34 research outputs found
Static plane symmetric relativistic fluids and empty repelling singular boundaries
We present a detailed analysis of the general exact solution of Einstein's
equation corresponding to a static and plane symmetric distribution of matter
with density proportional to pressure. We study the geodesics in it and we show
that this simple spacetime exhibits very curious properties. In particular, it
has a free of matter repelling singular boundary and all geodesics bounce off
it.Comment: 9 pages, 1 figure, accepted for publication in Classical and Quantum
Gravit
An alternative well-posedness property and static spacetimes with naked singularities
In the first part of this paper, we show that the Cauchy problem for wave
propagation in some static spacetimes presenting a singular time-like boundary
is well posed, if we only demand the waves to have finite energy, although no
boundary condition is required. This feature does not come from essential
self-adjointness, which is false in these cases, but from a different
phenomenon that we call the alternative well-posedness property, whose origin
is due to the degeneracy of the metric components near the boundary.
Beyond these examples, in the second part, we characterize the type of
degeneracy which leads to this phenomenon.Comment: 34 pages, 3 figures. Accepted for publication in Class. Quantum Gra
Dirac Operator on a disk with global boundary conditions
We compute the functional determinant for a Dirac operator in the presence of
an Abelian gauge field on a bidimensional disk, under global boundary
conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the
connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde
On the energy-momentum tensor
We clarify the relation among canonical, metric and Belinfante's
energy-momentum tensors for general tensor field theories. For any tensor field
T, we define a new tensor field \til {\bm T}, in terms of which the
Belinfante tensor is readily computed. We show that the latter is the one that
arises naturally from Noether Theorem for an arbitrary spacetime and it
coincides on-shell with the metric one.Comment: 11 pages, 1 figur
Duality and bosonization in Schwinger-Keldysh formulation
We present a path-integral bosonization approach for systems out of
equilibrium based on a duality transformation of the original Dirac fermion
theory combined with the Schwinger-Keldysh time closed contour technique, to
handle the non-equilibrium situation. The duality approach to bosonization that
we present is valid for space-time dimensions leading for to
exact results. In this last case we present the bosonization rules for fermion
currents, calculate current-current correlation functions and establish the
connection between the fermionic and bosonic distribution functions in a
generic, nonequilibrium situation.Comment: 16 pages, 1 figur
Empty singularities in higher-dimensional Gravity
We study the exact solution of Einstein's field equations consisting of a
()-dimensional static and hyperplane symmetric thick slice of matter, with
constant and positive energy density and thickness , surrounded by
two different vacua. We explicitly write down the pressure and the external
gravitational fields in terms of and , the pressure is positive and
bounded, presenting a maximum at an asymmetrical position. And if
is small enough, the dominant energy condition is satisfied
all over the spacetime. We find that this solution presents many interesting
features. In particular, it has an empty singular boundary in one of the vacua.Comment: 13 page
The electromagnetic energy-momentum tensor
We clarify the relation between canonical and metric energy-momentum tensors.
In particular, we show that a natural definition arises from Noether's Theorem
which directly leads to a symmetric and gauge invariant tensor for
electromagnetic field theories on an arbitrary space-time of any dimension
Determinants of Dirac operators with local boundary conditions
We study functional determinants for Dirac operators on manifolds with
boundary. We give, for local boundary conditions, an explicit formula relating
these determinants to the corresponding Green functions. We finally apply this
result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy
Abelian and Non-Abelian Induced Parity Breaking Terms at Finite Temperature
We compute the exact canonically induced parity breaking part of the
effective action for 2+1 massive fermions in particular Abelian and non Abelian
gauge field backgrounds. The method of computation resorts to the chiral
anomaly of the dimensionally reduced theory.Comment: 13 pages, RevTeX, no figure
Fermion Condensates of massless at Finite Density in non-trivial Topological Sectors
Vacuum expectation values of products of local bilinears are
computed in massless at finite density. It is shown that chiral
condensates exhibit an oscillatory inhomogeneous behaviour depending on the
chemical potential. The use of a path-integral approach clarifies the
connection of this phenomenon with the topological structure of the theory.Comment: 16 pages, no figures, To be published in Phys.Rev.