arXiv subjects

A. Aurilia

Publications and source records attributed to A. Aurilia.

At least 19 recordsLinked to original sources

arXiv2013

Planck's uncertainty principle and the saturation of Lorentz boosts by Planckian black holes

A basic inconsistency arises when the Theory of Special Relativity meets with quantum phenomena at the Planck scale. Specifically, the Planck length is Lorentz invariant and should not be affected by a Lorentz boost. We argue that Planckian relativity must necessarily involve the effect of black hole formation. Recent proposals for resolving the noted inconsistency seem unsatisfactory in that they ignore the crucial role of gravity in the saturation of Lorentz boosts. Furthermore, an invariant length at he Planck scale amounts to a universal quantum of resolution in the fabric of spacetime. We argue, therefore, that the universal Planck length requires an extension of the Uncertainty Principle as well. Thus, the noted inconsistency lies at the core of Quantum Gravity. In this essay we reflect on a possible resolution of these outstanding problems.

gr-qc↗

arXiv2004

Quantum effects of a massive 3-form coupled to a Dirac field

We consider the coupling of A_{μνρ} to the generic current of matter field, later identified with the spin density current of a Dirac field. In fact, one of the objectives of this paper is to investigate the impact of the quantum fluctuations of A_{μνρ} on the effective dynamics of the spinor field. The consistency of the field equations, even at the classical level, requires the introduction of a mass term for A_{μνρ}. In this case, the Casimir vacuum pressure includes a contribution that is explicitly dependent on the mass of A_{μνρ} and leads us to conclude that the mass term plays the same role as the infrared cutoff needed to regularize the finite volume partition functional previously calculated in the massless case. Remarkably, even in the presence of a mass term, A_{μνρ} contains a mixture of massless and massive spin-0 fields so that the resulting equation is still gauge invariant. This is yet another peculiar, but physically relevant property of A_{μνρ} since it is reflected in the effective dynamics of the spinor fields and confirms the confining property of A_{μνρ} already expected from the earlier calculation of the Wilson loop.

hep-th↗

arXiv2004

Quantum fluctuations of a "constant" gauge field

It is argued here that the quantum computation of the vacuum pressure must take into account the contribution of zero-point oscillations of a rank-three gauge field. The field A_{μνρ} possesses no radiative degrees of freedom, its sole function being that of polarizing the vacuum through the formation of \textit{finite} domains characterized by a non-vanishing, constant, but otherwise arbitrary pressure. This extraordinary feature, rather unique among quantum fields, is exploited to associate the A_{μνρ} field with the ``bag constant'' of the hadronic vacuum, or with the cosmological term in the cosmic case. We find that the quantum fluctuations of A_{μνρ} are inversely proportional to the confinement volume and interpret the result as a Casimir effect for the hadronic vacuum. With these results in hands and by analogy with the electromagnetic and string case, we proceed to calculate the Wilson loop of the three-index potential coupled to a ``test'' relativistic bubble. From this calculation we extract the static potential between two opposite points on the surface of a spherical bag and find it to be proportional to the enclosed volume.

hep-th↗

arXiv2001

Quenched, Minisuperspace, Bosonic p-brane Propagator

We borrow the minisuperspace approximation from Quantum Cosmology and the quenching approximation from QCD in order to derive a new form of the bosonic p-brane propagator. In this new approximation we obtain an exact description of both the collective mode deformation of the brane and the center of mass dynamics in the target spacetime. The collective mode dynamics is a generalization of string dynamics in terms of area variables. The final result is that the evolution of a p-brane in the quenched-minisuperspace approximation is formally equivalent to the effective motion of a particle in a spacetime where points as well as hypersurfaces are considered on the same footing as fundamental geometrical objects. This geometric equivalence leads us to define a new tension-shell condition that is a direct extension of the Klein-Gordon condition for material particles to the case of a physical p-brane.

hep-th↗

arXiv2001

Vacuum Bubbles Nucleation and Dark Matter Production through Gauge Symmetry Rearrangement

Modern particle physics and cosmology support the idea that a background of invisible material pervades the whole universe, and identify in the cosmic vacuum the ultimate source of matter-energy, both seen and unseen. Within the framework of the theory of fundamental relativistic membranes, we suggest a self-consistent, vacuum energy-driven mechanism for dark matter creation through gauge symmetry rearrangement.

hep-ph↗

arXiv2000

The Dual Higgs Mechanism and the Origin of Mass in the Universe

The idea that a background of invisible material pervades the whole universe is as old as the history of natural philosophy. Modern particle physics and cosmology support that idea and identify in the cosmic vacuum the ultimate source of matter-energy, both seen and unseen, in the universe. In the framework of the inflation-axion scenario, we suggest an unusual realization of the Higgs mechanism which converts the latent energy of the vacuum into observable mass. The existence of a new spontaneously broken symmetry is pointed out which has the same effect of the Peccei-Quinn symmetry in creating axions as pseudo-Goldstone bosons. However such particles are eliminated from the physical spectrum in favor of massive pseudoscalar particles.

hep-ph↗

arXiv2000

p-Branes Electric-Magnetic Duality and Stueckelberg/Higgs Mechanism: a Path-Integral Approach

We study the vacuum functional for a system of p-branes interacting with Maxwell fields of higher rank. This system represents a generalization of the usual electrodynamics of point particles, with one essential difference: namely, that the world-history of a p-brane, due to the spatial extension of the object, may possess a physical boundary. Thus, the objective of this study is twofold: first, we wish to exploit the breaking of gauge invariance due to the presence of a physical boundary, in order to generate mass as an alternative to the Higgs mechanism; second, we wish to investigate how the new mechanism of mass generation is affected by the duality transformation between electric and magnetic branes. The whole analysis is performed by using the path-integral method, as opposed to the more conventional canonical approach. The advantage of the path integral formulation is that it enables us to Fourier transform the field strength directly, rather than the gauge potential. To our knowledge, this field strength formulation represents a new application of the path integral method, and leads, in a straightforward way, to the dual representation of the vacuum functional. We find that the effect of the dual transformation is essentially that of exchanging the role of the gauge fields defined respectively on the " bulk'' and "boundary" of the p-brane history.

hep-th↗

arXiv1999

Dualization of Interacting Theories Including p=d-1 Limiting Cases

We study the vacuum partition functional Z [J] for a system of closed, bosonic p-branes coupled to p-forms in the limiting case: p+1 = space-time dimension. We suggest an extension of the duality transformation which can be applied to the limiting case even though no dual gauge potential exists in the conventional sense. The dual action thus obtained describes a current-current, static interaction within the bulk volume bounded by the d-1-brane. Guided by these results, we then construct a general expression for the parent Lagrangian that allows for a unified treatment of p-duality, even in the presence of external currents, using a first order formalism instead of the Bianchi identities. Finally, we show how this generalized dualization approach can accommodate the inclusion of a massive topological term in the parent action of an Abelian gauge theory.

hep-th↗

arXiv1999

Particle Propagator in Elementary Quantum Mechanics: a New Path Integral Derivation

This paper suggests a new way to compute the path integral for simple quantum mechanical systems. The new algorithm originated from previous research in string theory. However, its essential simplicity is best illustrated in the case of a free non relativistic particle, discussed here, and can be appreciated by most students taking an introductory course in Quantum Mechanics. Indeed, the emphasis is on the role played by the {\it entire family of classical trajectories} in terms of which the path integral is computed exactly using a functional representation of the Dirac delta-distribution. We argue that the new algorithm leads to a deeper insight into the connection between classical and quantum systems, especially those encountered in high energy physics.

quant-ph↗

arXiv1998

Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime

We discuss the relation between string quantization based on the Schild path integral and the Nambu-Goto path integral. The equivalence between the two approaches at the classical level is extended to the quantum level by a saddle--point evaluation of the corresponding path integrals. A possible relationship between M-Theory and the quantum mechanics of string loops is pointed out. Then, within the framework of ``loop quantum mechanics'', we confront the difficult question as to what exactly gives rise to the structure of spacetime. We argue that the large scale properties of the string condensate are responsible for the effective Riemannian geometry of classical spacetime. On the other hand, near the Planck scale the condensate ``evaporates'', and what is left behind is a ``vacuum'' characterized by an effective fractal geometry.

hep-th↗

arXiv1997

Effective dynamics of self-gravitating extended objects

We introduce an effective Lagrangian which describes the classical and semiclassical dynamics of spherically symmetric, self-gravitating objects that may populate the Universe at large and small (Planck) scale. These include wormholes, black holes and inflationary bubbles. We speculate that such objects represent some possible modes of fluctuation in the primordial spacetime foam out of which our universe was born. Several results obtained by different methods are encompassed and reinterpreted by our effective approach. As an example, we discuss: i) the gravitational nucleation coefficient for a pair of Minkowski bubbles, and ii) the nucleation coefficient of an inflationary vacuum bubble in a Minkowski background

gr-qc↗

arXiv1997

Classical and Quantum Shell Dynamics, and Vacuum Decay

Following a minisuperspace approach to the dynamics of a spherically symmetric shell, a reduced Lagrangian for the radial degree of freedom is derived directly from the Einstein-Hilbert action. The key feature of this new Lagrangian is its invariance under time reparametrization. Indeed, all classical and quantum dynamics is encoded in the Hamiltonian constraint that follows from that invariance. Thus, at the classical level, we show that the Hamiltonian constraint reproduces, in a simple gauge, Israel's matching condition which governs the evolution of the shell. In the quantum case, the vanishing of the Hamiltonian (in a weak sense), is interpreted as the Wheeler-DeWitt equation for the physical states, in analogy to the corresponding case in quantum cosmology. Using this equation, quantum tunneling through the classical barrier is then investigated in the WKB approximation, and the connection to vacuum decay is elucidated.

gr-qc↗

arXiv1997

Hausdorff dimension of a quantum string

In the path integral formulation of quantum mechanics, Feynman and Hibbs noted that the trajectory of a particle is continuous but nowhere differentiable. We extend this result to the quantum mechanical path of a relativistic string and find that the ``trajectory'', in this case, is a fractal surface with Hausdorff dimension three. Depending on the resolution of the detecting apparatus, the extra dimension is perceived as ``fuzziness'' of the string world-surface. We give an interpretation of this phenomenon in terms of a new form of the uncertainty principle for strings, and study the transition from the smooth to the fractal phase.

hep-th↗

arXiv1995

Membrane Vacuum as a Type II Superconductor

We study a functional field theory of membranes coupled to a rank--three tensor gauge potential. We show that gauge field radiative corrections lead to membrane condensation which turns the gauge field into a {\it massive spin--0 field}. This is the Coleman--Weinberg mechanism for {\it membranes}. An analogy is also drawn with a type--II superconductor. The ground state of the system consists of a two--phase medium in which the superconducting background condensate is ``pierced'' by four dimensional domains, or ``bags'', of non superconducting vacuum. Bags are bounded by membranes whose physical thickness is of the order of the inverse mass acquired by the gauge field.

hep-th↗

arXiv1995

String Propagator: a Loop Space Representation

The string quantum kernel is normally written as a functional sum over the string coordinates and the world--sheet metrics. As an alternative to this quantum field--inspired approach, we study the closed bosonic string propagation amplitude in the functional space of loop configurations. This functional theory is based entirely on the Jacobi variational formulation of quantum mechanics, {\it without the use of a lattice approximation}. The corresponding Feynman path integral is weighed by a string action which is a {\it reparametrization invariant} version of the Schild action. We show that this path integral formulation is equivalent to a functional ``Schrodinger'' equation defined in loop--space. Finally, for a free string, we show that the path integral and the functional wave equation are {\it exactly } solvable.

hep-th↗

arXiv1995

Conformal p-branes as a Source of Structure in Spacetime

We discuss a model of a conformal p-brane interacting with the world volume metric and connection. The purpose of the model is to suggest a mechanism by which gravity coupled to p-branes leads to the formation of structure rather than homogeneity in spacetime. Furthermore, we show that the formation of structure is accompanied by the appearance of a multivalued cosmological constant, i.e., one which may take on different values in different domains, or cells, of spacetime. The above results apply to a broad class of non linear gravitational lagrangians as long as metric and connection on the p-brane manifold are treated as independent variables.

hep-th↗

arXiv1994

Postmodern String Theory: Stochastic Formulation

In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carathéodory formulation of the Nambu-Goto action, supplemented by an averaging procedure over the family of classical string world-sheets which are solutions of the equation of motion. In this new framework, the string geodesic field is reinterpreted as the Gibbs current density associated with the string statistical ensemble. Next, we show that the classical field equations derived from the string gauge action, can be obtained as the semi-classical limit of the string functional wave equation. For closed strings, the wave equation itself is completely analogous to the Wheeler-DeWitt equation used in quantum cosmology. Thus, in the string case, the wave function has support on the space of all possible spatial loop configurations. Finally, we show that the string distribution induces a multi-phase, or {\it cellular} structure on the spacetime manifold characterized by domains with a purely Riemannian geometry separated by domain walls over which there exists a predominantly Weyl geometry.

hep-th↗

arXiv1993

Gauge Theory of Relativistic Membranes

In this paper we show that a relativistic membrane admits an equivalent representation in terms of the Kalb-Ramond gauge field $F_{μνρ}=\partial_{\,[\,μ}B_{νρ]}$ encountered in string theory. By `` equivalence '' we mean the following: if $x=X(ξ)$ is a solution of the classical equations of motion derived from the Dirac-Nambu-Goto action, then it is always possible to find a differential form of {\it rank three}, satisfying Maxwell-type equations. The converse proposition is also true. In the first part of the paper, we show that a relativistic membrane, regarded as a mechanical system, admits a Hamilton-Jacobi formulation in which the H-J function describing a family of classical membrane histories is given by $\displaystyle{F=dB=dS^1\wedge dS^2\wedge dS^3}$. In the second part of the paper, we introduce a {\it new} lagrangian of the Kalb-Ramond type which provides a {\it first order} formulation for both open and closed membranes. Finally, for completeness, we show that such a correspondence can be established in the very general case of a p-brane coupled to gravity in a spacetime of arbitrary dimensionality.

hep-th↗