Quantum dissipation and friction attributed to plasmons

In this paper, we computed quantum friction of two parallel metal plates separated by a small distance moving with constant relative velocity [Formula: see text]. The plasmons as the internal degrees of freedom living on the two plates are coupled to a vacuum field in the gap between the two plates. We got the in–out quantum action which contained all the dynamical information of the system. Furthermore, we associated the imaginary part of the in–out quantum action with dissipation and frictional force. For the case of dispersionless plasmons, the imaginary part of the in–out quantum action is strongly suppressed as [Formula: see text]. The frictional force exhibits the same feature as [Formula: see text]. The difference is that the frictional force increases as [Formula: see text] and decreases as [Formula: see text]. For the case of dispersive plasmons, there is a threshold for the imaginary part of the in–out quantum action and the frictional force, that is, there is no dissipation when the relative velocity [Formula: see text] is not big enough. We gave a classical argument of the existence of the threshold, and this argument matched the mathematical results.

Two-loop application of the Breitenlohner-Maison/’t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

We apply the BMHV scheme for non-anticommuting γ5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

Complexity measures in QFT and constrained geometric actions

We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates. Inhomogeneous cost functions — many examples of which have been recently proposed in the literature — are ruled out by our analysis. Such measures are shown to be unrelated to circuit complexity in general and to produce severe violations of Lloyd’s bound in simple situations. Among the metrics which do provide lower bounds, the idea is to select those which produce the tightest possible ones. This establishes a hierarchy of cost functions and considerably reduces the list of candidate complexity measures. In particular, the criterion suggests a canonical way of dealing with penalties, consisting in assigning infinite costs to directions not belonging to the gate set. We discuss how this can be implemented through the use of Lagrange multipliers. We argue that one of the surviving cost functions defines a particularly canonical notion in the sense that: i) it straightforwardly follows from the standard Hermitian metric in Hilbert space; ii) its associated complexity functional is closely related to Kirillov’s coadjoint orbit action, providing an explicit realization of the “complexity equals action” idea; iii) it arises from a Hamilton-Jacobi analysis of the “quantum action” describing quantum dynamics in the phase space canonically associated to every Hilbert space. Finally, we explain how these structures provide a natural framework for characterizing chaos in classical and quantum systems on an equal footing, find the minimal geodesic connecting two nearby trajectories, and describe how complexity measures are sensitive to Lyapunov exponents.

Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model

In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS2. We propose a generic dual theory of gravity in the AdS2 and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still “freezes” as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

Recursive construction of the operator product expansion in curved space

I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the coefficients themselves in powers of the coupling constants, this formula allows to compute them recursively to arbitrary order. As input, only the OPE coefficients in the free theory are needed, which are easily obtained using Wick’s theorem. I illustrate the method by computing the OPE of two scalars ϕ in hyperbolic space (Euclidean Anti-de Sitter space) up to terms vanishing faster than the square of their separation to first order in the quartic interaction gϕ4, as well as the OPE coefficient "Image missing" at second order in g.

Quantum corrections to generic branes: DBI, NLSM, and more

We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

Action at a distance

Action at a distance is typically characterized in terms of some cause producing a spatially separated effect in the absence of any medium by which the causal interaction is transmitted. Historically it has been viewed with suspicion; Leibniz famously accused Newton of introducing ‘occult’ forces because according to his theory, gravity appeared to act at a distance. However, the grounds for ruling it out are not always so clear. One might insist that all forces are ‘contact forces’, but why should this be so? Alternatively, it could be argued that if action at a distance is accepted, then certain ‘facts’ about physical interactions would be left unexplained: the nature of Newton’s law of gravitation might be explicable if some underlying medium is presupposed, but otherwise it simply has to be accepted as a brute feature. But this assumes that the ‘nature’ of physical laws requires this sort of explanation. Finally, if it is acknowledged that such action at a distance cannot be instantaneous, on pain of violating Special Relativity, then it turns out that there are problems satisfying conservation of energy. Again, even this consequence can be side-stepped if one were to adopt an anti-realist view of energy. With the development of field theories and Einstein’s liberation of physics from the grip of the ether, it appeared that action at a distance had been pushed out of the picture by the beginning of the twentieth century. However, the non-local nature of quantum entanglement appears to have allowed it back in. Of course the form of this putative quantum action at a distance is very different from the classical kind: for one thing, it cannot be used instantaneously to send information and so there is still ‘peaceful co-existence’ with Special Relativity. Again, however, its acceptance depends on certain assumptions – on how one understands quantum entanglement, for example. Shifting the focus to violation of a form of ‘separability’ between systems, rather than locality, may allow us to accept quantum holism without having to swallow action at distance as well.

Renormalisation II: Improving perturbation theory

This chapter introduces the quantum action as the generating functional of 1PI Green functions. The Ward identities of QED are derived and the vacuum polarisation is calculated. The renormalisation group equations are introduced. Critical phenomena and Wilsonian effective theories are discussed.