2,966 research outputs found
Hawking radiation in different coordinate settings: Complex paths approach
We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semiclassical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation as far as these
coordinates are concerned.Comment: 18 pages, 2 figures, Uses IOP style file; final version; accepted in
Class. Quant. Gra
Hawking radiation in different coordinate settings: Complex paths approach
We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semiclassical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation as far as these
coordinates are concerned.Comment: 18 pages, 2 figures, Uses IOP style file; final version; accepted in
Class. Quant. Gra
Generalized Konishi anomaly, Seiberg duality and singular effective superpotentials
Using the generalized Konishi anomaly (GKA) equations, we derive the
effective superpotential of four-dimensional N=1 supersymmetric SU(n) gauge
theory with n+2 fundamental flavors. We find, however, that the GKA equations
are only integrable in the Seiberg dual description of the theory, but not in
the direct description of the theory. The failure of integrability in the
direct, strongly coupled, description suggests the existence of
non-perturbative corrections to the GKA equations.Comment: 20 pages; v3: corrected the comparison to the SU(2) cas
Combining Representation Learning with Logic for Language Processing
The current state-of-the-art in many natural language processing and
automated knowledge base completion tasks is held by representation learning
methods which learn distributed vector representations of symbols via
gradient-based optimization. They require little or no hand-crafted features,
thus avoiding the need for most preprocessing steps and task-specific
assumptions. However, in many cases representation learning requires a large
amount of annotated training data to generalize well to unseen data. Such
labeled training data is provided by human annotators who often use formal
logic as the language for specifying annotations. This thesis investigates
different combinations of representation learning methods with logic for
reducing the need for annotated training data, and for improving
generalization.Comment: PhD Thesis, University College London, Submitted and accepted in 201
Field Dependent Gauge Couplings in Locally Supersymmetric Effective Quantum Field Theories
We investigate the field dependence of the gauge couplings of locally
supersymmetric effective quantum field theories. We find that the Weyl
rescaling of supergravity gives rise to Wess-Zumino terms that affect the gauge
couplings at the one-loop level. These Wess-Zumino terms are crucial in
assuring supersymmetric consistency of both perturbative and non-perturbative
gauge interactions. At the perturbative level, we distinguish between the
holomorphic Wilsonian gauge couplings and the physically-measurable
momentum-dependent effective gauge couplings; the latter are affected by the
Konishi and the super-Weyl anomalies and their field-dependence is
non-holomorphic. At the non-perturbative level, we show how consistency of the
scalar potential generated by infrared-strong gauge interactions with the local
supersymmetry requires a very specific form of the effective superpotential. We
use this superpotential to determine the dependence of the supersymmetric
condensates of a strongly interacting gauge theory on its (field-dependent)
Wilsonian gauge coupling and the Yukawa couplings of the matter fields. The
article concludes with the discussion of the field-dependent non-perturbative
phenomena in the context of string unification.Comment: UTTG-94-1 and LMU-TPW-94-1 (107 pages, PHYZZX macros; EPSF figures
appended
Lifted rule injection for relation embeddings
Methods based on representation learning currently hold the state-of-the-art in many natural language processing and knowledge base inference tasks. Yet, a major challenge is how to efficiently incorporate commonsense knowledge into such models. A recent approach regularizes relation and entity representations by propositionalization of first-order logic rules. However, propositionalization does not scale beyond domains with only few entities and rules. In this paper we present a highly efficient method for incorporating implication rules into distributed representations for automated knowledge base construction. We map entity-tuple embeddings into an approximately Boolean space and encourage a partial ordering over relation embeddings based on implication rules mined from WordNet. Surprisingly, we find that the strong restriction of the entity-tuple embedding space does not hurt the expressiveness of the model and even acts as a regularizer that improves generalization. By incorporating few commonsense rules, we achieve an increase of 2 percentage points mean average precision over a matrix factorization baseline, while observing a negligible increase in runtime
Phase Space Quantum Mechanics on the Anti-De Sitter Spacetime and its Poincar\'e Contraction
In this work we propose an alternative description of the quantum mechanics
of a massive and spinning free particle in anti-de~Sitter spacetime, using a
phase space rather than a spacetime representation. The regularizing character
of the curvature appears clearly in connection with a notion of localization in
phase space which is shown to disappear in the zero curvature limit. We show in
particular how the anti-de~Sitter optimally localized (coherent) states
contract to plane waves as the curvature goes to zero. In the first part we
give a detailed description of the classical theory {\it \a la Souriau\/}. This
serves as a basis for the quantum theory which is constructed in the second
part using methods of geometric quantization. The invariant positive K\"ahler
polarization that selects the anti-de~Sitter quantum elementary system is shown
to have as zero curvature limit the Poincar\'e polarization which is no longer
K\"ahler. This phenomenon is then related to the disappearance of the notion of
localization in the zero curvature limit.Comment: 37 pgs+3 figures (not included), PlainTeX, Preprint CRM-183
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