1,457 research outputs found
Complexified Path Integrals and the Phases of Quantum Field Theory
The path integral by which quantum field theories are defined is a particular
solution of a set of functional differential equations arising from the
Schwinger action principle. In fact these equations have a multitude of
additional solutions which are described by integrals over a complexified path.
We discuss properties of the additional solutions which, although generally
disregarded, may be physical with known examples including spontaneous symmetry
breaking and theta vacua. We show that a consideration of the full set of
solutions yields a description of phase transitions in quantum field theories
which complements the usual description in terms of the accumulation of
Lee-Yang zeroes. In particular we argue that non-analyticity due to the
accumulation of Lee-Yang zeros is related to Stokes phenomena and the collapse
of the solution set in various limits including but not restricted to, the
thermodynamic limit. A precise demonstration of this relation is given in terms
of a zero dimensional model. Finally, for zero dimensional polynomial actions,
we prove that Borel resummation of perturbative expansions, with several
choices of singularity avoiding contours in the complex Borel plane, yield
inequivalent solutions of the action principle equations.Comment: 15 pages, 9 figures (newer version has better images
Strong Coupling Phenomena on the Noncommutative Plane
We study strong coupling phenomena in U(1) gauge theory on the
non-commutative plane. To do so, we make use of a T-dual description in terms
of an limit of U(N) gauge theory on a commutative torus. The
magnetic flux on this torus is taken to be , while the area scales like
1/N, keeping fixed. With a few assumptions, we argue that the
speed of high frequency light in pure non-commutative QED is modified in the
non-commutative directions by the factor , where
is the non-commutative parameter. If charged flavours are included,
there is an upper bound on the momentum of a photon propagating in the
non-commutative directions, beyond which it is unstable against production of
charged pairs. We also discuss a particular limit of pure
non-commutative QED which is T-dual to a more conventional limit
with fixed. In the non-commutative description, this limit gives rise to
an exotic theory of open strings.Comment: 24 pages, latex, 2 figures, corrected typo in eqn 6.
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