Past Quantum Field Theory Seminar

2 June 2015
Sylvie Paycha (Potsdam)

[based on joint work with Li Guo and  Bin Zhang]

 We apply to  the study of exponential sums on lattice points in
convex rational polyhedral cones, the generalised algebraic approach of
Connes and Kreimer to  perturbative quantum field theory.  For this purpose
we equip the space of    cones   with a connected coalgebra structure.
The  algebraic Birkhoff factorisation of Connes and Kreimer   adapted  and
generalised to this context then gives rise to a convolution factorisation
of exponential sums on lattice points in cones. We show that this
factorisation coincides with the classical Euler-Maclaurin formula
generalised to convex rational polyhedral cones by Berline and Vergne by
means of  an interpolating holomorphic function.
We define  renormalised conical zeta values at non-positive integers as the
Taylor coefficients at zero of the interpolating holomorphic function.  When
restricted to Chen cones, this  yields yet another way to renormalise
multiple zeta values  at non-positive integers.


  • Quantum Field Theory Seminar
17 February 2015
John Cardy

In a quantum quench, a system is prepared in some state
$|\psi_0\rangle$, usually the ground state of a hamiltonian $H_0$, and then
evolved unitarily with a different hamiltonian $H$. I study this problem
when $H$ is a 1+1-dimensional conformal field theory on a large circle of
length $L$, and the initial state has short-range correlations and
entanglement. I argue that (a) for times $\ell/2<t<(L-\ell)/2$  the
reduced density matrix of a subinterval of length $\ell$ is exponentially
close to that of a thermal ensemble; (b) despite this, for a rational CFT
the return amplitude $\langle\psi_0|e^{-iHt}|\psi_0\rangle$ is $O(1)$ at
integer multiples of $2t/\ell$ and has interesting structure at all rational
values of this ratio. This last result is related to the modular properties
of Virasoro characters.

  • Quantum Field Theory Seminar
20 January 2015
David Marsh (Perimeter Institute)

Axions are ubiquitous in string theory compactifications. They are
pseudo goldstone bosons and can be extremely light, contributing to
the dark sector energy density in the present-day universe. The
mass defines a characteristic length scale. For 1e-33 eV<m< 1e-20
eV this length scale is cosmological and axions display novel
effects in observables. The magnitude of these effects is set by
the axion relic density. The axion relic density and initial
perturbations are established in the early universe before, during,
or after inflation (or indeed independently from it). Constraints
on these phenomena can probe physics at or beyond the GUT scale. I
will present multiple probes as constraints of axions: the Planck
temperature power spectrum, the WiggleZ galaxy redshift survey,
Hubble ultra deep field, the epoch of reionisation as measured by
cmb polarisation, cmb b-modes and primordial gravitational waves,
and the density profiles of dwarf spheroidal galaxies. Together

these probe the entire 13 orders of magnitude in axion mass where
axions are distinct from CDM in cosmology, and make non-trivial
statements about inflation and axions in the string landscape. The
observations hint that axions in the range 1e-22 eV<m<1e-20 eV may
play an interesting role in structure formation, and evidence for
this could be found in the future surveys AdvACT (2015), JWST, and
Euclid (>2020). If inflationary B-modes are observed, a wide range
of axion models including the anthropic window QCD axion are
excluded unless the theory of inflation is modified. I will also
comment briefly on direct detection of QCD axions.


  • Quantum Field Theory Seminar
2 December 2014
Boris Zilber

We treat the problem of geometric interpretation of the formalism
of algebraic quantum mechanics as a special case of the general problem of
extending classical 'algebra - geometry' dualities (such as the
Gel'fand-Naimark theorem) to non-commutative setting.  
I will report on some progress in establishing such dualities. In
particular, it leads to a theory of approximate representations of Weyl
in finite dimensional  "Hilbert spaces". Some calculations based on this
theory will be discussed.

  • Quantum Field Theory Seminar