Scientific Series

The standard method to study nonperturbative properties of quantum field theories is to Wick rotate the theory to Euclidean space and regulate it on a Euclidean Lattice. An alternative is "fuzzy field theory". This involves replacing the lattice field theory by a matrix model that approximates the field theory of interest, with the approximation becoming better as the matrix size is increased. The regulated field theory is one on a background noncommutative space. I will describe how this method works and present recent progress and surprises.

If the universe is a quantum mechanical system it has a quantum state. This state supplies a probabilistic measure for alternative histories of the universe. During eternal inflation these histories typically develop large inhomogeneities that lead to a mosaic structure on superhorizon scales consisting of homogeneous patches separated by inflating regions. As observers we do not see this structure directly. Rather our observations are confined to a small, nearly homogeneous region within our past light cone. This talk will describe how the probabilities for these observations can be calculated from the probabilities supplied by the quantum state without introducing a further ad hoc measure. The talk will emphasize the principles behind this result --- a quantum state, quantum spacetime leading to an ensemble of classical histories, quantum observers, a focus in local observations, and the use of coarse-grainings adapted to these observations. The principles will be illustrated in simple models in particular using the no-boundary wave function as a model of the quantum state. Applied to a model landscape we obtain specific predictions for features of the CMB spectrum and improvements in the `anthropic' bounds on the cosmological constant.

We present a new formulation of quantum mechanics for closed systems like the universe using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for alternative histories that are the basis of settleable bets. However, quantum mechanics describes alternative histories are not the basis for settleable bets as in the two-slit experiment. These alternatives can be assigned extended probabilities that are sometimes negative. We will compare this with the decoherent (consistent) histories formulation of quantum theory. The prospects for using this formulation as a starting point for testable alternatives to quantum theory or further generalizations of it will be briefly discussed.

I discuss how the results of dark matter experiments can be used to draw conclusions about the nature of WIMP dark matter that are to a large extent model-independent. Specifically, I show that combining the results of direct detection experiments with data from neutrino telescopes can help establish whether the dark matter particle is its own anti-particle. I go on to discuss how limits on the diffuse and line spectra obtained from gamma ray telescopes can be used to constrain the annihilation modes of dark matter.

For quantum fields with m=0, it is pointed out that timelike separated fields are quantized as independent subsystems. This allows us to ask the question of whether the field in the future region is entangled with the field in the past region of Minkowski space, in the Minkowski vacuum state. I will show that the answer is "yes," and then explore some consequences, including a thermal effect and a procedure for extracting the timelike entanglement with two inertial Unruh-DeWitt detectors.

The upcoming launch of the space-based gravitational wave interferometer detector LISA will yield an unprecedented amount of astrophysical and cosmological science from a variety of gravitational wave sources. Among these, the extreme mass ratio inspirals (EMRIs) of stellar-mass compact objects into supermassive black holes will provide a unique opportunity to test the predictions of General Relativity for strongly gravitating systems since the masses and spins of these sources are expected to be measured with precisions better than about 1 part in 10^4. Such highly precise measurements require modeling the dynamics of EMRIs and their gravitational waves with high accuracy. In this talk, I discuss using methods of effective field theory (EFT) to accomplish this. Since EMRIs lose energy to gravitational waves, I introduce an open systems framework that proves to be a necessary ingredient to correctly describe EMRIs within the EFT formalism. I will discuss my recent derivation of the equations of motion and waveforms through third order in the mass ratio for a class of nonlinear scalar models that are analogous to the perturbative General Relativistic description of EMRIs. Time permitting, I will also discuss new results that are non-perturbative in the mass ratio in this model.

In this talk I will discuss a new class of cosmological scalar fields. Similarly to gravity, these theories are described by actions linearly depending on second derivatives. The latter can not be excluded without breaking the generally covariant formulation of the action principle. Despite the presence of these second derivatives the equations of motion are of the second order. Hence there are no new pathological degrees of freedom. Because of this structure of the theory the scalar field kinetically mixes with the metric without direct non-minimal couplings to curvature - the phenomenon we have called Kinetic Gravity Braiding. These theories have rather unusual cosmological dynamics which is useful to model Dark Energy and Inflation. I will discuss an equivalent hydrodynamical formulation of these theories and cosmological applications.

Usually in quantum field theory one considers two different interpretations: 1: The field is an infinite number of quantum oscillators, giving rise to a wave functional \Psi(\phi). 2: The positive frequency component of a field, \phi_+(x), is a wave function analogous to standard quantum mechanics. While interpretation 2 is often only mentioned implicitly it is crucial to standard computations of measurable scattering probabilities. We extend the interpretation of QFT as relativistic quantum mechanics (option 2) and show how the total Klein Gordon field which consists of positive and negative frequency contributions, \phi = \phi_+ + \phi_- , can be interpreted as a wave function. Our construction manifestly shows that signal propagation in QFT cannot exceed the speed of light. This follows from the replacement of the Feynman propagator by the Wheeler propagator, which is just the time ordered commutator. Our second observation is that interpretation 2 is not consistent if one uses the Newton Wigner position operator, therefore we introduce a more natural bilinear position operator. We show by an explicit example that the bilinear operator, contrary to the Newton Wigner operator, allows relativistic particles to be perfectly localized, precisely as in non relativistic quantum mechanics.

The nature of antimatter is examined in the context of algebraic quantum field theory. It is shown that the notion of antimatter is more general than that of antiparticles. Properly speaking, then, antimatter is not matter made up of antiparticles --- rather, antiparticles are particles made up of antimatter. We go on to discuss whether the notion of antimatter is itself completely general in quantum field theory. Does the matter-antimatter distinction apply to all field theoretic systems? The answer depends on which of several possible criteria we should impose on the space of physical states.

I will present analytic solutions to a class of cosmological models described by a canonical scalar field minimally coupled to gravity and experiencing self interactions through a hyperbolic potential. Using models and methods of solution inspired by 2T-physics, I will show how analytic solutions can be obtained including radiation and spacial curvature. Among the analytic solutions, there are many interesting geodesically complete cyclic solutions, both singular and non-singular ones. Cyclic cosmological models provide an alternative to inflation for solving the horizon and flatness problems as well as generating scale-invariant perturbations. I will argue in favor of the geodesically complete solutions as being more attractive for constructing a more satisfactory model of cosmology. When geodesic completeness is imposed, it restricts models and their parameters to certain a parameter subspace, including some quantization conditions on parameters. I will explain the theoretical origin of our model from the point of view of 2T-gravity as well as from the point of view of the colliding branes scenario. If time permits, I will discuss how to associate solutions of the quantum Wheeler-deWitt equation with the classical analytic solutions, physical aspects of some of the cyclic solutions, and outline future directions.

I will describe a method to compute from first principles the anomalous dimension of short operators in N=4 super Yang-Mills theory at strong coupling, where they are described in terms of superstring vertex operators in an anti-de Sitter background. I will focus on the Konishi multiplet, dual to the first massive level of the superstring, and compute the one-loop correction to its anomalous dimension at strong coupling, using the pure spinor formalism for the superstring.

Reducing a higher dimensional theory to a 4-dimensional effective theory results in a number of scalar fields describing, for instance, fluctuations of higher dimensional scalar fields (dilaton) or the volume of the compact space (volume modulus). But the fields in the effective theory must be constructed with care: artifacts from the higher dimensions, such as higher dimensional diffeomorphisms and constraint equations, can affect the identification of the degrees of freedom. The effective theory including these effects resembles in many ways cosmological perturbation theory. I will show how constraints and diffeomorphisms generically lead the dilaton and volume modulus to combine into a single degree of freedom in the effective theory, the "breathing mode". This has important implications for models of moduli stabilization and inflation with extra dimensions.