415 research outputs found
U(N|M) quantum mechanics on Kaehler manifolds
We study the extended supersymmetric quantum mechanics, with supercharges
transforming in the fundamental representation of U(N|M), as realized in
certain one-dimensional nonlinear sigma models with Kaehler manifolds as target
space. We discuss the symmetry algebra characterizing these models and, using
operatorial methods, compute the heat kernel in the limit of short propagation
time. These models are relevant for studying the quantum properties of a
certain class of higher spin field equations in first quantization.Comment: 21 pages, a reference adde
Quantum theories of (p,q)-forms
We describe quantum theories for massless (p,q)-forms living on Kaehler
spaces. In particular we consider four different types of quantum theories: two
types involve gauge symmetries and two types are simpler theories without gauge
invariances. The latter can be seen as building blocks of the former. Their
equations of motion can be obtained in a natural way by first-quantizing a
spinning particle with a U(2)-extended supersymmetry on the worldline. The
particle system contains four supersymmetric charges, represented quantum
mechanically by the Dolbeault operators and their hermitian conjugates. After
studying how the (p,q)-form field theories emerge from the particle system, we
investigate their one loop effective actions, identify corresponding heat
kernel coefficients, and derive exact duality relations. The dualities are seen
to include mismatches related to topological indices and analytic torsions,
which are computed as Tr(-1)^F and Tr[(-1)^F F] in the first quantized
supersymmetric nonlinear sigma model for a suitable fermion number operator F.Comment: 44 pages, 2 figures, a reference adde
Quantum theory of massless (p,0)-forms
We describe the quantum theory of massless (p,0)-forms that satisfy a
suitable holomorphic generalization of the free Maxwell equations on Kaehler
spaces. These equations arise by first-quantizing a spinning particle with a
U(1)-extended local supersymmetry on the worldline. Dirac quantization of the
spinning particle produces a physical Hilbert space made up of (p,0)-forms that
satisfy holomorphic Maxwell equations coupled to the background Kaehler
geometry, containing in particular a charge that measures the amount of
coupling to the U(1) part of the U(d) holonomy group of the d-dimensional
Kaehler space. The relevant differential operators appearing in these equations
are a twisted exterior holomorphic derivative and its hermitian conjugate
(twisted Dolbeault operators with charge q). The particle model is used to
obtain a worldline representation of the one-loop effective action of the
(p,0)-forms. This representation allows to compute the first few heat kernel
coefficients contained in the local expansion of the effective action and to
derive duality relations between (p,0) and (d-p-2,0)-forms that include a
topological mismatch appearing at one-loop.Comment: 32 pages, 3 figure
Worldline approach to vector and antisymmetric tensor fields
The N=2 spinning particle action describes the propagation of antisymmetric
tensor fields, including vector fields as a special case. In this paper we
study the path integral quantization on a one-dimensional torus of the N=2
spinning particle coupled to spacetime gravity. The action has a local N=2
worldline supersymmetry with a gauged U(1) symmetry that includes a
Chern-Simons coupling. Its quantization on the torus produces the one-loop
effective action for a single antisymmetric tensor. We use this worldline
representation to calculate the first few Seeley-DeWitt coefficients for
antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side
results we obtain the correct trace anomaly of a spin 1 particle in four
dimensions as well as exact duality relations between differential form gauge
fields. This approach yields a drastic simplification over standard heat-kernel
methods. It contains on top of the usual proper time a new modular parameter
implementing the reduction to a single tensor field. Worldline methods are
generically simpler and more efficient in perturbative computations then
standard QFT Feynman rules. This is particularly evident when the coupling to
gravity is considered.Comment: 30 pages, 5 figures, references adde
Dimensional regularization of nonlinear sigma models on a finite time interval
We extend dimensional regularization to the case of compact spaces. Contrary
to previous regularization schemes employed for nonlinear sigma models on a
finite time interval (``quantum mechanical path integrals in curved space'')
dimensional regularization requires only a covariant finite two-loop
counterterm. This counterterm is nonvanishing and given by R/8.Comment: 9 pages, 7 figures, LaTeX, minor changes in text and reference
Higher spin fields from a worldline perspective
Higher spin fields in four dimensions, and more generally conformal fields in
arbitrary dimensions, can be described by spinning particle models with a
gauged SO(N) extended supergravity on the worldline. We consider here the
one-loop quantization of these models by studying the corresponding partition
function on the one-dimensional torus. After gauge fixing the supergravity
multiplet, the partition function reduces to an integral over the corresponding
moduli space which is computed using orthogonal polynomial techniques. We
obtain a compact formula which gives the number of physical degrees of freedom
for all N in all dimensions. As an aside we compute the physical degrees of
freedom of the SO(4) = SU(2)xSU(2) model with only a SU(2) factor gauged, which
has attracted some interest in the literature.Comment: 21 page
Detours and Paths: BRST Complexes and Worldline Formalism
We construct detour complexes from the BRST quantization of worldline
diffeomorphism invariant systems. This yields a method to efficiently extract
physical quantum field theories from particle models with first class
constraint algebras. As an example, we show how to obtain the Maxwell detour
complex by gauging N=2 supersymmetric quantum mechanics in curved space. Then
we concentrate on first class algebras belonging to a class of recently
introduced orthosymplectic quantum mechanical models and give generating
functions for detour complexes describing higher spins of arbitrary symmetry
types. The first quantized approach facilitates quantum calculations and we
employ it to compute the number of physical degrees of freedom associated to
the second quantized, field theoretical actions.Comment: 1+35 pages, 1 figure; typos corrected and references added, published
versio
Photon-graviton mixing in an electromagnetic field
Einstein-Maxwell theory implies the mixing of photons with gravitons in an
external electromagnetic field. This process and its possible observable
consequences have been studied at tree level for many years. We use the
worldline formalism for obtaining an exact integral representation for the
one-loop corrections to this amplitude due to scalars and fermions. We study
the structure of this amplitude, and obtain exact expressions for various
limiting cases.Comment: 13 pages, 1 figure, talk given by C. Schubert at QFEXT07, Leipzig,
17-21 Sep 2007, final published version (slightly extended
Dimensional regularization of the path integral in curved space on an infinite time interval
We use dimensional regularization to evaluate quantum mechanical path
integrals in arbitrary curved spaces on an infinite time interval. We perform
3-loop calculations in Riemann normal coordinates, and 2-loop calculations in
general coordinates. It is shown that one only needs a covariant two-loop
counterterm (V_{DR} = R/8) to obtain the same results as obtained earlier in
other regularization schemes. It is also shown that the mass term needed in
order to avoid infrared divergences explicitly breaks general covariance in the
final result.Comment: 13 pages, 10 figures, LaTe
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