperature is increased. By investigating a complex scalar field theory on the lattice we demonstrate that Goldstone bosons at non-zero temperature behave like screened massless particle-like excitations, so-called thermoparticles, which continue to exist even in the symmetry-restored phase of the theory. We provide non-perturbative evidence for the functional form of the Goldstone mode's dissipative behaviour, and determine its corresponding spectral properties. Since the persistence of thermal Goldstone modes within symmetry-restored phases is predicted to be a model-independent characteristic, this has fundamental consequences for systems in which continuous symmetries are restored at high temperatures.

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arXiv2024

Spectral properties of pseudo-scalar mesons through the QCD chiral crossover

We summarise recent progress towards the non-perturbative determination of thermal spectral functions for pseudo-scalar mesons in QCD by exploiting constraints imposed by micro-causality at finite temperature. For temperatures not much above the vacuum particle mass, continuous contributions from scattering, Landau damping and collective excitations are found to be negligible. This allows for a quantitative description of spatial and temporal lattice correlators in terms of thermoparticles, i.e.~vacuum excitations modified by medium effects, with resonance-like structures persisting for a range above the chiral crossover.

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arXiv2024

Non-perturbative constraints on perturbation theory at finite temperature

It has long been understood that the inclusion of temperature in the perturbative treatment of quantum field theories leads to complications that are not present at zero temperature. In these proceedings we report on the non-perturbative obstructions that arise, and how these lead to deviations in the predictions of lattice scalar correlation functions in massive $\phi^{4}$ theory. Using the known non-perturbative spectral constraints satisfied by finite-temperature correlation functions we outline why the presence of distinct particle-like excitations could provide a resolution to these issues.

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arXiv2024

On the (in)consistency of perturbation theory at finite temperature

A well-known difficulty of perturbative approaches to quantum field theory at finite temperature is the necessity to address theoretical constraints that are not present in the vacuum theory. In this work, we use lattice simulations of scalar correlation functions in massive $\phi^{4}$ theory to analyse the extent to which these constraints affect the perturbative predictions. We find that the standard perturbative predictions deteriorate even in the absence of infrared divergences at relatively low temperatures, and that this is directly connected to the analytic structure of the propagators used in the expansion. This suggests that the incorporation of non-perturbative thermal effects in the propagators is essential for a consistent perturbative formulation of scalar quantum field theories at finite temperature. By utilising the spectral constraints imposed on finite-temperature correlation functions, we explore how these effects manifest themselves in the lattice data, and discuss why the presence of distinct thermoparticle excitations provides a potential resolution to these issues.

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arXiv2023

Pseudo-scalar meson spectral properties in the chiral crossover region of QCD

Determining the type of excitations that can exist in a thermal medium is key to understanding how hadronic matter behaves at extreme temperatures. In this work we study this question for pseudo-scalar mesons comprised of light-strange and strange-strange quarks, analysing how their low-energy spectral properties are modified as one passes through the high-temperature chiral crossover region between $T=145.6 \, \text{MeV}$ and $172.3 \, \text{MeV}$. We utilise the non-perturbative constraints satisfied by correlation functions at finite temperature in order to extract the low-energy meson spectral function contributions from spatial correlator lattice data in $N_{f}=2+1$ flavour QCD. The robustness of these contributions are tested by comparing their predictions with data for the corresponding temporal correlator at different momentum values. We find that around the pseudo-critical temperature $T_{\text{pc}}$ the data in both the light-strange and strange-strange channels is consistent with the presence of a distinct stable particle-like ground state component, a so-called thermoparticle excitation. As the temperature increases this excitation undergoes collisional broadening, and this is qualitatively the same in both channels. These findings suggest that pseudo-scalar mesons in QCD have a bound-state-like structure at low energies within the chiral crossover region which is still strongly influenced by the vacuum states of the theory.

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arXiv2022

Non-perturbative insights into the spectral properties of QCD at finite temperature

In quantum field theories at finite temperature spectral functions describe how particle systems behave in the presence of a thermal medium. Although data from lattice simulations can in principle be used to determine spectral function characteristics, existing methods rely on the extraction of these quantities from temporal correlators, which requires one to circumvent an ill-posed inverse problem. In these proceedings we report on a recent approach that instead utilises the non-perturbative constraints imposed by field locality to extract spectral function information directly from spatial correlators. In particular, we focus on the application of this approach to lattice QCD data of the spatial pseudo-scalar meson correlator in the temperature range $220-960 \, \text{MeV}$, and outline why this data supports the conclusion that there exists a distinct pion state above the chiral pseudo-critical temperature $T_{\!\text{pc}}$.

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arXiv2022

On chiral spin symmetry and the QCD phase diagram

Recently, an approximate $SU(4)$ chiral spin-flavour symmetry was observed in multiplet patterns of QCD meson correlation functions, in a temperature range above the chiral crossover. This symmetry is larger than the chiral symmetry of massless QCD, and can only arise effectively when colour-electric quark-gluon interactions dynamically dominate the quantum effective action. At temperatures about three times the crossover temperature, these patterns disappear again, indicating the screening of colour-electric interactions, and the expected chiral symmetry is recovered. In this contribution we collect independent evidence for such an intermediate temperature range, based on screening masses and the pion spectral function. Both kinds of observables behave non-perturbatively in this window, with resonance-like peaks for the pion and its first excitation disappearing gradually with temperature. Using symmetry arguments and the known behaviour of screening masses at small densities, we discuss how this chiral spin symmetric band continues into the QCD phase diagram.

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arXiv2022

Pion spectral properties above the chiral crossover of QCD

Spectral functions encode a wealth of information about the dynamics of any given system, and the determination of their non-perturbative characteristics is a long-standing problem in quantum field theory. Whilst numerical simulations of lattice QCD provide ample data for various Euclidean correlation functions, the inversion required to extract spectral functions is an ill-posed problem. In this work, we pursue previously established constraints imposed by field locality at finite temperature $T$, namely that spectral functions possess a non-perturbative representation which generalises the well-known K\"{a}ll\'{e}n-Lehmann spectral form to $T>0$. Using this representation, we analyse lattice QCD data of the spatial pseudo-scalar correlator in the temperature range $220-960 \, \text{MeV}$, and obtain an analytic expression for the corresponding spectral function, with parameters fixed by the data. From the structure of this spectral function we find evidence for the existence of a distinct pion state above the chiral pseudo-critical temperature $T_{\text{pc}}$, and contributions from its first excitation, which gradually melt as the temperature increases. As a non-trivial test, we find that the extracted spectral function reproduces the corresponding temporal lattice correlator data for $T=220 \, \text{MeV}$.

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arXiv2022

Real-time observables from Euclidean thermal correlation functions

In this work we apply a local quantum field theory approach in order to analyse the connection between real-time observables and Euclidean thermal correlation functions. In particular, using data generated from the functional renormalisation group in the quark-meson model, we demonstrate that in-medium effects can be directly extracted from the spatial momentum dependence of the Euclidean propagators, in contrast to conventional approaches, which rely on the reconstruction from different Matsubara frequencies. As an application, we determine the analytic features that arise from the discrete spectral contribution to the pion correlation function, and calculate the non-perturbative shear viscosity arising from these states.

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arXiv2022

Euclidean thermal correlation functions in local QFT

In this work we outline the general analytic characteristics satisfied by scalar correlation functions at finite temperature in local quantum field theory. We demonstrate that the locality of the fields in particular imposes significant constraints on the spectral structure of the theory, and that this enables the non-perturbative effects experienced by thermal particle states to be directly calculated from Euclidean correlation functions, avoiding the inverse problem.

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arXiv2021

Non-perturbative BRST symmetry and the spectral structure of the ghost propagator

In BRST-quantised Yang-Mills theory the existence of BRST symmetry imposes significant constraints on the analytic structure of the continuum theory. In particular, the presence of this symmetry in the non-perturbative regime implies that any on-shell state with vanishing norm must have an associated partner state with identical mass, but negative inner product. In this work we demonstrate that for quantum chromodynamics (QCD) this constraint gives rise to an interconnection between the ghost and gluon spectra, and in doing so provides a non-trivial test of whether BRST symmetry is realised non-perturbatively. By analysing infrared lattice data for the minimal Landau gauge ghost propagator in pure $\mathrm{SU}(3)$ Yang-Mills theory, and comparing this with previous results for the gluon propagator, we show that this interconnection is violated, and hence conclude that continuum and current lattice formulations of Yang-Mills theory in Landau gauge represent two distinct realisations of the theory.

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arXiv2021

Spectral representation of the shear viscosity for local scalar QFTs at finite temperature

In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K\"{a}ll\'{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $\eta_{0}$. As an example, we calculate $\eta_{0}$ in $\phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.

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arXiv2020

Comparing light-front quantization with instant-time quantization

We compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the restriction to equal times that makes the commutation (or anticommutation) relations appear to be so different. While our results are valid for both bosons and fermions, for fermions there are subtleties associated with tip of the light cone contributions that need to be taken care of. At the level of Feynman diagrams we show for non-vacuum Feynman diagrams that the pole terms in four-dimensional light-front Feynman diagrams reproduce the three-dimensional light-front on-shell Hamiltonian Fock space formulation in which the light-front energy and light-front momentum are on shell. However, because of circle at infinity contributions we show that this equivalence fails for four-dimensional light-front vacuum tadpole diagrams. Then, precisely because of these circle at infinity contributions, light-front vacuum tadpole diagrams are not only nonzero, they are actually equal to instant-time vacuum tadpole diagrams. Light-front vacuum diagrams are not correctly describable by the on-shell Hamiltonian formalism, and thus not by the closely related infinite momentum frame prescription either. With the transformation from instant-time fields to light-front fields being a spacetime translation, not only are instant-time quantization and light-front quantization equivalent, they are unitarily equivalent.

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arXiv2020

Analytic constraints on the energy-momentum tensor in conformal field theories

In this work we investigate the matrix elements of the energy-momentum tensor for massless on-shell states in four-dimensional unitary, local, and Poincar\'e covariant quantum field theories. We demonstrate that these matrix elements can be parametrised in terms of covariant multipoles of the Lorentz generators, and that this gives rise to a form factor decomposition in which the helicity dependence of the states is factorised. Using this decomposition we go on to explore some of the consequences for conformal field theories, deriving the explicit analytic conditions imposed by conformal symmetry, and using examples to illustrate that they uniquely fix the form of the matrix elements. We also provide new insights into the constraints imposed by the existence of massless particles, showing in particular that massless free theories are necessarily conformal.

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arXiv2020

Gravitational form factor constraints and their universality

By adopting a local QFT framework one can derive in a non-perturbative manner the constraints imposed by Poincar\'e symmetry on the form factors appearing in the Lorentz covariant decomposition of the energy-momentum tensor matrix elements. In particular, this approach enables one to prove that these constraints are in fact independent of the internal properties of the states appearing in the matrix elements. Here we outline the rationale behind this approach, and report on some of the implications of these findings.

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