Past Quantum Field Theory Seminar

In recent decades, quantum field theory (QFT) has become the framework for

several basic and outstandingly successful physical theories. Indeed, it has

become the lingua franca of entire branches of physics and even mathematics.

The universal scope of QFT opens fascinating opportunities for philosophy.

Accordingly, although the philosophy of physics has been dominated by the

analysis of quantum mechanics, relativity and thermo-statistical physics,

several philosophers have recently undertaken conceptual analyses of QFT.

One common feature of these analyses is the emphasis on rigorous approaches,

such as algebraic and constructive QFT; as against the more heuristic and

physical formulations of QFT in terms of functional (also knows as: path)

integrals.

However, I will follow the example of some recent mathematicians such as

Atiyah, Connes and Kontsevich, who have adopted a remarkable pragmatism and

opportunism with regard to heuristic QFT, not corseted by rigor (as Connes

remarks). I will conceptually discuss the advances that have marked

heuristic QFT, by analysing some of the key ideas that accompanied its

development.  I will also discuss the interactions between these concepts in

the various relevant fields, such as particle physics, statistical

mechanics, gravity and geometry. 

Attractive features of Lifshitz type theories are described with different

examples,

as the improvement of graphs convergence, the introduction of new

renormalizable

interactions, dynamical mass generation, asymptotic freedom, and other

features

related to more specific models. On the other hand, problems with the

expected

emergence of Lorentz symmetry in the IR are discussed, related to the

different

effective light cones seen by different particles when they interact.

Quaternionic quantum Hamiltonians describing nonrelativistic spin particles

require the ambient physical space to have five dimensions. The quantum

dynamics of a spin-1/2 particle system characterised by a generic such

Hamiltonian is described. There exists, within the structure of quaternionic

quantum mechanics, a canonical reduction to three spatial dimensions upon

which standard quantum theory is retrieved. In this dimensional reduction,

three of the five dynamical variables oscillate around a cylinder, thus

behaving in a quasi one-dimensional manner at large distances. An analogous

mechanism exists in the case of octavic Hamiltonians, where the ambient

physical space has nine dimensions. Possible experimental tests in search

for the signature of extra dimensions at low energies are briefly discussed.

(Talk based on joint work with Eva-Maria Graefe, Imperial.)

I will present some new results on classifying 123 TQFTs,
using a 2-categorical approach. The invariants defined by a TQFT are
described using a new graphical calculus, which makes them easier to
define and to work with. Some new and interesting physical phenomena
are brought out by this perspective, which we investigate. I will
finish by banishing some TQFT myths! This talk is based on joint work
with Bruce Bartlett, Chris Schommer-Pries and Chris Douglas.

I define what it means for a quantum

field theory to be asymptotically safe and

discuss possible applications to theories

of gravity and matter.

Communication between observers in a relativistic scenario has proved to be

a setting for a fruitful dialogue between quantum field theory and quantum

information theory. A state that an inertial observer in Minkowski space

perceives to be the vacuum will appear to an accelerating observer to be a

thermal bath of radiation. We study the impact of this Davies-Fulling-Unruh

noise on communication, particularly quantum communication from an inertial

sender to an accelerating observer and private communication between two

inertial observers in the presence of an accelerating eavesdropper. In both

cases, we establish compact, tractable formulas for the associated

communication capacities assuming encodings that allow a single excitation

in one of a fixed number of modes per use of the communications channel.

String field theory is a candidate for a full non-perturbative definition

of string theory. We aim to define string field theory on a space-time

lattice to investigate its behaviour at the quantum level. Specifically, we

look at string field theory in a one dimensional linear dilaton background,

using level truncation to restrict the theory to a finite number of fields.

I will report on our preliminary results at level-0 and level-1.

Much effort has been devoted to the study of weak scale particles, e.g. supersymmetric neutralinos, which have a relic abundance from thermal equilibrium in the early universe of order what is inferred for dark matter. This does not however provide any connection to the comparable abundance of baryonic matter, which must have a non-thermal origin. However "dark baryons" of mass ~5 GeV from a new strongly interacting sector would naturally provide dark matter and are consistent with recent putative signals in experiments such as CoGeNT and DAMA. Such particles would accrete in the Sun and affect heat transport in the interior so as to affect low energy neutrino fluxes and can possibly resolve the current conflict between helioseismological data and the Standard Solar Model.

I will define and discuss the properties of the analytic torsion of

twisted cohomology and briefly of Z_2-graded elliptic complexes

in general, as an element in the graded determinant line of the

cohomology of the complex, generalizing most of the variants of Ray-

Singer analytic torsion in the literature. IThe definition uses pseudo-

differential operators and residue traces. Time permitting, I will

also give a couple of applications of this generalized torsion to

mathematical physics. This is joint work with Siye Wu.

The QCD axion is the leading solution to the strong-CP problem, a

dark matter candidate, and a possible result of string theory

compactifications. However, for axions produced before inflation, high

symmetry-breaking scales (such as those favored in string-theoretic axion

models) are ruled out by cosmological constraints unless both the axion

misalignment angle and the inflationary Hubble scale are extremely

fine-tuned. I will discuss how attempting to accommodate a high-scale axion

in inflationary cosmology leads to a fine-tuning problem that is worse than

the strong-CP problem the axion was originally invented to solve, and how

this problem is exacerbated when additional axion-like fields from string

theory are taken into account. This problem remains unresolved by anthropic

selection arguments commonly applied to the high-scale axion scenario.

Topology can be generalised in at least two directions: pointless

topology, leading ultimately to topos theory, or noncommutative

geometry. The former has the advantage that it also carries a logical

structure; the latter captures quantum settings, of which the logic is

not well understood generally. We discuss a construction making a

generalised space in the latter sense into a generalised space in the

former sense, i.e. making a noncommutative C*-algebra into a locale.

This construction is interesting from a logical point of view,

and leads to an adjunction for noncommutative C*-algebras that extends

Gelfand duality.