Abstracts for March-April 2016

  • Unruh effect without trans-horizon entanglement
    Carlo Rovelli and Matteo Smerlak
    We estimate the transition rates of a uniformly accelerated Unruh-DeWitt detector coupled to a quantum field with reflecting conditions on a boundary plane (a “mirror”). We find that these are essentially indistinguishable from the usual Unruh rates, viz. that the Unruh effect persists in the presence of the mirror. This shows that the Unruh effect (thermality of detector rates) is not merely a consequence of the entanglement between left and right Rindler quanta in the Minkowski vacuum. Since in this setup the state of the field in the Rindler wedge is pure, we argue furthermore that the relevant entropy in the Unruh effect cannot be the von Neumann entanglement entropy. We suggest, an alternative, that it is the Shannon entropy associated with Heisenberg uncertainty.

    See also the related works by Gooding and Unruh, which connect to Pikovski et al. (blogged here).

  • What is the Entropy in Entropic Gravity?
    Sean M. Carroll and Grant N. Remmen
    We investigate theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein's equation arises from keeping entropy stationary in equilibrium under variations of the geometry and quantum state of a small region, and thermodynamic gravity, in which Einstein's equation emerges as a local equation of state from constraints on the area of a dynamical lightsheet in a fixed spacetime background. Examining holographic gravity, we argue that its underlying assumptions can be justified in part using recent results on the form of the modular energy in quantum field theory. For thermodynamic gravity, on the other hand, we find that it is difficult to formulate a self-consistent definition of the entropy, which represents an obstacle for this approach. This investigation points the way forward in understanding the connections between gravity and entanglement.

    The systematic approach of this paper is very gratifying. It also comes with an accessible introduction on Sean’s blog by his grad student Grant.

  • We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical field equations to the time evolution of the quantum field. We discuss the field in thermodynamical equilibrium and find the explicit solution of the equations of motion for the so-called "roll-over" phase transition. Finally, we briefly discuss the approximate methods for the evaluation of the Wigner functional that may be used to numerically simulate the initial value problem.
    [arXiv.]

    The authors construct the Wigner function in what seems to me to be the most sensible way: instead of position and momentum, the quasiprobability distribution is a function over field amplitudes and conjugate momenta. From scanning the paper it looks like everything behaves as you’d expect. Here’s are slides from a talk.

    Other approaches to Wigner functions for fields seem to get caught up on the idea that QFTs are often Lorentz covariant, and so your Wigner object has to be too. But the Wigner functions only break Lorentz covariance in the same way as Hamiltonian treatments of QFTs or GR (the ADM formalism). Yes, a Hamiltonian formulation misses some of beauty and simplicity found in a formalism where time and space are on equal footing, but there’s nothing broken or wrong with it. It’s just another, equally valid representation, like the Wigner function is in single-particle, nonrelativistic quantum mechanics. Even within fundamental physics, if you’re operating somewhere which dramatically breaks Lorentz symmetry — like the entire field of cosmology — then this shouldn’t bother you.

  • It is well known that both the symplectic structure and the Poisson brackets of classical field theory can be constructed directly from the Lagrangian in a covariant way, without passing through the non-covariant canonical Hamiltonian formalism. This is true even in the presence of constraints and gauge symmetries. These constructions go under the names of the covariant phase space formalism and the Peierls bracket. We review both of them, paying more careful attention, than usual, to the precise mathematical hypotheses that they require, illustrating them in examples. Also an extensive historical overview of the development of these constructions is provided. The novel aspect of our presentation is a significant expansion and generalization of an elegant and quite recent argument by Forger & Romero showing the equivalence between the resulting symplectic and Poisson structures without passing through the canonical Hamiltonian formalism as an intermediary. We generalize it to cover theories with constraints and gauge symmetries and formulate precise sufficient conditions under which the argument holds. These conditions include a local condition on the equations of motion that we call hyperbolizability, and some global conditions of cohomological nature. The details of our presentation may shed some light on subtle questions related to the Poisson structure of gauge theories and their quantization.

    Philosophically related to the previous abstract. Phase-space formulations don’t have to break Lorentz covariance! (H/t Peter Woit.)

  • The Euclidean quantum field theory for the fields ϕΔx(x), which depend on both the position x and the resolution Δx, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
    [arXiv.] (H/t Elliot Nelson.)

    Wavelets give a surprisingly illuminating window into quantum field theory. See here for the Daubechies wavelets, which are discretely indexed and orthonormal.

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