Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTransPlanckian Particles and the Quantization of Time
48
0
0.0
(
0
)
Authors
G. t Hooft
Ask ChatGPT about the research
No Arabic abstract
Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value. There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix Ansatz. By compactifying one of the three physical spacial dimensions, the scattering matrix Ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit lengths, each of which being described by a representation of the SO(2,1) Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field in space-time. The parameter t turns out to be quantized in Planckian units, divided by the period R of the compactified dimension.
rate research
Read More
The symplectic quantization scheme proposed for matter scalar fields in the companion paper Symplectic quantization I is generalized here to the case of space-time quantum fluctuations. Symplectic quantization considers an explicit dependence of the metric tensor $g_{mu u}$ on an additional time variable, named proper time at variance with the coordinate time of relativity. The physical meaning of proper time is to label the sequence of $g_{mu u}$ quantum fluctuations at a given point of the four-dimensional space-time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative $dot{g}_{mu u}$ of the metric field with respect to proper time, corresponding to the conjugated momentum $pi_{mu u}$. Symplectic quantization describes the quantum fluctuations of gravity by means of the symplectic dynamics generated by a generalized action functional $mathcal{A}[g_{mu u},pi_{mu u}] = mathcal{K}[g_{mu u},pi_{mu u}] - S[g_{mu u}]$, playing formally the role of a Hamilton function, where $S[g_{mu u}]$ is the Einstein-Hilbert action and $mathcal{K}[g_{mu u},pi_{mu u}]$ is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define a pseudo-microcanonical ensemble for the quantum fluctuations of $g_{mu u}$, built on the conservation of the generalized action $mathcal{A}[g_{mu u},pi_{mu u}]$ rather than of energy. $S[g_{mu u}]$ plays the role of a potential term along the symplectic action-preserving dynamics: its fluctuations are the quantum fluctuations of $g_{mu u}$. It is shown how symplectic quantization maps to the path-integral approach to gravity. By doing so we explain how the integration over the conjugated momentum field $pi_{mu u}$ gives rise to a cosmological constant term in the path-integral.
We examine the propagation of collisionless particles emitted from a spherical shell to infinity. The number distribution at infinity, calculated as a function of the polar angle, exhibits a small deviation from uniformity. The number of particles moving from the polar region toward the equatorial plane is slightly larger than that of particles in the opposite direction, for an emission radius $ > 4.5M$ in extreme Kerr space-time. This means that the black hole spin exerts an anti-collimation effect on the particles stream propagating along the rotation axis. We also confirm this property in the weak field limit. The quadrupole moment of the central object produces a force toward the equatorial plane. For a smaller emission radius $r<4.5M$, the absorption of particles into the black hole, the non-uniformity and/or the anisotropy of the emission distribution become much more important.
The classical electromagnetic and gravitomagnetic fields in the vacuum, in (3+2) dimensions, described by the Maxwell-Nordstrom equations, are quantized. These equations are rederived from the field tensor which follows from a five-dimensional form of the Dirac equation. The electromagnetic field depends on the customary time t, and the hypothetical gravitomagnetic field depends on the second time variable u. The total field energy is identified with the component T44 of the five-dimensional energy-stress tensor of the electromagnetic and gravitomagnetic fields. In the ground state, the electromagnetic field and the gravitomagnetic field energies cancel out. The quanta of the gravitomagnetic field have spin 1.
We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly-spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numerical accuracy, the area spectrum obtained from a Schrodinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Diracs formalism I construct for each case the classical reduced phase space and study the dependence on the gauge fixing used. Two separate features of these systems can make this construction difficult: the actions are not invariant at the boundaries, and the constraints may have disconnected solution spaces. The relativistic particle is affected by both, while the non-relativistic particle displays only by the first. Analyzing the role of canonical transformations in the reduced phase space, I show that a change of gauge fixing is equivalent to a canonical transformation. In the relativistic case, quantization of one branch of the constraint at the time is applied and I analyze the electromagenetic backgrounds in which it is possible to quantize simultaneously both branches and still obtain a covariant unitary quantum theory. To preserve unitarity and space-time covariance, second quantization is needed unless there is no electric field. I motivate a definition of the inner product in all these cases and derive the Klein-Gordon inner product for the relativistic case. I construct phase space path integral representations for amplitudes for the BFV and the Faddeev path integrals, from which the path integrals in coordinate space (Faddeev-Popov and geometric path integrals) are derived.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
