arXiv subjects
Publications and source records attributed to Peter Millington.
We present explicit expressions for Fock-space projection operators that correspond to realistic final states in scattering experiments. Our operators automatically sum over unobserved quanta and account for non-emission into sub-regions of momentum space.
We review how to describe a field theory that includes a non-Hermitian mass term in the region of parameter space where the Lagrangian is $PT$-symmetric. The discrete symmetries of the system are essential for understanding the consistency of the model, and the link between conserved current and variation of the Lagrangian has to be revisited in the case of continuous symmetries.
Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of PT-symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether's theorem, and we give specific examples for illustration.
We show that the radial acceleration relation for rotationally-supported galaxies may be explained, in the absence of cold dark matter, by a non-minimally coupled scalar field, whose fifth forces are partially screened on galactic scales by the symmetron mechanism. In addition, we show that sufficient energy is stored in the symmetron field to explain the dynamic stability of galactic disks.
With the Higgs mass now measured at the sub-percent level, the potential metastability of the electroweak vacuum of the Standard Model (SM) motivates renewed study of false vacuum decay in quantum field theory. In this note, we describe an approach to calculating quantum corrections to the decay rate of false vacua that is able to account fully and self-consistently for the underlying inhomogeneity of the solitonic tunneling configuration. We show that this method can be applied both to theories in which the instability arises already at the level of the classical potential and those in which the instability arises entirely through radiative effects, as is the case for the SM Higgs vacuum. We analyse two simple models in the thin-wall regime, and we show that the modifications of the one-loop corrections from accounting fully for the inhomogeneity can compete at the same level as the two-loop homogeneous corrections.
Working within the context of PT-symmetric quantum mechanics, we begin by describing a non-Hermitian extension of QED that is both Lorentz invariant and consistent with unitarity. We show that the non-Hermitian Dirac mass matrix of this theory exhibits an exceptional point, corresponding to an effectively massless theory whose conserved current is either right- or left-chiral dominated. With this inspiration, we are able to construct a non-Hermitian model of light Dirac neutrino masses from Hermitian and anti-Hermitian Yukawa couplings that are both of order unity. We finish by highlighting potential phenomenological implications of this model.
We present a novel approach to computing transition probabilities in quantum field theory, which allows them to be written directly in terms of expectation values of nested commutators and anti-commutators of field operators, rather than squared matrix elements. We show that this leads to a diagrammatic expansion in which the retarded propagator plays a dominant role. As a result, one is able to see clearly how faster-than-light signalling is prevented between sources and detectors. Finally, we comment on potential implications of this approach for dealing with infra-red divergences.
We describe a symmetron model in which the screening of fifth forces arises at the one-loop level through the Coleman-Weinberg mechanism of spontaneous symmetry breaking. We show that such a theory can avoid current constraints on the existence of fifth forces but still has the potential to give rise to observable deviations from general relativity, which could be seen in cold atom experiments.
We show how the two physically-distinct sources of CP-asymmetry relevant to scenarios of leptogenesis: (i) resonant mixing and (ii) oscillations between different flavours can be unambiguously identified within the Kadanoff-Baym formalism. These contributions are isolated by analyzing the spectral structure of the non-equilibrium propagators without relying on the definition of particle number densities. The mixing source is associated with the usual mass shells, whereas the oscillation source is identified with a third intermediate shell. In addition, we identify terms lying on the oscillation shell that can be interpreted as the destructive interference between mixing and oscillation. We confirm that identical shell structure is obtained in both the Heisenberg- and interaction-picture realizations of the Kadanoff-Baym formalism. In so doing, we illustrate the self-consistency and complementarity of these two approaches. The interaction-picture approach in particular has the advantage that it may be used to analyze all forms of mass spectra from quasi-degenerate through to hierarchical.
We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.
We propose a novel method of evaluating the effective action, wherein the physical one- and two-point functions are obtained in the limit of non-vanishing external sources. We illustrate the self-consistency of this method by recovering the usual 2PI effective action due to Cornwall, Jackiw and Tomboulis, differing only by the fact that the saddle-point evaluation of the path integral is performed along the extremal quantum, rather than classical, path. As such, this approach is of particular relevance to situations where the dominant quantum and classical paths are non-perturbatively far away from one-another. A pertinent example is the decay of false vacua in radiatively-generated potentials, as may occur for the electroweak vacuum of the Standard Model. In addition, we describe how the external sources may instead be chosen so as to yield the two-particle-point-irreducible (2PPI) effective action of Coppens and Verschelde. Finally, in the spirit of the symmetry-improved effective action of Pilaftsis and Teresi, we give an example of how the external sources can be used to preserve global symmetries in truncations of the 2PI effective action. Specifically, in the context of an O(2) model with spontaneous symmetry breaking, we show that this approach allows the Hartree-Fock approximation to be re-organized, such that the Goldstone boson remains massless algebraically in the symmetry-broken phase and we obtain the correct second-order thermal phase transition.
We use a Green's function approach in order to develop a method for calculating the tunneling rate between radiatively-generated non-degenerate vacua. We apply this to a model that exhibits spontaneous symmetry breaking via the Coleman-Weinberg mechanism, where we determine the self-consistent tunneling configuration and illustrate the impact of gradient effects that arise from accounting for the underlying space-time inhomogeneity.
An extension of QED is considered in which the Dirac fermion has both Hermitian and anti-Hermitian mass terms, as well as both vector and axial-vector couplings to the gauge field. Gauge invariance is restored when the Hermitian and anti-Hermitian masses are of equal magnitude, and the theory reduces to that of a single massless Weyl fermion. An analogous non-Hermitian Yukawa theory is considered, and it is shown that this model can explain the smallness of the light-neutrino masses and provide an additional source of leptonic CP violation.
Flavour effects play an important role in the statistical evolution of particle number densities in several particle physics phenomena. We present a fully flavour-covariant formalism for transport phenomena, in order to consistently capture all flavour effects in the system. We explicitly study the scenario of Resonant Leptogenesis (RL), and show that flavour covariance requires one to consider generically off-diagonal number densities, rank-4 rate tensors in flavour space, and non-trivial generalization of the discrete symmetries C, P and T. The flavour-covariant transport equations, obtained in our semi-classical framework, describe the effects of three relevant physical phenomena: coherent heavy-neutrino oscillations, quantum decoherence in the charged-lepton sector, and resonant CP violation due to heavy-neutrino mixing. We show quantitatively that the final asymmetry is enhanced by up to an order of magnitude, for electroweak-scale heavy neutrinos, as compared to that obtained from flavour-diagonal or partially flavour off-diagonal equations. A full field-theoretic treatment in the weakly-resonant regime, based on the Kadanoff-Baym (KB) equations, confirms that heavy-neutrino oscillations and mixing are two distinct phenomena, and reproduces the results obtained in our semi-classical framework. Finally, we show that the quasi-particle ansaetze, often employed in KB approaches to RL, discard the phenomenon of mixing, capturing only oscillations and leading to an underestimate of the final asymmetry by a factor of order 2.
We amend the incorrect discussion in Nucl. Phys. B 886 (2014) 569 [1] concerning the numerical examples considered there. In particular, we discuss the viability of minimal radiative models of Resonant Leptogenesis and prove that no asymmetry can be generated at $\mathcal{O}(h^4)$ in these scenarios. We present a minimal modification of the model considered in [1], where electroweak-scale right-handed Majorana neutrinos can easily accommodate both successful leptogenesis and observable signatures at Lepton Number and Flavour Violation experiments. The importance of the fully flavour-covariant rate equations, as developed in [1], for describing accurately the generation of the lepton asymmetry is reconfirmed.
We present a fully flavour-covariant formalism for transport phenomena and apply it to study the flavour-dynamics of Resonant Leptogenesis (RL). We show that this formalism provides a complete and unified description of RL, consistently accounting for three distinct physical phenomena: (i) resonant mixing and (ii) coherent oscillations between different heavy-neutrino flavours, as well as (iii) quantum decoherence effects in the charged-lepton sector. We describe the necessary emergence of higher-rank tensors in flavour space, arising from the unitarity cuts of partial self-energies. Finally, within a Resonant $τ$-Genesis model, we illustrate the importance of this formalism by showing that the final lepton asymmetry can vary by as much as an order of magnitude between partially flavour-dependent treatments, which do not capture all of the pertinent flavour effects.
We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an application, we take the $λϕ^4$ theory, extended with $N$ additional heavier scalars, wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself.
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.