Mass gap

Résumé

In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle. Since the energies of exact (i.e. nonperturbative) energy eigenstates are spread out and therefore they are not technically eigenstates, a more precise definition is that the mass gap is the greatest lower bound of the energy of any state which is orthogonal to the vacuum. The analog of a mass gap in many-body physics on a discrete lattice arises from a gapped Hamiltonian. Mathematical definitions For a given real-valued quantum field \phi(x), where x = (\boldsymbol{x},t), we can say that the theory has a mass gap if the two-point function has the property :\langle\phi(0,t)\phi(0,0)\rangle\sim \sum_nA_n\exp\left(-\Delta

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https://en.wikipedia.org/wiki/Mass_gap

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Two-point functions and bootstrap applications in quantum field theories

Denis Karateev

We study two-point functions of local operators and their spectral representation in UV complete quantum field theories in generic dimensions focusing on conserved currents and the stress-tensor. We establish the connection with the central charges of the UV and IR fixed points. We re-derive "c-theorems" in 2d and show the absence of their direct analogs in higher dimensions. We conclude by focusing on quantum field theories with a mass gap. We study the stress tensor two-particle form factor, derive implications of unitarity and define concrete bootstrap problems in generic dimensions.

SPRINGER2022

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We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inner products between asymptotic states (in and out) and states created by the action of local operators on the vacuum. The corresponding matrix elements involve scattering amplitudes, form factors and spectral densities of local operators. We test this method in two-dimensional QFTs by setting up a linear optimization problem that gives a lower bound on the central charge of the UV CFT associated to a QFT with a given mass spectrum of stable particles (and couplings between them). Some of our numerical bounds are saturated by known form factors in integrable theories like the sine-Gordon, E-8 and O(N) models.

SPRINGER2020

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Open-boundary conditions in the deconfined phase

Adrien Florio

In this work, we consider open-boundary conditions at high temperatures, as they can potentially be of help to measure the topological susceptibility. In particular, we measure the extent of the boundary effects at T = 1.5T(C) and T = 2.7T(C). In the first case, it is larger than at T = 0 while we find it to be smaller in the second case. The length of this "boundary zone" is controlled by the screening masses. We use this fact to measure the scalar and pseudo-scalar screening masses at these two temperatures. We observe a mass gap at T = 1.5T(C) but not at T = 2.7T(C). Finally, we use our pseudo-scalar channel analysis to estimate the topological susceptibility. The results at T = 1.5T(C) are in good agreement with the literature. At T = 2.7T(C), they appear to suffer from topological freezing, which prevents us from providing a precise determination of the topological susceptibility.

Springer2019

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