78 research outputs found
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
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
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
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
A Novel View on the Physical Origin of E8
We consider a straightforward extension of the 4-dimensional spacetime
to the space of extended events associated with strings/branes, corresponding
to points, lines, areas, 3-volumes, and 4-volumes in . All those objects
can be elegantly represented by the Clifford numbers . This leads to the
concept of the so-called Clifford space , a 16-dimensional manifold
whose tangent space at every point is the Clifford algebra . The latter space besides an algebra is also a vector space whose
elements can be rotated into each other in two ways: (i) either by the action
of the rotation matrices of SO(8,8) on the components or (ii) by the left
and right action of the Clifford numbers exp [\alpha^A \gam_A] and
exp [\beta^A \gam_A] on . In the latter case, one does not recover all
possible rotations of the group SO(8,8). This discrepancy between the
transformations (i) and (ii) suggests that one should replace the tangent space
with a vector space whose basis elements are
generators of the Clifford algebra , which contains the Lie
algebra of the exceptional group E as a subspace. E thus arises from
the fact that, just as in the spacetime there are -volumes generated
by the tangent vectors of the spacetime, there are -volumes,
, in the Clifford space , generated by the tangent
vectors of .Comment: 14 page
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
Path and Path Deviation Equations for p-branes
Path and path deviation equations for neutral, charged, spinning and spinning
charged test particles, using a modified Bazanski Lagrangian, are derived. We
extend this approach to strings and branes. We show how the Bazanski Lagrangian
for charged point particles and charged branes arises `a la Kaluza-Klein from
the Bazanski Lagrangian in 5-dimensions.Comment: 13 pages, LaTeX fil
A Fluid Generalization of Membranes
In a certain sense a perfect fluid is a generalization of a point particle.
This leads to the question as to what is the corresponding generalization for
extended objects. The lagrangian formulation of a perfect fluid is much
generalized and this has as a particular example a fluid which is a classical
generalization of a membrane, however there is as yet no indication of any
relationship between their quantum theories.Comment: To appear in CEJP, updated to coincide with published versio
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