1,754 research outputs found
BRS and Anti-BRS Symmetry in Topological Yang--Mills Theory
We incorporate both BRS symmetry and anti-BRS symmetry into the quantisation
of topological Yang--Mills theory. This refines previous treatments which
consider only the BRS symmetry. Our formalism brings out very clearly the
geometrical meaning of topological Yang--Mills theory in terms of connections
and curvatures in an enlarged superspace; and its simple relationship to the
geometry of ordinary Yang--Mills theory. We also discover a certain SU(3)
triality between physical spacetime, and the two ghost directions of
superspace. Finally, we demonstrate how to recover the usual gauge-fixed
topological Yang--Mills action from our formalism.Comment: 17 pages, harvmac, DAMTP R92/3
A Clifford analysis approach to superspace
A new framework for studying superspace is given, based on methods from
Clifford analysis. This leads to the introduction of both orthogonal and
symplectic Clifford algebra generators, allowing for an easy and canonical
introduction of a super-Dirac operator, a super-Laplace operator and the like.
This framework is then used to define a super-Hodge coderivative, which,
together with the exterior derivative, factorizes the Laplace operator. Finally
both the cohomology of the exterior derivative and the homology of the Hodge
operator on the level of polynomial-valued super-differential forms are
studied. This leads to some interesting graphical representations and provides
a better insight in the definition of the Berezin-integral.Comment: 15 pages, accepted for publication in Annals of Physic
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
Nonrelativistic Quantum Particle in a Curved Space as a Constrained System
The operator and the functional formulations of the dynamics of constrained
systems are explored for determining unambiguously the quantum Hamiltonian of a
nonrelativistic particle in a curved space.Comment: 11 pages, latex, revtex, no figures. Accepted for publication in
Phys. Lett.
Quantum metamorphosis of conformal symmetry in N = 4 super Yang-Mills theory
In gauge theories, not all rigid symmetries of the classical action can be
maintained manifestly in the quantization procedure, even in the absence of
anomalies. If this occurs for an anomaly-free symmetry, the effective action is
invariant under a transformation that differs from its classical counterpart by
quantum corrections. As shown by Fradkin and Palchik years ago, such a
phenomenon occurs for conformal symmetry in quantum Yang-Mills theories with
vanishing beta function, such as the N = 4 super Yang-Mills theory. More
recently, Jevicki et al demonstrated that the quantum metamorphosis of
conformal symmetry sheds light on the nature of the AdS/CFT correspondence. In
this paper, we derive the conformal Ward identity for the bosonic sector of the
N = 4 super Yang-Mills theory using the background field method. We then
compute the leading quantum modification of the conformal transformation for a
specific Abelian background which is of interest in the context of the AdS/CFT
correspondence. In the case of scalar fields, our final result agrees with that
of Jevicki et al. The resulting vector and scalar transformations coincide with
those which are characteristic of a D3-brane embedded in AdS5 x S5.Comment: 20 pages, latex, no figures; comments and references added, the final
version to appear in NPB, the title changed on referee's reques
One-loop Effective Actions in Shape-invariant Scalar Backgrounds
The field-theoretic one-loop effective action in a static scalar background
depending nontrivially on a single spatial coordinate is related, in the
proper-time formalism, to the trace of the evolution kernel (or heat kernel)
for an appropriate, one dimensional, quantum-mechanical Hamiltonian. We
describe a recursive procedure applicable to these traces for shape-invariant
Hamiltonians, resolving subtleties from the continuum mode contributions by
utilizing the expression for the regularized Witten index. For some cases which
include those of domain-wall-type scalar backgrounds, our recursive procedure
yields the full expression for the scalar or fermion one-loop effective action
in both (1+1) and (3+1)-dimensions.Comment: 11 pages, LaTeX2
The d=6 trace anomaly from quantum field theory four-loop graphs in one dimension
We calculate the integrated trace anomaly for a real spin-0 scalar field in
six dimensions in a torsionless curved space without a boundary. We use a path
integral approach for a corresponding supersymmetric quantum mechanical model.
Weyl ordering the corresponding Hamiltonian in phase space, an extra two-loop
counterterm is
produced in the action. Applying a recursive method we evaluate the components
of the metric tensor in Riemann normal coordinates in six dimensions and
construct the interaction Langrangian density by employing the background field
method.
The calculation of the anomaly is based on the end-point scalar propagator
and not on the string inspired center-of-mass propagator which gives incorrect
results for the local trace anomaly. The manipulation of the Feynman diagrams
is partly relied on the factorization of four dimensional subdiagrams and
partly on a brute force computer algebra program developed to serve this
specific purpose. The computer program enables one to perform index
contractions of twelve quantum fields (10395 in the present case) a task which
cannot be accomplished otherwise. We observe that the contribution of the
disconnected diagrams is no longer proportional to the two dimensional trace
anomaly (which vanishes in four dimensions). The integrated trace anomaly is
finally expressed in terms of the 17 linearly independent scalar monomials
constructed out of covariant derivatives and Riemann tensors.Comment: 23 pages, 17 figure
Loop calculations in quantum-mechanical non-linear sigma models
By carefully analyzing the relations between operator methods and the
discretized and continuum path integral formulations of quantum-mechanical
systems, we have found the correct Feynman rules for one-dimensional path
integrals in curved spacetime. Although the prescription how to deal with the
products of distributions that appear in the computation of Feynman diagrams in
configuration space is surprising, this prescription follows unambiguously from
the discretized path integral. We check our results by an explicit two-loop
calculation.Comment: 17 pages, LaTeX, and one figur
Gravitomagnetic Field of a Rotating Superconductor and of a Rotating Superfluid
The quantization of the extended canonical momentum in quantum materials
including the effects of gravitational drag is applied successively to the case
of a multiply connected rotating superconductor and superfluid. Experiments
carried out on rotating superconductors, based on the quantization of the
magnetic flux in rotating superconductors, lead to a disagreement with the
theoretical predictions derived from the quantization of a canonical momentum
without any gravitomagnetic term. To what extent can these discrepancies be
attributed to the additional gravitomagnetic term of the extended canonical
momentum? This is an open and important question. For the case of multiply
connected rotating neutral superfluids, gravitational drag effects derived from
rotating superconductor data appear to be hidden in the noise of present
experiments according to a first rough analysis
Probing singularities in quantum cosmology with curvature scalars
We provide further evidence that the canonical quantization of cosmological
models eliminates the classical Big Bang singularity, using the {\it
DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for
absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum
cosmological models is the non-vanishing of the expectation value of the scale
factor. We compute the `local expectation value' of the Ricci and Kretschmann
scalars, for some quantum FRW models. We show that they are finite for all
time. Since these scalars are elements of general scalar polynomials in the
metric and the Riemann tensor, this result indicates that, for the quantum
models treated here, the `local expectation value' of these general scalar
polynomials should be finite everywhere. Therefore, we have further evidence
that the quantization of the models treated here eliminates the classical Big
Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.Comment: 9 pages, 6 figure
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