1,325 research outputs found
New Energy Definition for Higher Curvature Gravities
We propose a novel but natural definition of conserved quantities for gravity
models quadratic and higher in curvature. Based on the spatial asymptotics of
curvature rather than of metric, it avoids the GR energy machinery's more
egregious problems--such as zero energy "theorems" and failure in flat
backgrounds -- in this fourth-derivative realm. In D>4, the present expression
indeed correctly discriminates between second derivative Gauss-Bonnet and
generic, fourth derivative, actions.Comment: 3 pages, Typos fixe
Energy and Angular Momentum in Generic F(Riemann) Theories
We construct the conserved charge of generic gravity theories built on
arbitrary contractions of the Riemann tensor (but not on its derivatives) for
asymptotically (anti)-de Sitter spacetimes. Our construction is a
generalization of the ADT charges of linear and quadratic gravity theories in
cosmological backgrounds. As an explicit example we find the energy and angular
momentum of the BTZ black hole in the 2+1 dimensional Born-Infeld gravity.Comment: 7 page
Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism
A conjecture in quantum mechanics states that any quantum canonical
transformation can decompose into a sequence of three basic canonical
transformations; gauge, point and interchange of coordinates and momenta. It is
shown that if one attempts to construct the three basic transformations in
star-product form, while gauge and point transformations are immediate in
star-exponential form, interchange has no correspondent, but it is possible in
an ordinary exponential form. As an alternative approach, it is shown that all
three basic transformations can be constructed in the ordinary exponential form
and that in some cases this approach provides more useful tools than the
star-exponential form in finding the generating function for given canonical
transformation or vice versa. It is also shown that transforms of c-number
phase space functions under linear-nonlinear canonical transformations and
intertwining method can be treated within this argument.Comment: 15 pages, no figures. Accepted for publication in Int. J. Mod. Phys.
Gravitational charges of transverse asymptotically AdS spacetimes
Using Killing-Yano symmetries, we construct conserved charges of spacetimes
that asymptotically approach to the flat or Anti-de Sitter spaces only in
certain directions. In D dimensions, this allows one to define gravitational
charges (such as mass and angular momenta densities) of p-dimensional
branes/solitons or any other extended objects that curve the transverse space
into an asymptotically flat or AdS one. Our construction answers the question
of what kind of charges the antisymmetric Killing-Yano tensors lead to.Comment: 11 pages, no figures, REVTeX 4; version 2: important corrections
made; version 3: one new paragraph and 2 references added, accepted for
publication in PR
Regret Bounds for Reinforcement Learning with Policy Advice
In some reinforcement learning problems an agent may be provided with a set
of input policies, perhaps learned from prior experience or provided by
advisors. We present a reinforcement learning with policy advice (RLPA)
algorithm which leverages this input set and learns to use the best policy in
the set for the reinforcement learning task at hand. We prove that RLPA has a
sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and
that both this regret and its computational complexity are independent of the
size of the state and action space. Our empirical simulations support our
theoretical analysis. This suggests RLPA may offer significant advantages in
large domains where some prior good policies are provided
Green's Matrix for a Second Order Self-Adjoint Matrix Differential Operator
A systematic construction of the Green's matrix for a second order,
self-adjoint matrix differential operator from the linearly independent
solutions of the corresponding homogeneous differential equation set is carried
out. We follow the general approach of extracting the Green's matrix from the
Green's matrix of the corresponding first order system. This construction is
required in the cases where the differential equation set cannot be turned to
an algebraic equation set via transform techniques.Comment: 19 page
Canonical transformations in three-dimensional phase space
Canonical transformation in a three-dimensional phase space endowed with
Nambu bracket is discussed in a general framework. Definition of the canonical
transformations is constructed as based on canonoid transformations. It is
shown that generating functions, transformed Hamilton functions and the
transformation itself for given generating functions can be determined by
solving Pfaffian differential equations corresponding to that quantities. Types
of the generating functions are introduced and all of them is listed.
Infinitesimal canonical transformations are also discussed. Finally, we show
that decomposition of canonical transformations is also possible in
three-dimensional phase space as in the usual two-dimensional one.Comment: 19 pages, 1 table, no figures. Accepted for publication in Int. J.
Mod. Phys.
Problems With Complex Actions
We consider Euclidean functional integrals involving actions which are not
exclusively real. This situation arises, for example, when there are -odd
terms in the the Minkowski action. Writing the action in terms of only real
fields (which is always possible), such terms appear as explicitly imaginary
terms in the Euclidean action. The usual quanization procedure which involves
finding the critical points of the action and then quantizing the spectrum of
fluctuations about these critical points fails. In the case of complex actions,
there do not exist, in general, any critical points of the action on the space
of real fields, the critical points are in general complex. The proper
definition of the function integral then requires the analytic continuation of
the functional integration into the space of complex fields so as to pass
through the complex critical points according to the method of steepest
descent. We show a simple example where this procedure can be carried out
explicitly. The procedure of finding the critical points of the real part of
the action and quantizing the corresponding fluctuations, treating the
(exponential of the) complex part of the action as a bounded integrable
function is shown to fail in our explicit example, at least perturbatively.Comment: 6+epsilon pages, no figures, presented at Theory CANADA
Shortcuts to Spherically Symmetric Solutions: A Cautionary Note
Spherically symmetric solutions of generic gravitational models are
optimally, and legitimately, obtained by expressing the action in terms of the
two surviving metric components. This shortcut is not to be overdone, however:
a one-function ansatz invalidates it, as illustrated by the incorrect solutions
of [1].Comment: 2 pages. Amplified derivation, accepted for publication in Class
Quant Gra
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