arXiv subjects

Peter Lowdon

Publications and source records attributed to Peter Lowdon.

32 records · Page 2Linked to original sources

arXiv2020

Universality of the Poincaré gravitational form factor constraints

Relativistic spin states are convention dependent. In this work we prove that the zero momentum-transfer limits of the leading two form factors in the decomposition of the energy-momentum tensor matrix elements are independent of this choice. In particular, we demonstrate that these constraints are insensitive to whether the corresponding states are massive or not, and that they arise purely due to the Poincaré covariance of the states.

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arXiv2020

The generalised infrared structure of the gluon propagator

Gauge theory correlators are potentially more singular in the infrared than those in non-gauge theories. We determine the implications that these singularities have on the spectrum of the theory, proving that the appearance of generalised poles implies the existence of on-shell states with fixed mass, but zero norm. For quantum chromodynamics these poles have direct relevance for the confinement of coloured states. Using lattice data for the Landau gauge gluon propagator we subsequently test for the presence of these poles, establishing that the data is indeed consistent with such a component.

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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 Poincaré 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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arXiv2019

Poincaré constraints on the gravitational form factors for massive states with arbitrary spin

In this work we analyse the constraints imposed by Poincaré symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distributional approach, we prove for the first time non-perturbatively that the zero momentum transfer limit of the leading two form factors in the decomposition are completely independent of the spin of the states. It turns out that these constraints arise due to the general Poincaré transformation and on-shell properties of the states, as opposed to the specific characteristics of the individual Poincaré generators themselves. By expressing these leading form factors in terms of generalised parton distributions, we subsequently derive the linear and angular momentum sum rules for states with arbitrary spin.

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arXiv2019

Structure of light front vacuum sector diagrams

We study the structure of scalar field light front quantization vacuum graphs. In instant time quantization both non-vacuum and vacuum graphs can equivalently be described by either the off-shell four-dimensional Feynman diagram approach or the on-shell three-dimensional Fock space approach, with this being the case since the relevant Feynman diagrams are given entirely by pole terms. This is also the case for light front quantization non-vacuum graphs. However this is the not the case for light front vacuum sector diagrams, since then there are also circle at infinity contributions to Feynman diagrams. These non-pole contributions cause vacuum diagrams to be nonzero and to not be given by a light-front Hamiltonian Fock space analysis. The three-dimensional approach thus fails in the light front vacuum sector. In consequence, the closely related infinite momentum frame approach also fails in the light front vacuum sector.

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arXiv2018

On the analytic structure of QCD propagators

Local formulations of quantum field theory provide a powerful framework in which non-perturbative aspects of QCD can be analysed. Here we report on how this approach can be used to elucidate the general analytic features of QCD propagators, and why this is relevant for understanding confinement.

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arXiv2018

Dyson-Schwinger equation constraints on the gluon propagator in BRST quantised QCD

The gluon propagator plays a central role in determining the dynamics of QCD. In this work we demonstrate for BRST quantised QCD that the Dyson-Schwinger equation imposes significant analytic constraints on the structure of this propagator. In particular, we find that these constraints control the appearance of massless components in the gluon spectral density.

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arXiv2018

Non-perturbative constraints on the quark and ghost propagators

In QCD both the quark and ghost propagators are important for governing the non-perturbative dynamics of the theory. It turns out that the dynamical properties of the quark and ghost fields impose non-perturbative constraints on the analytic structure of these propagators. In this work we explicitly derive these constraints. In doing so we establish that the corresponding spectral densities include components which are multiples of discrete mass terms, and that the propagators are permitted to contain singular contributions involving derivatives of $δ(p)$, both of which are particularly relevant in the context of confinement.

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arXiv2017

Rigorous constraints on the matrix elements of the energy-momentum tensor

The structure of the matrix elements of the energy-momentum tensor play an important role in determining the properties of the form factors $A(q^{2})$, $B(q^{2})$ and $C(q^{2})$ which appear in the Lorentz covariant decomposition of the matrix elements. In this paper we apply a rigorous frame-independent distributional-matching approach to the matrix elements of the Poincaré generators in order to derive constraints on these form factors as $q \rightarrow 0$. In contrast to the literature, we explicitly demonstrate that the vanishing of the anomalous gravitomagnetic moment $B(0)$ and the condition $A(0)=1$ are independent of one another, and that these constraints are not related to the specific properties or conservation of the individual Poincaré generators themselves, but are in fact a consequence of the physical on-shell requirement of the states in the matrix elements and the manner in which these states transform under Poincaré transformations.

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arXiv2017

The non-perturbative structure of the photon and gluon propagators

The non-perturbative structure of the photon and gluon propagators plays an important role in governing the dynamics of quantum electrodynamics (QED) and quantum chromodynamics (QCD) respectively. Although it is often assumed that these interacting field propagators can be decomposed into longitudinal and transverse components, as for the free case, it turns out that in general this is not possible. Moreover, the non-abelian gauge symmetry of QCD permits the momentum space gluon propagator to contain additional singular terms involving derivatives of $δ(p)$, the appearance of which is related to confinement. Despite the possibility of the failure of the transverse-longitudinal decomposition for the photon and gluon propagators, and the appearance of singular terms in the gluon propagator, the Slavnov-Taylor identity nevertheless remains preserved.

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arXiv2017

Non-manifest symmetries in quantum field theory

Non-manifest symmetries are an important feature of quantum field theories (QFTs), and yet their characteristics are not fully understood. In particular, the construction of the charge operators associated with these symmetries is ambiguous. In this paper we adopt a rigorous axiomatic approach in order to address this issue. It turns out that charge operators of non-manifest symmetries are not unique, and that although this does not affect their property as generators of the corresponding symmetry transformations, additional physical input is required in order to determine how they act on states. Applying these results to the examples of spacetime translation and Lorentz symmetry, it follows that the assumption that the vacuum is the unique translationally invariant state is sufficient to uniquely define the charges associated with these symmetries. In the case of supersymmetry though there exists no such physical requirement, and this therefore implies that the supersymmetric charge, and hence the supersymmetric space of states, is not uniquely defined.

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arXiv2016

Conditions on the violation of the cluster decomposition property in QCD

The behaviour of correlators at large distances plays an important role in the dynamics of quantum field theories. In many instances, correlators satisfy the so-called \textit{cluster decomposition property} (CDP), which means that they tend to zero for space-like asymptotic distances. However, under certain conditions it is possible for correlators to violate this property. In the context of quantum chromodynamics (QCD), a violation of the CDP for correlators of clusters involving coloured fields implies that the strength of the correlations between the coloured degrees of freedom in these clusters increases at large distances, which is a sufficient condition for confinement. In this paper we establish a criterion for when the CDP is violated. By applying this criterion to QCD, it turns out that certain lattice results involving the quark and gluon propagators can be interpreted as evidence that quarks and gluons are confined due to a violation of the CDP.

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arXiv2015

Spectral density constraints in quantum field theory

Determining the structure of spectral densities is important for understanding the behaviour of any quantum field theory (QFT). However, the exact calculation of these quantities often requires a full non-perturbative description of the theory, which for physically realistic theories such as quantum chromodynamics (QCD) is currently unknown. Nevertheless, it is possible to infer indirect information about these quantities. In this paper we demonstrate an approach for constraining the form of spectral densities associated with QFT propagators, which involves matching the short distance expansion of the spectral representation with the operator product expansion (OPE) of the propagators. As an application of this procedure we analyse the scalar propagator in $ϕ^4$-theory and the quark propagator in QCD, and show that constraints are obtained on the spectral densities and the OPE condensates. In particular, it is demonstrated that the perturbative and non-perturbative contributions to the quark condensate in QCD can be decomposed, and that the non-perturbative contributions are related to the structure of the continuum component of the scalar spectral density.

hep-th↗

arXiv2014

Boundary terms in quantum field theory and the spin structure of QCD

Determining how boundary terms behave in a quantum field theory (QFT) is crucial for understanding the dynamics of the theory. Nevertheless, boundary terms are often neglected using classical-type arguments which are no longer justified in the full quantum theory. In this paper we address this problem by establishing a necessary and sufficient condition for arbitrary spatial boundary terms to vanish in a general QFT. As an application of this condition we examine the issue of whether the angular momentum operator in Quantum Chromodynamics (QCD) has a physically meaningful quark-gluon decomposition. Using this condition it appears as though this is not the case, and that it is in fact the non-perturbative QCD structure which prevents the possibility of such a decomposition.

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