115 research outputs found
Fock-Schwinger proper time formalism for p-branes
The theory of the usual, constrained p-branes is embedded into a larger
theory in which there is no constraints. In the latter theory the
Fock-Schwinger proper time formalism is extended from point-particles to
p-branes which can be considered as a points in an infinite dimensional space
M. The quantization appears to be straightforward and elegant. The conventional
p-brane states are particular stationary solutions to the functional
Schr\"odinger equation which describes the evolution of a membrane's state with
respect to the invariant evolution parameter . It is also shown that
states of a lower dimensional p-brane can be considered as particular states of
a higher dimensional p-brane.Comment: 6 page
The Dirac-Nambu-Goto p-Branes as Particular Solutions to a Generalized, Unconstrained Theory
The theory of the usual, constrained p-branes is embedded into a larger
theory in which there is no constraints. In the latter theory the
Fock-Schwinger proper time formalism is extended from point-particles to
membranes of arbitrary dimension. For this purpose the tensor calculus in the
infinite dimensional membrane space M is developed and an action which is
covariant under reparametrizations in M is proposed. The canonical and
Hamiltonian formalism is elaborated in detail. The quantization appears to be
straightforward and elegant. No problem with unitarity arises. The conventional
p-brane states are particular stationary solutions to the functional
Schroedinger equation which describes the evolution of a membrane's state with
respect to the invariant evolution parameter tau. A tau-dependent solution
which corresponds to the wave packet of a null p-brane is found. It is also
shown that states of a lower dimensional membrane can be considered as
particular states of a higher dimensional membrane.Comment: 28 page
The Classical and Quantum Theory of Relativistic p-Branes without Constraints
It is shown that a relativistic (i.e. a Poincar{\' e} invariant) theory of
extended objects (called p-branes) is not necessarily invariant under
reparametrizations of corresponding -dimensional worldsheets (including
worldlines for ). Consequnetly, no constraints among the dynamical
variables are necessary and quantization is straightforward. Additional degrees
of freedom so obtained are given a physical interpretation as being related to
membrane's elastic deformations ("wiggleness"). In particular, such a more
general, unconstrained theory implies as solutions also those p-brane states
that are solutions of the conventional theory of the Dirac-Nambu-Goto type.Comment: 21 page
An Alternative to Matter Localization in the "Brane World": An Early Proposal and its Later Improvements
Here we place the Latex typeset of the paper M. Pavsic, Phys. Lett. A116
(1986) 1-5. In the paper we presented the picture that our spacetime is a
3-brane moving in a higher dimensional space. The dynamical equations were
derived from the action which is just that for the usual Dirac-Nambu-Goto
-brane. We also considered the case where not only one, but many branes of
various dimensionalities are present, and showed that their intersections with
the 3-brane manifest as matter in 4-dimensional spacetime. We considered a
particular case, where the intersections behaved as point particles, and found
out that they follow the geodesics on the 3-brane worldsheet (identified with
our spacetime). In a series of subsequent papers the original idea has been
further improved and developped. This is discussed in a note at the end, where
it is also pointed out that such a model resolves the problem of massive matter
confinement on the brane, recently discussed by Rubakov et al. and Mueck et al.Comment: 11 page
On the Resolution of Time Problem in Quantum Gravity Induced from Unconstrained Membranes
The relativistic theory of unconstrained -dimensional membranes
(-branes) is further developed and then applied to the embedding model of
induced gravity. Space-time is considered as a 4-dimensional unconstrained
membrane evolving in an -dimensional embedding space. The parameter of
evolution or the evolution time is a distinct concept from the
coordinate time . Quantization of the theory is also discussed. A
covariant functional Schr\" odinger equations has a solution for the wave
functional such that it is sharply localized in a certain subspace of
space-time, and much less sharply localized (though still localized) outside
. With the passage of evolution the region moves forward in space-time.
Such a solution we interpret as incorporating two seemingly contradictory
observations: (i) experiments clearly indicate that space-time is a continuum
in which events are existing; (ii) not the whole 4-dimensional space-time, but
only a 3-dimensional section which moves forward in time is accessible to our
immediate experience. The notorious problem of time is thus resolved in our
approach to quantum gravity. Finally we include sources into our unconstrained
embedding model. Possible sources are unconstrained worldlines which are free
from the well known problem concerning the Maxwell fields generated by charged
unconstrained point particles.Comment: 22 Page
Higher Derivative Gravity and Torsion from the Geometry of C-spaces
We start from a new theory (discussed earlier) in which the arena for physics
is not spacetime, but its straightforward extension-the so called Clifford
space (-space), a manifold of points, lines, areas, etc..; physical
quantities are Clifford algebra valued objects, called polyvectors. This
provides a natural framework for description of supersymmetry, since spinors
are just left or right minimal ideals of Clifford algebra. The geometry of
curved -space is investigated. It is shown that the curvature in -space
contains higher orders of the curvature in the underlying ordinary space. A
-space is parametrized not only by 1-vector coordinates but also by
the 2-vector coordinates , 3-vector coordinates , etc., called also {\it holographic coordinates}, since they
describe the holographic projections of 1-lines, 2-loops, 3-loops, etc., onto
the coordinate planes. A remarkable relation between the "area" derivative \p/
\p \sigma^{\mu \nu} and the curvature and torsion is found: if a scalar valued
quantity depends on the coordinates this indicates the
presence of torsion, and if a vector valued quantity depends so, this implies
non vanishing curvature. We argue that such a deeper understanding of the
-space geometry is a prerequisite for a further development of this new
theory which in our opinion will lead us towards a natural and elegant
formulation of -theory.Comment: 19 pages; A section describing the main physical implications of
C-space is added, and the rest of the text is modified accordingl
Towards the Unification of Gravity and other Interactions: What has been Missed?
Faced with the persisting problem of the unification of gravity with other
fundamental interactions we investigate the possibility of a new paradigm,
according to which the basic space of physics is a multidimensional space
associated with matter configurations. We consider general
relativity in . In spacetime, which is a 4-dimensional subspace of
, we have not only the 4-dimensional gravity, but also other
interactions, just as in Kaluza-Klein theories. We then consider a finite
dimensional description of extended objects in terms of the center of mass,
area, and volume degrees of freedom, which altogether form a 16-dimensional
manifold whose tangent space at any point is Clifford algebra Cl(1,3). The
latter algebra is very promising for the unification, and it provides
description of fermions.Comment: 11 pages; Talk presented at "First Mediterranean Conference on
Classical and Quantum Gravity", Kolymbari, Crete, Greece, 14-18 September
200
Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
A theory in which 4-dimensional spacetime is generalized to a larger space,
namely a 16-dimensional Clifford space (C-space) is investigated. Curved
Clifford space can provide a realization of Kaluza-Klein theory. A covariant
Dirac equation in curved C-space is explored. The generalized Dirac field is
assumed to be a polyvector-valued object (a Clifford number) which can be
written as a superposition of four independent spinors, each spanning a
different left ideal of Clifford algebra. The general transformations of a
polyvector can act from the left and/or from the right, and form a large gauge
group which may contain the group U(1)xSU(2)xSU(3) of the standard model. The
generalized spin connection in C-space has the properties of Yang-Mills gauge
fields. It contains the ordinary spin connection related to gravity (with
torsion), and extra parts describing additional interactions, including those
described by the antisymmetric Kalb-Ramond fields.Comment: 57 pages; References added, section 2 rewritten and expande
A STRAINED SPACE-TIME TO EXPLAIN THE LARGE SCALEPROPERTIES OF THE UNIVERSE
Space-time can be treated as a four-dimensional material continuum. The corresponding generally curved manifold can be thought of as having been obtained, by continuous deformation, from a four-dimensional Euclidean manifold. In a three-dimensional ordinary situation such a deformation process would lead to strain in the manifold. Strain in turn may be read as half the di®erence between the actual metric tensor and the Euclidean metric tensor of the initial unstrained manifold. On the other side we know that an ordinary material would react to the attempt to introduce strain giving rise to internal stresses and one would have correspondingly a deformation energy term. Assuming the conditions of linear elasticity hold, the deformation energy is easily written in terms of the strain tensor. The Einstein-Hilbert action is generalized to include the new deformation energy term. The new action for space-time has been applied to a Friedmann-Lemaitre- Robertson-Walker universe filled with dust and radiation. The accelerated expansion is recovered, then the theory has been put through four cosmological tests: primordial isotopic abundances from Big Bang Nucleosynthesis; Acoustic Scale of the CMB; Large Scale Structure formation; luminosity/redshift relation for type Ia supernovae. The result is satisfying and has allowed to evaluate the parameters of the theor
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