564 research outputs found
Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of
matter fields to be formulated in terms of a unitarily evolving state vector
defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike
surfaces, as in the case of spacetimes with closed timelike curves, a more
general formulation of quantum mechanics is required. In such generalizations
the transition matrix between alternatives in regions of spacetime where states
{\it can} be defined may be non-unitary. This paper describes a generalized
quantum mechanics whose probabilities consistently obey the rules of
probability theory even in the presence of such non-unitarity. The usual notion
of state on a spacelike surface is lost in this generalization and familiar
notions of causality are modified. There is no signaling outside the light
cone, no non-conservation of energy, no ``Everett phones'', and probabilities
of present events do not depend on particular alternatives of the future.
However, the generalization is acausal in the sense that the existence of
non-chronal regions of spacetime in the future can affect the probabilities of
alternatives today. The detectability of non-unitary evolution and violations
of causality in measurement situations are briefly considered. The evolution of
information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0
The sigma term and the quark number operator in QCD
We discuss the relationship of the forward matrix element of the operator
, related to the so-called sigma term, to the quark number. We
show that in the naive quark model in the canonical formalism these quantities
coincide in the limit of small average quark momenta. In the QCD parton model
defined through light-front quantization this result is preserved at leading
perturbative order but it receives radiative corrections. We analyze the
theoretical and phenomenological consequences of this result, which provides a
bridge between a current algebra quantity, the sigma term, and a deep-inelastic
quantity, the parton number.Comment: 30 pages, 1 figure, DFTT-92-6 (April 1993
Consistent histories of systems and measurements in spacetime
Traditional interpretations of quantum theory in terms of wave function
collapse are particularly unappealing when considering the universe as a whole,
where there is no clean separation between classical observer and quantum
system and where the description is inherently relativistic. As an alternative,
the consistent histories approach provides an attractive "no collapse"
interpretation of quantum physics. Consistent histories can also be linked to
path-integral formulations that may be readily generalized to the relativistic
case. A previous paper described how, in such a relativistic spacetime path
formalism, the quantum history of the universe could be considered to be an
eignestate of the measurements made within it. However, two important topics
were not addressed in detail there: a model of measurement processes in the
context of quantum histories in spacetime and a justification for why the
probabilities for each possible cosmological eigenstate should follow Born's
rule. The present paper addresses these topics by showing how Zurek's concepts
of einselection and envariance can be applied in the context of relativistic
spacetime and quantum histories. The result is a model of systems and
subsystems within the universe and their interaction with each other and their
environment.Comment: RevTeX 4; 37 pages; v2 is a revision in response to reviewer
comments, connecting the discussion in the paper more closely to consistent
history concepts; v3 has minor editorial corrections; accepted for
publication in Foundations of Physics; v4 has a couple minor typographical
correction
Quasi-Black Holes from Extremal Charged Dust
One can construct families of static solutions that can be viewed as
interpolating between nonsingular spacetimes and those containing black holes.
Although everywhere nonsingular, these solutions come arbitrarily close to
having a horizon. To an observer in the exterior region, it becomes
increasingly difficulty to distinguish these from a true black hole as the
critical limiting solution is approached. In this paper we use the
Majumdar-Papapetrou formalism to construct such quasi-black hole solutions from
extremal charged dust. We study the gravitational properties of these
solutions, comparing them with the the quasi-black hole solutions based on
magnetic monopoles. As in the latter case, we find that solutions can be
constructed with or without hair.Comment: 18 page
The Superfluid and Conformal Phase Transitions of Two-Color QCD
The phase structure of two-color QCD is examined as a function of the
chemical potential and the number of light quark flavors. We consider effective
Lagrangians for two-color QCD containing the Goldstone excitations, spin-one
particles and negative intrinsic parity terms. We discuss the possibility of a
conformal phase transition and the enhancement of the global symmetries as the
number of flavors is increased. The effects of a quark chemical potential on
the spin-one particles and on the negative intrinsic parity terms are analyzed.
It is shown that the phase diagram that is predicted by the linearly realized
effective Lagrangian at tree-level matches exactly that predicted by chiral
perturbation theory.Comment: ReVTeX, 23 pages, 3 figures. Discussion of vector condensation
extended, two figures added, references adde
Nonlinear Realization of Chiral Symmetry on the Lattice
We formulate lattice theories in which chiral symmetry is realized
nonlinearly on the fermion fields. In this framework the fermion mass term does
not break chiral symmetry. This property allows us to use the Wilson term to
remove the doubler fermions while maintaining exact chiral symmetry on the
lattice. Our lattice formulation enables us to address non-perturbative
questions in effective field theories of baryons interacting with pions and in
models involving constituent quarks interacting with pions and gluons. We show
that a system containing a non-zero density of static baryons interacting with
pions can be studied on the lattice without encountering complex action
problems. In our formulation one can also decide non-perturbatively if the
chiral quark model of Georgi and Manohar provides an appropriate low-energy
description of QCD. If so, one could understand why the non-relativistic quark
model works.Comment: 34 pages, 2 figures, revised version to be published in J. High
Energy Phys. (changes in the 1st paragraph, additional descriptions on the
nature of the coordinate singularities in Sec.2, references added
Spinor gravity and diffeomorphism invariance on the lattice
The key ingredient for lattice regularized quantum gravity is diffeomorphism
symmetry. We formulate a lattice functional integral for quantum gravity in
terms of fermions. This allows for a diffeomorphism invariant functional
measure and avoids problems of boundedness of the action. We discuss the
concept of lattice diffeomorphism invariance. This is realized if the action
does not depend on the positioning of abstract lattice points on a continuous
manifold. Our formulation of lattice spinor gravity also realizes local Lorentz
symmetry. Furthermore, the Lorentz transformations are generalized such that
the functional integral describes simultaneously euclidean and Minkowski
signature. The difference between space and time arises as a dynamical effect
due to the expectation value of a collective metric field. The quantum
effective action for the metric is diffeomorphism invariant. Realistic gravity
can be obtained if this effective action admits a derivative expansion for long
wavelengths.Comment: 13 pages, proceedings 6th Aegean Summer School, Naxos 201
Wave function of the Universe in the early stage of its evolution
In quantum cosmological models, constructed in the framework of
Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its
further expansion is described as a tunneling transition through an effective
barrier between regions with small and large values of the scale factor at
non-zero (or zero) energy. The approach for describing this tunneling consists
of constructing a wave function satisfying an appropriate boundary condition.
There are various ways for defining the boundary condition that lead to
different estimates of the barrier penetrability and the tunneling time.
In order to describe the escape from the tunneling region as accurately as
possible and to construct the total wave function on the basis of its two
partial solutions unambiguously, we use the tunneling boundary condition that
the total wave function must represent only the outgoing wave at the point of
escape from the barrier, where the following definition for the wave is
introduced: the wave is represented by the wave function whose modulus changes
minimally under a variation of the scale factor . We construct a new method
for a direct non-semiclassical calculation of the total stationary wave
function of the Universe, analyze the behavior of this wave function in the
tunneling region, near the escape point and in the asymptotic region, and
estimate the barrier penetrability. We observe oscillations of modulus of wave
function in the external region starting from the turning point which decrease
with increasing of and which are not shown in semiclassical calculations.
The period of such an oscillation decreases uniformly with increasing and
can be used as a fully quantum dynamical characteristic of the expansion of the
Universe.Comment: 19 pages, 21 files for 10 EPS figures, LaTeX svjour style. The Sec.2
(formalism of Wheeler-De Witt equation) is reduced. In Sec.3.1 definition of
the outgoing wave from barrier is defined more accurately. In Sec.4.1
semiclassical calculations of wavew function and penetrability are performed
and comparison with results in fully quantum approach is adde
Global Strings in High Density QCD
We show that several types of global strings occur in colour superconducting
quark matter due to the spontaneous violation of relevant U(1) symmetries.
These include the baryon U(1)_B, and approximate axial U(1)_A symmetries as
well as an approximate U(1)_S arising from kaon condensation. We discuss some
general properties of these strings and their interactions. In particular, we
demonstrate that the U(1)_A strings behave as superconducting strings. We draw
some parallels between these strings and global cosmological strings and
discuss some possible implications of these strings to the physics in neutron
star cores.Comment: LaTeX JHEP-format (26 pages) Option in source for REVTeX4 forma
Improved Effective Potential in Curved Spacetime and Quantum Matter - Higher Derivative Gravity Theory
\noindent{\large\bf Abstract.} We develop a general formalism to study the
renormalization group (RG) improved effective potential for renormalizable
gauge theories ---including matter--gravity--- in curved spacetime. The
result is given up to quadratic terms in curvature, and one-loop effective
potentials may be easiliy obtained from it. As an example, we consider scalar
QED, where dimensional transmutation in curved space and the phase structure of
the potential (in particular, curvature-induced phase trnasitions), are
discussed. For scalar QED with higher-derivative quantum gravity (QG), we
examine the influence of QG on dimensional transmutation and calculate QG
corrections to the scalar-to-vector mass ratio. The phase structure of the
RG-improved effective potential is also studied in this case, and the values of
the induced Newton and cosmological coupling constants at the critical point
are estimated. Stability of the running scalar coupling in the Yukawa theory
with conformally invariant higher-derivative QG, and in the Standard Model with
the same addition, is numerically analyzed. We show that, in these models, QG
tends to make the scalar sector less unstable.Comment: 23 pages, Oct 17 199
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